Common Stock Valuation & Performance Measurement

Module 4

Common Stock Valuation &

Performance Measurement

by

Jason G. Hovde, CIMA®, CFP®, APMA®

7350

© 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

This publication may not be duplicated in any way without the express written consent of the publisher. The information contained herein is for the personal use of the reader and may not be incorporated in any commercial programs, other books, databases, or any kind of software or any kind of electronic media including, but not limited to, any type of digital storage mechanism without written consent of the publisher or authors. Making copies of this material or any portion for any purpose other than your own is a violation of United States copyright laws.

The College for Financial Planning does not certify individuals to use the CFP, CERTIFIED FINANCIAL

PLANNER™, and CFP (with flame logo)® marks. CFP® certification is granted solely by Certified Financial Planner Board of Standards Inc. to individuals who, in addition to completing an educational requirement such as this CFP Board-Registered Program, have met its ethics, experience, and examination requirements. Certified Financial Planner Board of Standards Inc. owns the certification marks CFP, CERTIFIED

FINANCIAL PLANNER™, and federally registered CFP (with flame logo)®, which it awards to individuals who successfully complete initial and ongoing certification requirements.

At the College’s discretion, news, updates, and information regarding changes/updates to courses or programs may be posted to the College’s website at www.cffp.edu, or you may call the Student Services Center at 1-800-237-9990.

Table of Contents Study Plan/Syllabus ................................................................ 1

Learning Activities ............................................................. 2

Exam Formula Sheet ........................................................... 4

Chapter 1: Dividends on Stock ............................................... 5

Importance of Dividends ..................................................... 5

Dividend Basics .................................................................. 6

Chapter 2: Equity Valuation ................................................ 13

Definitions ........................................................................ 13

DDM Alternatives ............................................................ 15

The Zero Growth Model ................................................... 17

Constant Growth DDM ..................................................... 18

The Non-Constant Growth Model ..................................... 25

Valuation Exercise—Merck & Co. .................................... 29

P/E Ratio .......................................................................... 32

Summary .......................................................................... 35

Chapter 3: Security Performance Evaluation ...................... 38

Investment Policy Statements (IPS) .................................. 38

Security and Portfolio Performance Evaluation ................. 45

Risk/Return ...................................................................... 47

Jensen Index (alpha) ......................................................... 50

Sharpe Index ..................................................................... 52

Treynor Index ................................................................... 55

Information Ratio (IR) ...................................................... 56

Determining the Market Rate ............................................. 57

Asset Class Benchmarks .................................................... 61

Risk-Adjusted Performance ............................................... 65

Mutual Fund Comparison .................................................. 67

Summary ................................................................................ 75

Module Review ...................................................................... 77

Questions .......................................................................... 77

Answers ............................................................................ 93

About the Author ................................................................. 127

References ............................................................................ 128

Index .................................................................................... 129

Study Plan/Syllabus 1 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Study Plan/Syllabus he efficient market hypothesis is one of the most controversial elements

of modern portfolio theory, and its proponents argue that beating the

indexes is next to impossible. This module will deal with its detractors

who argue that the anomalies to the theory support active portfolio management.

This module will discuss stock valuation techniques and how to make securities

decisions using these techniques. Performance measurement approaches are

discussed, including how to use those approaches to improve security selection.

The chapters in this module are:

Dividends on Stock

Equity Valuation

Security Performance Evaluation

Upon completion of this module you should be able to apply the dividend growth

model to compute a security’s intrinsic value, and be able to apply security

performance measures to evaluate how well a security performed against

various market indexes. You should also be able to determine which market

indexes are appropriate for evaluating different asset classes within a portfolio.

This module starts with a discussion of dividends, which then leads into the

various valuation models that are used extensively by investment analysts to

determine if a particular stock is overvalued, undervalued, or appropriately

valued. You are expected to understand the valuation concepts, apply the

concepts, and then use the concepts to help clients make investment decisions.

The ability to determine value is essential, and you should experiment with your

own scenarios to test the depth of your understanding of the concepts.

Next we cover the basics of investment policy statements, the use of which has

become widespread in the investment community. You should know the basic

components of an IPS. Some very important performance measurements are then

T

2 Common Stock Valuation & Performance Measurement © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

introduced including Jensen (alpha), Treynor, and Sharpe. You should become

very familiar with these measurements including how and when to use them.

Choosing the appropriate benchmark is important, as is understanding when or

when not to use beta. This is an extremely important module, and you should

take the time necessary to master its learning objectives. For those in the

investment field, this is knowledge that you should have in order to better serve

your clients.

Learning Activities Learning Activities

Learning Objective Readings

Module Review Questions

4–1 Analyze the impact of different types of cash and stock distributions on shareholders and on the company.

Module 4, Chapter 1: Dividends on Stock

1–13

4–2 Explain terminology related to equity investment valuation models.

Module 4, Chapter 2: Equity Valuation

14–18

4–3 Calculate the intrinsic value of a stock using various stock valuation techniques or calculate the expected return of a stock.

19–23

4–4 Evaluate the appropriateness of investment decisions based on stock valuation models.

24–33

4–5 Explain the various components of the Investment Policy Statement (IPS).

Module 4, Chapter 3: Security Performance Evaluation

34, 35

4–6 Explain the characteristics, uses, and limitations of stock performance measurement indexes.

Module 4, Chapter 3: Security Performance Evaluation

36–40

Study Plan/Syllabus 3 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Learning Activities

Learning Objective Readings

Module Review Questions

4–7 Calculate one or more stock performance measurement indexes for given portfolio returns and risk.

41–43

4–8 Specify relationships among various indicators of security returns.

44–49

4–9 Evaluate the risk-adjusted performances of alternative investment securities or portfolios to recommend the most appropriate selection for a given client situation.

50–53


Exam Formula Sheet

gr

DV

−= 1

gP

Dr += 1

ifmfi rrrr β)( −+=

1 n

)r (r

2n

−−

= σ

i

i

i

i

mean

Sor

xCV −=

σ

imm

i RS

S×=β or

m

iimi σ

σρβ =

ijjijjii COVW2W W W 2222

p ++= σσσ

ij jiijCOV σσρ=

ji

ijij

Rσσ ×

=COV

yyc

ycty

y

yDur

t +−+−++−+=]1)1[(

)()1(1

+Δ−=Δ

y

yDP

1

sPCP

ParCV ×=

Pc

PcISHPR

−+=

RatetionCapitalizaNOIV =

p

fpp

rrT

β−

=

p

fpp

rrS

σ−

=

[ ]pfmfp rrrra β)( −+−=

A

BP RRIR

σ−=

PLEASE NOTE: You do not need to memorize these formulas for the exam. An exact copy of this formula sheet will be provided to you when you log on to take your IP exam. Also, the formula sheet for the CFP Certification Examination will be different from this exam formula sheet. Prior to taking the exam, please check with the CFP Board regarding their current exam formula sheet.

Chapter 1: Dividends on Stock 5 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Chapter 1: Dividends on Stock Reading this chapter will enable you to:

4–1 Analyze the impact of different types of cash and stock distributions

on shareholders and on the company.

Importance of Dividends

uring the investment market of the mid-1990s, many investors tended to

minimize the relevance of dividends. One of the reasons they did this

was the fact that dividends took a back seat to capital appreciation during

the bull market run of the decade. Another reason was that many corporations

reduced their dividend payout rate, which led to the lowest historical dividend yield

on stocks in the 20th century.

In spite of this trend, dividends play an important role in both theory and practice

in the investment area. Historically, dividends have accounted for approximately

40% of the total return on securities (Dow Jones & Company website, 2006).

One of the EMH anomalies mentioned in Module 3 is that stocks with high

dividend rates often have historically outperformed stocks with low dividend

rates. For example, the “Dogs of the Dow” investment strategy uses the 10 Dow

Industrial Average stocks with the highest dividend yields to form a portfolio.

Dividends play an important role in the valuation of stocks, as you will see in the

next chapter. The dividend discount model is the key element used by many

professional investment managers in determining stock valuation. Famed Omaha

investor Warren Buffett uses the model in his valuation computations.

D


Dividend Basics

The focus of most investment analysis is earnings per share. A company’s

earnings, and especially its earnings surprises, drive the performance of the

company’s stock.

Many companies, especially the large, mature companies typically found in the

major stock market indexes such as the S&P 500 average, pay a portion of their

earnings per share to shareholders in the form of dividends. Unlike interest

payments on a company’s bonds, a company does not have a legal requirement to

pay dividends. The company’s board of directors determines if a dividend should

be paid. As a practical matter, once established, boards tend to be reluctant to cut

or eliminate dividend payments to stockholders, but will do so if slumping

business conditions make that prudent. Dividends on both preferred stock and

common stock normally are paid quarterly so a company that, say, pays $1.00 per

share annually would pay $0.25 per share every three months.

Preferred stockholders receive a fixed annual dividend amount per share. Some

preferred stock have a feature called “cumulative” which means if a dividend is

missed, all such dividends must be made up before common stockholders receive

their dividends.

Common stockholders receive a dividend only after the preferred stockholders

receive their dividends. Since common shareholders are entitled to a claim on the

residual earnings after bondholders and preferred stockholders are paid,

hopefully their dividends will increase over time as the company’s earnings

increase, a major attraction to owning common stock. Some dividend-paying

companies aim to pay a common stock dividend that is a set percentage of

earnings.

For example, assume that a company’s earnings per share is $2.00 and that the

company has decided that it likes to pay approximately 30% of its earnings as a

dividend. In this example, the company would pay 30% of $2.00, or $.60, per

share to common stockholders. This percentage is called the dividend payout

ratio or simply the payout ratio.


Special Dividend

Sometimes a company will pay a special dividend beyond their regular dividend

if they have had especially strong earnings in a year. Usually this is due to a

buildup of corporate cash, with the board deciding this is an appropriate way to

share the company’s success with the common stockholders.

For example, on October 24, 2012, Wynn Resorts Ltd. declared a cash dividend

of $8 a share, which included the usual $0.50 quarterly dividend and $7.50 per

share of a special dividend. This dividend was payable November 20 of that year

to shareholders on record as of November 7.

Key Dividend Distribution Dates

Many dates are associated with dividends. On the declaration date, the board of

directors of the corporation declares that a dividend will be paid and identifies

the key dates. On the distribution date, the dividend is actually paid to

shareholders. These dates are easy to remember.

The dates that students have difficulty with are the ex-dividend date and the

record date. The record date is the date that the corporation closes its books and

identifies who the shareholders are. Anyone who is a shareholder on the record

date is entitled to receive the dividend.

Securities laws require that all trades be cleared (settled) in three business days.

That is, anyone who receives a confirmation that a trade has been executed will

not actually be the owner of record until three business days later, when all

financial aspects of the trade are settled. Therefore, anyone who buys a security

three business days before the record date will be a registered shareholder on the

record date.

An investor who buys a security two business days before the record date will

have his or her trade cleared one day after the record date and will not be entitled

to the dividend. Therefore, the day two business days before the record date is

known as the ex-dividend (without dividend) date. In other words, an investor


who receives confirmation that a trade has been executed two business days

before the record date will not receive the dividend that is to be paid on the next

distribution date.

Example. Cash Cow Inc. is going to pay out a dividend with a distribution date

of September 10 to shareholders who were on the corporation’s books as

shareholders on the record date of August 10. Assuming that August 10 was a

Monday, two business days before that date was Thursday, August 6. Therefore,

August 6 will be the ex-dividend date because trades executed on August 6

would not be cleared until three business days thereafter, on August 11, which

was one day after the record date. Note that if you buy on Wednesday, August

5th, your trade will settle on August 10th—in time for the dividend.

Wednesday

Aug. 5thThursday

Aug. 6th

Ex-dividend

Tuesday

Aug. 11th

BusinessDay 3

BusinessDay 2

BusinessDay 1

Friday

Aug. 7thMonday

Aug. 10th

record date

A trade that will settle on the example record date of Aug.10th—in time for the dividend.

Stock Dividend

Most dividends are paid in cash. Some are paid in additional shares of a

company’s stock, called a stock dividend. (Be aware that cash dividend and stock

dividend are precise terms that refer to different types of dividends. Often

investors will loosely use the term stock dividend when they actually are

referring to a cash dividend.) The payment of a stock dividend may occur when a

company wants to conserve cash but does not want to alienate shareholders. It

could be that a company is having financial difficulties or it may simply decide


there are better uses for its cash. In these situations, the company does not want

to increase the cash dividend, so it provides a stock dividend instead.

Many stockholders perceive that their wealth has increased because they own

more shares after the stock distribution. Actually, shareholder wealth is

unchanged because the market price of the stock is lowered on the distribution

date to reflect the fact that the overall market value of the company remains

unchanged; it is now simply divided over an increased number of shares. Each

shareholder’s proportionate share of ownership of the company is unchanged

because each shareholder has experienced the same proportionate increase in the

number of shares owned.

Example—10% stock dividend. Assume an investor originally owns 100 shares

at $50 per share ($5,000 value). Immediately after a 10% stock dividend the

investor would own 110 shares priced at $45.45 (still a $5,000 value).

Stock Split

A stock split is somewhat like a stock dividend, in that each shareholder owns

more shares after the split than before. However, unlike a stock dividend, a stock

split is not authorized in lieu of paying cash dividends.

A stock split occurs when corporate management decides to lower the market

price of a stock in order to encourage more investors to purchase shares of the

company. By splitting the stock, management communicates to the investment

community that the company must be successful because its shares have

appreciated so much that the stock must split to lower its price to a more

reasonable level. It is both a psychological and a practical move for company

management.

The most common stock splits are two-for-one splits or three-for-two splits. In a two-for-one split, the investor who owns 200 shares before the split will own 400 shares after the split. In a three-for-two split, the investor who owns 200 shares before the split will own 300 shares after the split. The market value of the stock is adjusted on the day of the split. For example, in the two-for-one split, if the


market price of the stock is $40 per share on the day before the split, it will be $20 per share on the day of the split. Therefore, the investor’s total market value is unchanged ($8,000).

To calculate the new price per share in a stock split you would divide the original price per share by the ratio of the new stock to the old. Here are a few examples (assume a $100 original stock price in each example):

2 for 1 split $100/(2/1) = $50

3 for 2 split $100/(3/2) = $66.67

3 for 1 split $100/(3/1) = $33.33

Reverse Split

For various reasons some companies have their stock price decline to low levels. The problem with this is twofold. First, there is a perception problem with potential shareholders. Many investors do not want to invest in “penny stocks.” A low share price does not exude success. Another problem is with analysts and brokerage firms. Many firms will not even look at a stock that is trading at less than $5 or $10 per share. A way to address this problem is a reverse split, converting a certain number of “old” shares into one “new” share. For example, a company trading at 50 cents per share could do a 1-for-20 reverse split, converting 20 old shares into 1 new share. An investor with 100 pre-split shares valued at $50 (100 × $0.50) would now have 5 shares valued at $50 (5 × $10). A reverse split may temporarily help the share price, but the marketplace will continue to punish the stock price if the company does not correct the issues that drove down the price in the first place!

Dividend Reinvestment Plans (DRIPs)

Mutual fund investors have become accustomed to reinvesting all dividend and capital gains distributions by converting them into additional shares of the fund. Many individual companies also allow investors in their stocks to reinvest their cash dividend distributions by converting them into additional shares of the company’s stock.


Just as with mutual fund reinvestments, the reinvested dividend distributions are

taxable dividend income to the investor. The investor is assumed to have

received the cash dividend and then reinvested that cash into additional shares of

the company’s stock. The investor’s basis would then increase by the amount

reinvested.

The first share must be purchased from a broker or directly from the company

before an investor can participate in a DRIP program. Most DRIP investors have

purchased their first shares from a broker; increasingly, companies that offer

DRIP programs are setting up their own direct-stock-purchase programs.

Two principal advantages accrue to an individual investor who participates in a

DRIP. First, the investor is able to purchase a small number of shares

periodically without having to pay a brokerage commission on each of the

purchases. Since brokerage commissions on purchases of less than 100 shares are

quite expensive (in proportion to the dollar value of stock purchased), this can

mean significant savings, especially in the early years of a DRIP program. As the

account grows, and more than 100 shares are purchased with each transaction,

this savings becomes less significant.

Second, and most important, the DRIP investor must have a long-term

perspective, since he or she is participating in a buy-and-hold program and is

adding to his or her stock holdings using a dollar-cost-averaging approach over a

long period of time. This allows an investor to build a significant position in one

or more individual stocks and to increase his or her personal net worth using a

disciplined investment strategy, without worrying about day-to-day gyrations in

the stock’s price.

A potential disadvantage of DRIPs is that an investor is adding to his or her

position in a single stock, thereby increasing unsystematic risk. This can be

minimized if the investor participates in DRIP programs for stocks in a number

of different industries.

One potential disadvantage to current shareholders who own shares in a company

that offers a DRIP, but who do not participate in the DRIP, is dilution. If the

shares being issued are coming from treasury stock, then more shares are


introduced into the marketplace, which reduces the percentage of ownership of

nonparticipating shareholders. This dilution will also impact earnings, which will

be spread over an increased number of shares.

Stock Repurchases

Sometimes a firm will repurchase some of its outstanding shares of stock as an

alternative to paying dividends. This would then increase earnings per share since

the earnings would now be spread over a decreased number of shares. There can

be various reasons for a stock repurchase. There may be stock options that have

been granted to employees for which the shares are needed. The shares may also

be repurchased to ward off an unwanted takeover attempt. If the company has too

much cash this can attract suitors, so by repurchasing shares the company will

reduce its cash amount while reducing the number of outstanding shares, which

in turn will increase earnings. This should also result in a higher stock price,

making the stock a less-likely takeover candidate.

Chapter 2: Equity Valuation 13 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Chapter 2: Equity Valuation Reading the first part of this chapter will enable you to:


Definitions

he total return a security should achieve is determined by calculating its

required return. Required return is calculated by multiplying the market

risk premium by the security’s beta and then adding the risk-free return.

The security’s required return, then, is a function of its beta (systematic risk).

This is the capital asset pricing model (CAPM) that we have already covered:

ifmfi )rr(rr β−+=

Expected return is the total return an investor can expect from a security, given

its current price, the growth rate of its dividend, and the capital appreciation

expected (which is assumed to be the same as the expected growth rate of its

dividend). The calculation for this will be covered in more detail later in this

chapter:

gP

Dr += 1

The intrinsic value of a security is the value of a security that is computed using a

discounted cash flow approach to valuation. Dividends have been accepted by the

investment community as the critical cash flow element to discount.

An important assumption in this computation is that dividends are a constant

percentage of a corporation’s earnings; in other words, the payout ratio is

constant. If this assumption is considered valid, then the growth rate of earnings

is reflected in the growth rate of dividends. Another important assumption is that

both dividends and earnings will continue to grow indefinitely at that same

T


annual rate. If both dividends and earnings grow, then it can be assumed that the

value of the company’s stock will also continue to grow.

The equation used to compute a company’s intrinsic value using the discounted

cash flow approach is called the dividend discount model (DDM). It is also called

the dividend growth model or the constant growth dividend discount model:

gr

DV

−= 1

The calculation for this will be covered in more detail later. Once a company’s

intrinsic value is computed, then an investor will buy the stock if the current

market price is equal to or below the intrinsic value; the investor will not buy,

and indeed may sell, if the current market price is higher than the intrinsic value.

The two most difficult aspects of the dividend discount model computation are

estimating the appropriate discount rate to be used for the computation and

estimating the future growth rate of dividends.

The net discount rate used is the required return minus the dividend growth rate.

The assumption here is that the required return is the gross discount rate to be

used in computing the total return of a security. However, a percentage of the

required return is earned by the growth rate of the dividend; only the amount of

the required return that represents growth above the dividend growth rate (i.e.,

capital gain) needs to be represented as the net discount rate used in the equation.

Estimating dividend growth can be frustrating. In reality, neither earnings nor

dividends grow systematically and steadily. One year, earnings may grow at 24%

and dividends may grow at 15%; another year, earnings may decline and

dividends may remain constant. Every investor must derive some method of

smoothing out dividend growth so that a compound annual rate can be

determined.


DDM Alternatives

A popular alternative to using dividends in the model is to use cash flow,

especially when a company does not pay dividends. Details of this approach will

not be discussed here. Different assumptions may have to be made regarding the

appropriate required return rate and the growth rate of cash flow.

A second approach to determining the intrinsic value of a stock is to use the P/E

ratio. This is one of the most popular valuation methods that investors use. If a

company has positive earnings but pays no dividends, then this method must be

used because the dividend discount model can be used only when a company

pays dividends (assuming that the cash flow model is not used).

When using the P/E ratio approach, two benchmarks are considered—the industry

P/E ratio and the market P/E ratio. The ratio for the company in question is

computed and compared against both of these benchmarks. If the company ratio

is lower than either or both benchmarks, then the stock may be undervalued. If

the company ratio is higher than either or both, then the stock may be overvalued.

A third approach is the price-to-sales ratio (PSR). Like the P/E ratio, this method

can be used with any company; it is especially useful when a company pays no

dividends and has no earnings. To use the ratio, net sales are divided by the

number of shares outstanding to determine the sales per share. That number is

then divided into the price per share to determine the PSR. In general, stocks with

PSRs of less than 1.0 are undervalued; those with PSRs that are greater than 3.0

may be overvalued.

Another popular approach to valuation is the growth-adjusted P/E ratio, known

as the PEG (PE/growth) ratio. The PEG ratio is calculated by dividing the P/E

ratio by the earnings growth rate (EGR). The PEG ratio allows investors to

compare companies with different growth expectations. In other words, in an

industry where the average P/E ratio is 18, the P/E ratio of a stock with an

expected earnings growth rate of 26% should be higher than the P/E ratio of a

stock with an expected earnings growth rate of 12%.


Using the PEG ratio is more complex than using the other ratios. A general rule

is that a PEG ratio of less than 1.0 may identify an undervalued company.

However, one cannot assume that a company’s P/E ratio is too low simply

because the company’s PEG ratio is lower than the S&P 500 PEG ratio. For

example, the S&P 500 PEG ratio was approximately 1.5 in late 2006. If a growth

company has an estimated earnings growth rate of 30%, one might be tempted to

say that it is undervalued if its P/E ratio is less than 45 (1.5 × 30). The PEG ratio

is not a directly proportional relationship. The PEG ratio actually decreases as the

earnings-per-share growth rate increases.

Finally, an approach that has a rich historical basis is the price-to-book (P/B)

ratio. To calculate book value per share, the shareholders’ equity section of the

balance sheet is divided by the number of shares outstanding. The stock’s price

per share is divided by the book value per share to obtain the P/B ratio. A P/B

ratio of less than 1.0 was a common benchmark for identifying possibly

undervalued companies.

The strong stock market performance of the late 1980s and 1990s pushed the

average P/B ratio of the S&P 500 average to more than 5.0. By 1999, very few

stocks had P/B ratios near 1.0, other than those of companies that were near

bankruptcy. As a consequence, this method had fallen into disuse by all except

diehard Graham and Dodd value investors (Cottle, Murray, and Block 1988). In

late 2006, however, after the 2000–2002 correction and subsequent recovery,

the S&P 500 P/B ratio was at about 3.0.

No single equity valuation method should be used alone. Even if a company has

positive earnings and pays dividends, an investor should calculate the intrinsic

value using most or all of the previously listed methods. At times, each method

will lead you to the same conclusion; at other times, the methods may leave you

in limbo, wondering if your analysis is flawed. In the latter case, you may decide

that no rational decision can be made at the moment.


Reading the next part of this chapter will enable you to:

4–3 Calculate the intrinsic value of a stock using various stock valuation

techniques or calculate the expected return of a stock.

There are basically three different types of dividend growth valuation models that

you should be familiar with:

1. the zero growth or dividend in perpetuity,

2. the constant dividend growth model, and

3. the non-constant dividend growth model.

The Zero Growth Model The zero growth model is also known as the dividend in perpetuity model. This is

commonly used to evaluate stocks whose dividend is fixed and will never grow.

This situation is most frequently encountered with preferred stocks that have a

fixed dividend rate with no maturity date. This formula breaks down to a very

simple form, where we just take the cash flow (the annual dividend amount) and

divide it by the required return:

r

DV 0=

To illustrate this method we will look at a preferred stock trading on the NYSE:

Xcel Energy Series A $3.60 preferred stock. The stock has a stated dividend rate

of $3.60. This is a fixed rate and will not grow in the future. An investor who

required a return of 7% on his investment would use this for his “r” (required

return). The formula would yield the following valuation:

435107

603.

.

. =

The preferred stock is quoted at $74.50 to currently yield 4.83%. Based on the

fair value of $51.43 for a required return of 7%, one can see that this preferred


stock is overpriced. Another even easier way to assess valuation on a preferred

stock would be to simply look at the yield. If the yield is less than your required

return, it would be considered overvalued. A quick look at the yield on Xcel

Energy Series A preferred confirms this. The yield is 4.83%, which is lower than

the required return of 7%, making the stock overvalued at $74.50. The stock

would have to trade at $51.43 or below for the yield to equal or exceed the

required return of 7%.

There is a great amount of interest rate risk with preferred stocks, since there is

no stated maturity. For example, using the same Xcel preferred, let’s say interest

rates increase from 7% to 8%. To find the intrinsic value:

4508

603$

.

. =

The intrinsic value of the preferred when interest rates were 7% was $51.53.

With interest rates a point higher at 8% the intrinsic value drops to $45.00, a

decrease of $6.53 or 12.7%. Investors sometimes think of preferred stocks as

“safe,” but as can be seen by this 1% change in interest rates preferred stocks do

have quite a bit of interest rate risk.

Constant Growth DDM

The second type of dividend growth valuation is the constant growth dividend

discount model, which is used to calculate the intrinsic value of dividend paying

stock. It is essentially an extension of the zero growth model already covered.

The difference is that we now have a cash flow (annual dividend) that is growing

over time rather than a cash flow (annual dividend) that stays the same. To take

into account this growth, we introduce a growth rate into the formula, so

r

DV 0=

becomes:

gr

DV

−= 1


The D1 in the numerator stands for “D(1 + g)”—in other words we are now

going to increase the dividend by the amount we anticipate it will grow each year

by taking the annual dividend and multiplying by 1 plus the growth rate. Note: On the denominator, we are going to subtract the growth rate from the required

return rather than just using the required return as we did in the zero growth

model.

With the constant growth dividend discount model, the assumption made is that the dividends will continue to grow at the same rate in perpetuity.

Calculation

Calculating the intrinsic value of a stock using the constant growth DDM

requires three inputs:

1. current-year dividends

2. estimated growth rate of dividends

3. required return

Current-year dividends are the easy part. Calculating the estimated growth rate of

dividends is more difficult. If we assume that the payout ratio will remain

constant (an important assumption in the DDM), then we can use the estimated

growth rate of earnings as the estimated growth rate of dividends.


gr

D

gr

)g(DV

−=

−+= 10 1

where

V = Intrinsic value of the stock

D0 = Current-year dividend

r = Required return

g = Dividend growth rate

To thoroughly understand the formula and its application, you should experiment

with different assumptions of growth rate and required return to see what impact

they have on the final result for V.

The dividend growth rate is a function of the company’s return on equity (ROE)

and the retention rate of earnings (rr), which is 1 minus the dividend payout ratio.

Specifically, g = ROE × rr. It makes sense that, everything else held constant, the

higher the ROE, the faster dividends can grow. Likewise, the more earnings

retained to generate additional growth, the faster dividends can grow in the

future. This will be covered further in the next module on security analysis.

For the preceding equation to work, the required return must exceed the dividend

growth rate. If that is not the case, a different valuation method must be used.

Example. Thor Industries pays an annual dividend $2.00 per share, and its

dividends are expected to grow at 6% annually. If your required return is 10%

then what is the intrinsic value of Thor?

0610061002

..).(.

V−

=

Note that we use the decimal form, not a whole number, for the growth rate, so

6% is .06. Also note that since we are using the decimal form for the growth rate,

we must also do so for the required return, so this is expressed as .10.


0610061002

..).(.

V−

= = 04122

..

= $53.00

This then tells us that the intrinsic value of Thor Industries is $53.00, meaning if

it is priced in the marketplace at $53 or lower we would purchase it. If it is

trading above $53 a share we would not purchase it because it would be

overvalued, and we would be paying too much for it.

Fair Market Value Relative Value Action

Less than $53 Undervalued Buy

$53 Fairly valued Buy

Greater than $53 Overvalued Do not buy, or sell short

Expected Return

While we are looking at the constant growth DDM, let’s take a look at another

formula, the expected return formula:

gP

Dr

1 +=

The formula for the expected return of a security is derived from the formula for

computing a security’s intrinsic value. The distinction between the two formulas

is that in the intrinsic value formula, the objective is to compute the price at

which the security should sell; in the expected return formula, the security’s

current price is one of the known factors, and the objective is to determine the

total return that the security should achieve given its current price and its

expected dividend growth (current income) and market value growth

(appreciation). The dividend growth and the appreciation are assumed to be at the

same rate.

The intrinsic value is the price you would pay to earn the required return.

Overvalued securities lie below the capital market line (their prices are too high


to earn the required return) and undervalued securities lie above the capital

market line (their prices are so low that you will earn more than the required

return rate).

The required return is often confused with the expected return. In fact, the term

expected return is used by some analysts when what they really mean is required

return. Rather than trying to change people’s habits, which is impossible, you

will have to develop an ear for knowing when someone really means required

return instead of expected return.

Required return is the return required by an investor to induce him or her to part

with the dollars that will be required to invest in any particular security. If an

investor cannot feel some degree of comfort that a security’s required return can

be achieved, then the investor should not invest in the security. Required return

can be computed using the capital asset pricing model formula

ifmfi rrrr β)( −+= .

Expected return is the return that can be expected given the current price of a

security and the security’s expected growth (the “g” in the DDM). If the security

is undervalued using the DDM, then the expected return, as computed, will

exceed the required return; if the security is overvalued using the DDM, then the

expected return will be less than the required return.

Returning to our Thor Industries example, let’s see what happens using three

different market prices, $50, $53, and $56 in the formula:

%...).(.

r 2410102400650

061002==+=

%..).(.

r 101000653

061002==+=

%...).(.

r 799097900656

061002==+=


Note that when the stock is priced at $53 (the intrinsic value we came up with

earlier) the expected return is 10%, which matches our required return of 10%.

When the stock is undervalued (at $50) note that the expected return (10.24%) is

now greater than our required return. When the stock is overvalued (at $56) the

expected return (9.79%) is now less than our required return.

It is important to note the relationships here. If we calculate the intrinsic value of

a stock using the DDM, and know that this stock is fairly valued (trading at

intrinsic value), then we know our expected return will match our required return.

Or, approached another way, if we were to do the expected return calculation

first and the expected return matched our required return, we would know that

the current market price of the stock is equal to its intrinsic value.

If we calculate the intrinsic value of a stock using the DDM, and know that the

stock is undervalued, then we know that our expected return is going to exceed

our required return. If we were to do the expected return calculation first and the

expected return was more than our required return, we would then know that the

stock is undervalued.

If we calculate the intrinsic value of a stock using the DDM, and know that the

stock is overvalued, then we know that our expected return is going to be less

than our required return. If we were to do the expected return calculation first and

the expected return was less than our required return, we would then know that

the stock is overvalued.

Let’s look at a hypothetical scenario.

Example—Intrinsic Value

Victor and Helga Leichtenstein want to begin investing in stocks. They believe

that 12% is a reasonable required rate of return. They are considering buying one

of the following two stocks, which have the following characteristics:

ABC Corp. Dividends are currently $2.25 annually and are expected to increase

by 5% annually; the current market price is $42.


XYZ Corp. Dividends are currently $1.80 annually and are expected to increase

by 6% annually; the current market price is $26.

Which stock should they purchase and why?

Stock ABC:

$33.75.05.12

(1.05)2.25V =

−=

10.63%.1063.0542

(1.05)2.25r ==+=

Stock XYZ:

$31.80.06.12

(1.06)1.80V =

−=

13.34%.1334.0626

1.80(1.06)r ==+=

Stock ABC has an intrinsic value of $33.75, but is trading in the marketplace at

$42. It is clearly overvalued and should not be purchased. Note also that the

expected return of 10.63% is lower than their required return of 12%.

Stock XYZ, however, has an intrinsic value of $31.80, but is trading in the

marketplace at just $26, so it is undervalued and should be purchased. Note also

that the expected return of 13.34% is greater than their required return of 12%.

If their required rate of return were to decrease from 12% to 11%, would you

make the same selection?

Stock ABC:


$39.37.05.11

(1.05)2.25V =

−=

10.63%.1063.0542

(1.05)2.25r ==+=

Stock XYZ:

$38.16.06.11

(1.06)1.80V =

−=

13.34%.1334.0626

(1.06)1.80r ==+=

Now stock XYZ is even more undervalued, and would remain the correct choice

for the Leichtensteins. As the required return goes down, the intrinsic value of

the stock will go up. Conversely, as the required return goes up, the intrinsic

value of a stock will go down.

The Non-Constant Growth Model

The third type of dividend growth model, the non-constant or multistage growth

model, has been tested on the CFP® Certification Examination in recent exams.

Since there is no formula for it on the exam formula sheet, you will have to

memorize the steps. The theory behind this model is that many companies in

their earlier growth stages will have dividend growth rates that are not

sustainable over long periods of time. At some point the growth rate will slow as

the company enters a more mature stage of growth.

Example. Let’s look at a hypothetical company that recently paid a dividend of

$0.35 per share for the year just completed. The company is expected to grow

this dividend at a rate of 20% for the next three years, after which the growth rate

is expected to level off at 8% for subsequent years. The required return is 12%.

What is the stock price today?

This problem can be broken down into three basic steps.


Step One

What is the dollar amount of the dividend at the end of the first three years of

super normal growth?

Year 1 0.35 × 1.20 0.42

Year 2 0.42 × 1.20 0.504

Year 3 0.504 × 1.20 0.6048

You should take note of a common trap here. Make sure you don’t use the

dividend most recently paid as your dividend for Year 1. You must multiply by

the growth rate to get the dividend for Period D1.

Step Two

What is the value of the stock at the end of Year 3 based on the dividend at the

end of Year 3?

Use the constant growth formula for this step:

( )3316

0812

0816048.

..

.. =−

Make sure to realize that you are using the dividend at the end of Year 3 to

calculate the value for the stock at the end of Year 3.

Step Three

Use your calculator to solve for “NPV”—net present value, of an irregular cash

flow. The “NPV” key is the alternate function on the “PRC” key (found just

below the payment key) on the HP-10BII+. On the HP-12C the NPV key is the

alternate function on the “PV” key —“f, NPV.”

The cash flow key “CFj” on the HP-10BII+ is the second key below the “PV”

key. This is the key you will use for any cash flow entries.


On the HP-12C there are two cash flow keys. The initial cash flow is always

entered as “CFo,” and any subsequent cash flows are always entered as “CFj.”

On the HP-12C the “CFo” key is the alternate function on the “PV” key (g, CFo),

and the “CFj” key is the alternate function on the “PMT” key (g, CFj).

The keystrokes are as follows:

HP-10BII+ HP-12C

12 I/YR 12 i

0 CFj 0 CFo

0.42 CFj 0.42 CFj

0.504 CFj 0.504 CFj

0.6048 + 16.33 = 16.9348

CFj .6048 + 16.33 = 16.9348

.CFj

SHIFT, NPV 12.83 f, NPV 12.83

Note that in Year 3 you combine the dividend for that year with the discounted

value of the stock at the end of Year 3 based on the constant growth formula, and

enter just this one number (in this case 16.9348). Do not enter them separately!

This sum is then discounted back to the present using the discount rate of 12%.

Another way to think of this is in terms of a time line:


Here is another example of the non-constant growth dividend discount model:

Example. Robert Robertson III is interested in buying a stock that currently pays

a dividend of $0.60 cents per share annually. His required return on investments

is 9%. The dividend is expected to grow 15% annually for the next two years,

followed by an expected growth rate of 6% thereafter. What is the most that

Robert should pay for the stock?

Step 1: Find the amount of the dividend at the end of each of the two years

of non-constant growth:

0.79351.150.69

0.691.150.60

=×=×

Step 2: Find the value of the stock at the end of Year 2 based on the dividend

to be paid at the end of Year 3:

28.040.060.09

1.060.7935 =−

×

Step 3: Using the calculator, solve for the PV of unequal cash flows as

follows:

HP-10BII+ HP-12C

9 I/YR 9 i

0 CFj 0 CFo

0.69 CFj 0.69 CFj

0.7935 + 28.04 = 28.8335

CFj 0.7935 + 28.04 = 28.8835

CFj

SHIFT, NPV 24.90 SHIFT, NPV 24.90



4–4 Evaluate the appropriateness of investment decisions based on stock

valuation models.

Valuation Exercise—Merck & Co.

To demonstrate the calculation of the intrinsic value of a stock, we will use 2009

financial data from Merck & Co. (as of 9/30/2009), drawn from the Morningstar

and Smart Money websites.

Calculating the intrinsic value of MRK using the constant growth DDM requires

three inputs:

1. current-year dividends of MRK

2. estimated growth rate of MRK’s dividends

3. required return for MRK

Current-year dividends are the easy part. The annual dividend reported was $1.52

per share.

Calculating the estimated growth rate of dividends is more difficult. If we assume

that the payout ratio will remain constant (an important assumption in the DDM),

then we can use the estimated growth rate of earnings as the estimated growth

rate of dividends. The data for MRK shows that earnings are expected to grow at

a 3.3% rate over the next five years according to SmartMoney. We will use a

required return for large-cap stocks (the asset class of which MRK is a member)

of 9.6%, which is the long-term return number for large-caps from Ibbotson.

Using these inputs for the equation, the computation of the intrinsic value of

MRK using the DDM is as follows:


$24.92.033.096

.033)(11.52

gr

g)(1DV 0 =

−+=

−+=

where V = Intrinsic value of the stock


r = Required return


The intrinsic value of MRK is approximately $25 per share, based on the inputs

used. This compares with a recent market quote of $35, which would indicate

that the stock is approximately $10 overvalued. Note the importance of accurate

assumptions when using the formula. Let’s do the calculation assuming a 4.5%

earnings growth rate, which is Merck’s 5-year earnings growth rate according to

Morningstar:

$31.15.045.096

.045)(11.52

gr

g)(1DV 0 =

−+=

−+=

Or if we use the 10-year average earnings growth rate, which is 5.4%:

$38.15.054.096

.054)(11.52

gr

g)(1DV 0 =

−+=

−+=

So you can see that the formula is very sensitive to relatively small changes in

the input. With a growth rate of 4.5%, the intrinsic value comes out to be $31.15,

which is below the $35 market current price, meaning that the stock is

overvalued. However, if we use a growth rate of 5.4%, then the stock’s intrinsic

value is $38.15, which is above the current market price, meaning the stock is

undervalued.

To thoroughly understand the formula and its application, you should experiment

with different assumptions of growth rate and required return to see what impact

they have on the final result for V.


Using the same data for MRK, we can compute the expected return as follows for

the various growth rates:

3.3% growth rate:

7.79%.0779.03335

.033)(11.52g

P

g)(1Dr 0 ==++=++=

where

r = Expected return


P = Current price


4.5% growth rate:

9.04%.0904.04535

.045)(11.52g

P

g)(1Dr 0 ==++=++=

5.4% growth rate:

9.98%0998%.05435

.054)(11.52g

P

g)(1Dr 0 ==++=++=

Remember that our required return is 9.6%, and note that only the last scenario,

using 5.4% as our estimated growth rate, gives us an expected return greater than

9.6%. This, of course, is also the only scenario we looked at where the stock

comes out to be undervalued. If a stock is undervalued, then the expected return

will be greater than the required return. If a stock is overvalued, then the

expected return will be less than the required return.


P/E Ratio

To compute the projected value of MRK using the P/E (price to earnings) ratio, the input factors are the current price of the stock and the current and projected earnings of the company. The P/E ratios of the industry and of the market are also required.

The projected 2009 annual earnings (from SmartMoney) for Merck were $3.27, so to arrive at a P/E ratio we simply take the current price of $35 per share and divide by $3.27.

10.7$3.27

$35 =

When this analysis was done the P/E ratio for the market was approximately 20.9, and the P/E ratio for the drug industry was approximately 11.3.

For our P/E ratio calculation above, we used estimated 2009 earnings of $3.27 per share, and we should also look at the earnings estimate for 2010, which is $3.46 per share. The value of MRK using P/E multiples is shown in Table 1. The earnings per share are multiplied by the P/E ratios to obtain the valuation estimates.

Table 1: Valuation Based on P/E Ratios

Factor

Based on 2009 Projected Earnings $3.27

Based on 2010 Projected Earnings $3.46

MRK P/E 10.7 $35 $37.02

Industry P/E 11.3 $36.95 $39.10

Using industry and market P/E ratios, MRK has a projected value that is

somewhere between approximately $37 per share and $39 per share. The $37 is

close to both the current value of the stock, and the value computed using the

DDM with 4.5% and 5.4% growth rates.


The historical 5-year P/E range for Merck is from 6.30 to 41.40, with an average

P/E of 19.3. Merck’s current P/E at 10.7 is below the historic average, which

means there is a chance for an increase in price if there is an increase in the P/E

ratio.

PSR

The total revenues of MRK for the trailing 12-month (ttm) period ending

9/30/2009 were approximately $17.9 billion; total shares outstanding were 2.1

billion. Dividing revenue by shares gives us sales of $8.52 per share. The current

market price of the stock is approximately $35 per share. Therefore, the PSR for

MRK is calculated as follows:

4.1$8.52

$35 =

The industry average for price to sales according to Morningstar is 2.7. (This is

the average PSR for Merck, Abbott Labs, Bristol-Myers Squibb, Johnson &

Johnson, Eli Lilly, and Pfizer.) This indicates that Merck has a high price to sales

ratio relative to the industry, which leans to it being overvalued based just on this

ratio. The PSR for the general market is 1.2.

PEG Ratio

The PEG ratio is calculated by taking the P/E ratio and dividing it by the earnings

growth rate. Generally, the lower the PEG ratio, the more likely it is that a stock

may be undervalued; however, as with any one ratio or measurement, this

number alone will not tell the entire story.

We will look at PEG ratios based on SmartMoney growth estimates as of

11/19/2009:


Table 2: PEG Ratio

Forward P/E Ratio

Next 5 Years Growth Rate

Current Year PEG Ratio

MRK 10.8 3.3% 3.3

Drug industry 11.3 15.7% 0.7 Source: Morningstar

Table 2 shows us a couple of things. First, the P/E ratio of Merck is essentially

the same as the P/E ratio of the drug industry in general. However, drug stocks in

general have higher earnings growth rates than Merck. So this means that the

PEG ratio for the drug industry is lower than the PEG ratio for Merck, suggesting

that Merck may be overvalued relative to the overall drug industry. There may

better values found in other drug stocks, but again remember that this is just one

ratio.

P/B Ratio

The book value of a company is the amount reported as shareholders’ equity in

the balance sheet of the corporation. Most reporting services do the computation

on a per share basis so that investors do not have to search through financial

statements to find book value in dollars and make the conversion themselves.

The Morningstar website shows a book value for MRK of $7.26 per share. With

the current market price of MRK’s stock is approximately $35 per share the P/B

ratio is computed as follows:

4.8$7.26

$35 =

The price to book ratio average for the drug industry is 3.8. This analysis would

indicate that the current ratio for Merck is higher than that for the industry

average. Traditionally, a P/B ratio closer to 1.0 would indicate an undervalued

stock to a strict value investor. In recent years, however, P/B ratios have risen far

above 1.0, so an undervalued security would be one with a ratio less than the

market ratio or the industry ratio.


Summary

The valuation measures computed above are summarized in Table 3.

Table 3: Valuation Summary

Valuation Method Computed Value

DDM $25–$38

P/E projected 2009 $35–$37

P/E projected 2010 $37–$39

PSR 4.1

PEG ratio 3.3

P/B 4.8

During 2009 MRK traded between $20.05 and $38.10 per share. An investor who

is considering purchasing MRK stock must make a decision about the stock’s

appreciation potential, given the current price. Different analytical tools can lead

an investor to different conclusions. Let’s look at the factors we considered in our

decision-making process regarding a purchase of MRK stock.

DDM. The DDM shows that MRK stock is currently overvalued by up to

$10 per share. If the more favorable growth rate of 5.4% is used, then the

stock is undervalued by about $3 a share. The denominator is the key to

DDM valuation analysis. The discount rate used for required return was

9.6%. It could be less, or it could be more. Even a scientific approximation of

the appropriate required return rate could be questioned by another equally

qualified analyst. In our analysis we used different dividend growth rates.

If the spread between r and g is smaller than computed, then the intrinsic

value is higher than the figure computed; if the spread is larger, then the

intrinsic value is lower than the figure computed.

P/E ratio. The P/E ratio analysis shows that Merck is trading at a P/E lower

than the industry average for all drug stocks. Merck is also trading at a lower

P/E than its 5-year average. This would indicate that room exists for a P/E


multiple expansion that would increase the price of the stock. The company’s

financial statements should be analyzed in greater detail to determine whether

this conclusion is justified.

PSR. In the current market environment, the PSR of MRK appears high,

coming in at 4.1 compared with an industry average of 2.7. The PSR analysis

alone would indicate an overvalued stock with limited upside potential.

PEG ratio. The PEG ratio shows a fairly substantial premium when

compared to the PEG ratio for the industry. The PEG ratio does seem to

confirm the conclusion from the other analysis that the stock may be

overvalued.

P/B ratio. This analysis also indicates that MRK may be overvalued, selling

at a P/B ratio of 4.8 compared with an industry average of 3.8. P/B ratios are

not as significant to security analysts as they have been in years past, so the

P/B ratio should be given the least weight in the analysis.

Overall Conclusion

One can see that different methods of analysis will lead to different conclusions

regarding the fair value of a stock. It is important not only to analyze a

company’s current fundamentals, but that analysis should be compared with the

historical norms for the company, with the industry averages, and with the

market as a whole.

The use of the DDM, and the few ratios we have looked at, is just a start when it

comes to analyzing individual securities. There are many more ratios that can and

should be considered, such as liquidity and cash flow ratios, inventory turnover

ratios, profitability ratios, and return on equity, to name a few. There may also be

other fundamental information that is equally important, such as changes in

management, products, or competition. For example, Merck went through a

major acquisition in the fourth quarter of 2009 and acquired Schering-Plough— a

transaction that totals about $41 billion in cash and stock. Merck’s market


capitalization prior to the acquisition was in the neighborhood of $70 billion, so

this will have a major impact on Merck.

Many individuals who are interested in analyzing securities obtain the CFA

Charter (Chartered Financial Analyst), which is offered through the CFA

Institute (ww.cfainstitute.org). The CFP certification is geared more toward

helping individuals with their financial planning needs, and not toward becoming

an expert on security analysis. For the CFP certification you just need to know

the very basics when it comes to ratio analysis.

In the next module we will take a look at Investment Policy Statements, and at

three very important ratios: Jensen (alpha), Sharpe, and Treynor.


Chapter 3: Security Performance Evaluation

Reading the first part of this chapter will enable you to:

4–5 Explain the various components of the Investment Policy Statement

(IPS).

Investment Policy Statements (IPS)

ffective portfolio performance evaluation depends upon an appropriate

standard against which to evaluate investment decisions and

performance. Many such standards include relative performance against

an index, measured by returns on that index. There are also statistical measures

available that are discussed below: the Sharpe, Treynor, and Jensen (alpha)

indexes.

Absolute performance measures are also used, such as inflation plus some

percentage (e.g., inflation plus 5%).

Regardless of which of these absolute and relative performance measurement

approaches are used, performance against an investment policy statement should

be the first step in the evaluation process.

A well-drafted investment policy statement (IPS) reduces ambiguity and provides

guidance to any and all investment professionals needing to interact to implement

the IPS. If an IPS exists, a new relationship can be quickly established in the

event of an advisor change, providing clarity to the newly hired investment

professional. In addition, when investment recommendations are made, the

recommendations can be evaluated against the standards set in the IPS to

determine suitability.

E

Chapter 3: Security Performance Evaluation 39 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

According to Boone and Lubitz (Creating an Investment Policy Statement, FPA

Press), an IPS serves four basic purposes:

1. Setting objectives. This includes establishing and defining client expectations

concerning risk and return, and providing guidelines on how the assets are to

be invested.

2. Defining the asset allocation policy. This requires identifying various asset

classes that will be used to achieve the investor’s objectives, and determining

how best to allocate the assets to achieve a diversified portfolio.

3. Establishing management procedures. A guide needs to be put in place as

far as selecting and monitoring the investments, and making changes as

necessary. There also needs to be a way to evaluate the performance of

whoever is in charge of the investment process.

4. Determining communication procedures. A concise method of

communication needs to be in place so that all parties involved are aware of

the process and objectives, and responsibility must be assigned for

implementation.

Quoting Boone and Lubitz:

“For the typical investor, a lack of information, the absence of a systematic

approach, and emotional and behavioral factors often lead to irrational or

inappropriate investment decision. The creation and use of an IPS helps

clients and advisors make prudent, rational decisions about their investments.

This process will generally help both the investor and the advisor become

better and more successful in their respective roles.”

There are no set IPS statement standards, but the following minimum content

areas would result in a comprehensive and relatively complete IPS. A properly

crafted IPS will keep both the client and the advisor on track, and minimize any

disagreements or confusion.

Return requirement. This might include absolute or relative dollar or

percentage returns on a before-tax or after-tax basis. Also included might be

the requirement to provide the specified return on an inflation-adjusted basis.


Risk tolerance. At a minimum, this should state if the portfolio volatility is to

be low, below average, average, above average, or high. There are two major

areas to address with risk tolerance: (1) the ability to take risk, and (2) the

willingness to take risk. They are not the same thing. Ability has to do with

resources and circumstances. Someone in good health, properly insured, with

adequate savings, and $5 million in investments would most likely have a

high ability to take risk. However, this same individual may not like to see

his account balances move much, and may have a very low willingness to

take risk. Or, based on his return objective, he may not need to take much

risk to achieve his objective. Other statements reflecting risk tolerance issues

also can be addressed. If the risk level is to decline in several years due to an

expected change in circumstances—such as retirement—statements to that

effect should be included. One caveat here is that the risk tolerance objective

should be consistent with the return requirement. For example, if the return

requirement needed to meet the client’s goal is 10%, but they have a

conservative risk tolerance, something has to give. Either they are going to

have to take on more risk, lower their return requirement (thus downsizing

their goals), or a combination of the two.

Liquidity. Any liquidity constraints, such as an emergency fund, a fund for a

vacation or car purchase, or an amount needed within the next three to five

years to fund an anticipated cash expenditure, should be included here.

Generally, many advisors do not invest assets in the stock market that will be

needed within the next five years.

Time horizon. Short, intermediate, or long-term horizons should be indicated

for the achievement of investment goals. All three may be represented due to

the existence of short-, intermediate-, and long-term goals. For example, an

individual may have a personal short-term time horizon for education cost,

and then have a long-term time horizon for retirement. A long-term time

horizon may also be applicable to certain assets that are expected to be gifted

or willed to family members or charities.


Laws and regulations. Individuals have few laws and regulations with which

to be concerned. If an IPS is developed for a retirement plan or endowment,

then regulatory issues may be more complex—such as compliance with

ERISA.

Taxes. For individuals, the objective generally is to minimize the income tax

consequences of all investment transactions. Estate taxes may be an issue for

elderly clients. For retirement plans and IRAs, taxes generally are not an

issue, at least until required distributions must be made.

Unique preferences and circumstances. This refers to things the client

brings up as issues. Included may be statements about outside income that

may be received, such as royalties; restrictions on security transactions

applicable to insiders; trusts that may provide current or future income or

assets; prospective inheritances, especially if expected soon; and concerns

about any other issues, such as inflation and depression.

Permitted and excluded investments. All clients have some favorite types of

investments and some investments with which they may have had some

negative experiences over their investing lives. If the client wants to include

or exclude certain of these investment asset classes or types, they should be

listed here.

Constructing an IPS

A properly constructed IPS should be designed for that particular client—a

“cookie-cutter” or “one-size-fits-all” approach will not work well. One test of a

well-written IPS is whether the client could have remained committed to the

parameters of the IPS based on what the capital markets have done over the past

decades. Given the dramatic decline and volatility of the markets in 2008 and

2009, we may well see a different appreciation of what “risk” means going

forward.


Here is a template of how an IPS could be constructed:

Investment Policy Statement for John Doe

I. Investor Circumstances

II. Investment Objectives

a. General

b. Portfolio Return Objective

c. Rationale and Justification

III. Risk Tolerance

a. Ability to take risk

b. Willingness to take risk

c. Risk Tolerance Objective

IV. Client Liquidity Needs

a. Rationale and Justification

V. Time Horizon

a. Time Horizon Objective

b. Rationale and Justification

VI. Income Tax Constraints

VII. Other Unique Needs and Circumstances

VIII. Asset Allocation

For more information on investment policy statements and how to construct

them, you can refer to Creating an Investment Policy Statement by Boone and

Lubitz (FPA Press) or visit www.ipsadvisorpro.com.


SWOT Analysis

“SWOT” stands for Strengths, Weaknesses, Opportunities, and Threats and helps

both the advisor and the client understand the big picture. When an advisor does

a SWOT analysis he or she develops an understanding of how both the internal

and external environments impact the client. Strengths and weaknesses reflect the

internal environment unique to the client, such as income, net worth, too much

debt, deficient insurance, etc. These are areas over which the client has varying

amounts of control. The opportunities and threats, on the other hand, reflect the

external environment, over which the client has no control. These include such

things as current interest rates, rate of inflation, or the cost of education and

retirement. A well-thought-out SWOT analysis helps to focus the client on their

current situation as well as what they are up against. This analysis can also be

helpful in constructing a well-designed IPS, since several of the areas that will

come up in this analysis also are relevant to an IPS, such as risk and return, and

market expectations.

Following is an example of what a SWOT analysis might look like for a fictional

couple, Zack and Zoe Jones:

Strengths:

Zack has a steady job in a recession-proof industry that provides over

$70,000 a year in income.

Zoe works part-time and supplements the household income while doing

work she enjoys.

Zack and Zoe’s net worth is reasonable for their age.

Both are healthy and have adequate health insurance.


Weaknesses:

Zack is growing restless in his job and wants to pursue a new career, which

would lower their household income.

Too much debt relative to their net worth.

Unrealistic goals for the amount of saving and investing.

Investments are inappropriate and do not match their risk tolerance.

Neither Zack nor Zoe have long-term disability.

Estate planning is inadequate.

Opportunities:

Interest rates are historically low making borrowing, such as for a home,

more affordable.

Decline in stocks increases the chances for substantial appreciation going

forward, and it may be a good time to dollar cost average into the market.

Lower housing prices makes purchasing an affordable home more likely.

Threats:

Unemployment is high, and this may impact raises and/or employment.

Cost of college continues to rise, presenting challenges for sending Zack Jr.

to his dad’s alma mater.

Inflation may be increasing in the coming years.

One can see the strategic thinking that needs to go into a SWOT analysis would

also be helpful in constructing an IPS.



4–6 Explain the characteristics, uses, and limitations of stock

performance measurement indexes.

Security and Portfolio Performance Evaluation

The required return tells an investor the return that a security, or a portfolio,

should attain, given the risk level of the security or portfolio. Security

performance evaluation compares the actual return of the security or portfolio to

the required return or to a benchmark return.

Four performance index measurement tools are discussed in this chapter. The

Jensen index, also known as alpha, is used to compare the actual return to the

required return. Two other indexes, the Sharpe index and the Treynor index, are

used to compare the stock or mutual fund’s excess return with a benchmark index

or with another similar stock or mutual fund. The Sharpe index, in particular, is

very useful for comparing one security’s risk-adjusted return with that of another

security or with a benchmark return. The information ratio is similar to the

Sharpe index, but is focused on the manager’s excess return over the benchmark

return relative to the tracking error (the standard deviation of the difference

between the returns on the portfolio and the returns on the benchmark).

Alpha and Sharpe index figures are found on Morningstar Mutual Funds reports;

neither the Treynor index nor the information ratio is shown there. The Treynor

index is more limited in its use because beta is used in its calculation. Generally,

to use the Treynor index, the security or portfolio being analyzed must be part of

a diversified portfolio. If we could be certain that all investors would have

portfolios that resemble the S&P 500 index, then the beta used could be the

fund’s beta with respect to the S&P 500 index. However, most investors have

portfolios of mutual funds that differ sharply from the S&P 500 index. Because it

is impossible to know whether each owner of a particular fund has a truly


diversified portfolio or whether the fund is the only fund the investor owns,

showing a Treynor index for a fund might be misleading.

The information ratio measures active return over active risk. Active return is in

the numerator and active risk is in the denominator. An active manager takes

active risk by deviating from the benchmark holdings, making bets different from

the benchmark bets. In doing so, the manager’s risk level will change and the

manager’s return will change. If the risk level is higher than the benchmark risk

level, then it is hoped that the manager’s different-from-benchmark bets will

have a higher return than the benchmark. If so, then the information is likely to

be positive. If the manager’s risk level rose, but the bets didn’t pay off with

higher-than-benchmark returns, then the information ratio is likely to be negative.

Some of the same problems exist with respect to alpha. Beta is used in the

equation for required return. Required return is subtracted from a security’s

actual return to compute alpha. The use of beta presumes that the security or

portfolio is part of a diversified portfolio. Morningstar compensates for this

potential problem in its reports by reporting alpha with respect to the S&P 500

(or EAFE) index and then with respect to the best-fit index (the index with which

the fund in question has the highest R2). This gives investors the option to

consider how well the fund does with respect to the S&P 500 (if the fund is part

of a diversified portfolio that tracks well with the S&P 500 index) or with respect

to the industry with which the fund is most correlated.

The Sharpe index uses standard deviation, or total risk, in its denominator. It

assumes that the portfolio is not diversified. Therefore, the problem with respect

to beta does not exist with respect to the Sharpe index. Any security can be

directly compared with another security using the Sharpe index. However, this

index can also be confusing to investors. For example, if the large-cap mutual

fund sector has been the “hot” performer over the recent past and the emerging

markets sector has been the “dog,” then investors should expect that many large-

cap funds will have high Sharpe indexes and many emerging markets funds will

have low Sharpe indexes. In other words, high Sharpe indexes will appear in

asset classes that have performed well in the recent past. Such Sharpe indexes do

not predict that those same asset classes will also perform well in the future.


Comparing funds with each other using the Sharpe index is best confined to

comparisons of funds within a distinct asset class. An investor may want to

construct a diversified portfolio consisting of all major asset classes, including

emerging markets assets. If a decision were made solely on Sharpe ratios across

all asset classes, then no emerging markets funds would be likely to be chosen.

If, however, emerging markets funds were compared with each other, then an

emerging markets fund with a relatively high Sharpe index could be selected to

add to the existing portfolio.

Performance Measurement Comparisons

Formula

p

fpp σ

rr S

−=

p

fpp β

rrT

−=

[ ])βrr(r

ra

fmf

p

−+

−= A

BP

σRR

IR−=

Measures Variability Volatility Volatility Variability

Uses Std deviation

Beta Beta Tracking error

Portfolio well diversified

Does not assume

Does assume Does assume N/A

How much it outperformed Market

Does not indicate

Does not indicate

Does indicate N/A

Compares One Mgr to another

Yes Yes Yes No

Computes Relative value

Relative value Absolute value (alpha)

Relative value


4–7 Calculate one or more stock performance measurement indexes for

given portfolio returns and risk.

Risk/Return

Refer to the investment risk/return relationships shown in Figure 1, which

follows.


Figure 1: Investment Risk/Return Relationships


The title of each formula identified in Figure 1 is referenced by number to the set of formulas that follows.

(1) COV jijiji σσρ= (7) ifmfi )rr(rr β−+=

(2) jiCOVjWi2W jjW iiW 2222

p +σ+σ=σ (8) gr

DV

1

−=

(3) ji

ijij

COV R

σ×σ= (9)

p

fpp

rrT

β−

=

(4) 1 n

)r (r

2n

−

−=σ

(10) ])rr(r[ra fmfp β−+−=

(5) p

fpp

rr S

σ−

= (11) i

i

i

i

meanS

orx

CV −

σ=

(6) imm

i RSS

×=β or m

iimi σ

σρ=β

Here is the section of Figure 1 that deals with beta, and the formulas that rely on beta.


The Treynor and Jensen indexes are shown to be dependent on beta; if beta cannot

be relied upon because of a low R2 with a market index, then any of the

computations that include beta in the calculation are suspect and need further

investigation by the investor. Therefore, the Treynor and Jensen (alpha) indexes

may not be the most reliable indicators of portfolio performance.

It should also be noted in Figure 1 that the CAPM formula, which is used to

compute required return, is dependent on beta. If beta is not dependable, then the

required return computed using the CAPM formula may not reflect reality.

Likewise, when the required return, as computed using CAPM, is used in the

DDM, the computed intrinsic value may not be valid if the required return is not

valid.

The consequences of using beta improperly have caused many analysts,

investors, and academics to question the utility of relying on beta as a valid

measure of investment risk. Despite these concerns, beta continues to be used

extensively in investment theory.

Note that the Sharpe index, as shown in Figure 1, is not dependent on beta.

Therefore, the Sharpe index can be used in most circumstances

Jensen Index (alpha)

Alpha is determined as follows:

])rr(r[ra fmfp β−+−=

Note that all that is happening with alpha is that you are taking the return of the

portfolio and subtracting CAPM (your required return) from it! The formula in

the brackets ])rr(r[ fmf β−+ is the Capital Asset Pricing Model we have already

covered, and it tells us the amount of return we should achieve given the amount

of risk taken. Beta is the risk measurement we are using, and as beta increases

our required return will increase, or as beta decreases our required return will

decrease. We then subtract that required return from the portfolio return to

calculate alpha. Analysts like to use alpha because it is an absolute


measurement—it is telling you the percentage amount that a portfolio manager

has either overperformed or underperformed the market based on the amount of

risk taken.

Example. Return of the mutual fund is 8% with a beta of 0.84. The risk-free rate

is 5%, and the return of the market is 8%. What is the alpha of the mutual fund?

( )[ ]845858 .a −+−=

( )[ ]84358 .a +−=

[ ]52258 .a +−=

5278 .a −=

480.a +=

In this case the portfolio manager has obtained a return greater than that required

given the amount of risk that was taken (positive alpha). When comparing

managers with each other you are looking for positive alphas, and the higher the

better. Remember that alpha is an “absolute” measure. Sharpe and Treynor,

which we will cover next, are “relative” measures, and they are used for

comparative purposes.

Investment professionals are quite conversant with the term “alpha.” It is one of

the most widely used measures of investment performance because investors

believe that it measures the value added by an active portfolio manager. A

positive alpha indicates performance better than anticipated for the risk the

manager has taken; a negative alpha indicates performance worse than

anticipated for the risk the manager has taken; and an alpha of zero indicates

performance as anticipated for the risk the manager has taken. Remember that

CAPM is telling you the amount of return you should achieve for the amount of

risk taken (as measured by beta). If you achieve a higher return than required by

CAPM, you will have a positive alpha. If you do not achieve the return required

by CAPM, you will have a negative alpha.

Morningstar Mutual Funds reports alpha in two columns. In the first column, the

alpha with respect to the S&P 500 or EAFE index is listed; in the second column,


the alpha with respect to the best-fit index is listed. Morningstar uses an R2 of

70% (correlation coefficient of approximately +.84) as the point at which it

believes the beta starts becoming less reliable. Remember that beta is a measure

of systematic risk, so the higher the R2 the more accurate beta becomes. For

testing purposes you are looking for R2 s of 70 or higher in order for beta to be

considered reliable.

Here are three international funds:

American Funds

EuroPacific A First Eagle Overseas A

Vanguard Intl Value

Alpha 3.6 2.8 1.8

Beta 0.92 0.59 1.01

R-squared with EAFE index 96 92 98

Source: Morningstar Principia Pro, September 2009

Note that all three of these funds have high correlations (R-squareds) with the

same benchmark, the EAFE. Since these R-squareds are higher than 70 we can

use beta, and this is important since beta is used in the formula for alpha.

If you had narrowed your search down to these three funds, which would you

choose based on these performance measurements? Answer: American Funds

EuroPacific A, since it has the highest alpha. The alpha of 3.6 means that the

fund manager(s) earned a return 3.6% greater than that required based on the

amount of risk taken.

Sharpe Index

The Sharpe index is determined as follows:

p

fpp

rr S

σ−

=


The standard deviation for a fund can be found in a Morningstar report. Note that

all that is happening is that you are taking any excess return over the risk-free

rate (Rp – Rf), and then dividing by standard deviation. Unlike alpha which is an

absolute value, Sharpe is used for comparative purposes—it is a relative measure.

Example. Return of the mutual fund is 9% with a standard deviation of 12%, and

the current risk-free rate is 5%. What is the Sharpe ratio?

33012

.5 - 9

S ==

You would then compare this Sharpe ratio with the Sharpe ratio of other funds

you may be considering, and you would choose the one with the highest number.

When calculating Sharpe (and Treynor), using decimal representations will also

work:

33012

..

.05 - .09 S ==

Let’s take a look at the same three international funds we covered with alpha, and

add the Sharpe ratio:

American Funds

EuroPacific A First Eagle Overseas A

Vanguard Intl Value

Sharpe –0.03 0.01 –0.12

Alpha 3.6 2.8 1.8

Beta 0.92 0.59 1.01

R-squared w/EAFE index 96 92 98


Notice that the Sharpe ratios are very close to each other, and in this case the

First Eagle Overseas A has a slight edge. Now if the R-squareds were less than

70, meaning beta and subsequently alpha are questionable numbers, then we

would use Sharpe. However, since we have high R-squareds in this scenario, you


could and should use alpha to determine which fund to purchase. These numbers

will of course change over time, and should be monitored.

Let’s take a look at another example, this time with some gold funds:

Fidelity Select Gold

First Eagle Gold A

Van Eck Intl Inv Gold A

Sharpe 0.70 0.69 0.52

Alpha 16.5 12.5 5.74

Beta 7.67 8.65 17.76

R-squared with EAFE index 1 1 4


Note the high betas and alphas, but are they meaningful? No, because there is

essentially no correlation between these funds and the EAFE index it is being

compared to. An R-squared of 1 means that there is just 1% of systematic risk—

with the remaining 99% then being unsystematic risk. Another way to look at it

is that 1% of the price movement of these two funds is explained by the EAFE

index, and the other 99% is not. Remember that beta is a measure of systematic

risk, since it is telling you how volatile an investment is compared to a

benchmark. In order for beta to be considered a good number there has to be a

high enough correlation between the investment and the benchmark it is being

compared to. That is why you want an R-squared of 70 or higher in order to use

beta or any formulas that use beta. In this scenario, our R-squareds are much too

low and both beta and alpha (which uses beta) are meaningless. This leaves us

with the Sharpe ratio, and we can use Sharpe since it uses standard deviation.

Standard deviation is a measure of total risk, both systematic and unsystematic.

You should choose the fund with the highest Sharpe ratio, which is the Fidelity

Select Gold fund.

Now let’s take the same three funds, but now use the AMEX Gold Miners Index

as our benchmark rather than the EAFE:


Fidelity Select Gold

First Eagle Gold A

Van Eck Intl Inv Gold A

Sharpe 0.70 0.69 0.52

Alpha 6.9 5.6 9.95

Beta 0.93 0.81 1.01

R-squared with AMEX Gold Miners index

95 96 97


Notice the substantial change in the alpha and beta numbers. Since we now have

a high correlation (high R-squareds) between the funds and the benchmark, we

can now use beta and formulas that use beta. All three funds have high positive

alphas, and based on what is presented here you should choose the Van Eck gold

fund, which has the highest alpha.

Treynor Index

The Treynor index is determined as follows:

p

fpp

rrT

β−

=

Note that the Treynor index is very similar to Sharpe. The numerator is the same:

calculating any return over the risk-free rate (Rp – Rf). The difference is in the

denominator, which is now beta rather than standard deviation. Treynor is not

provided by Morningstar.

Example. Return of the mutual fund is 12%, with a beta of .90, and the current

risk-free rate is 5%. What is the Treynor ratio?

=−=900

512

.T 7.78


Or expressed in decimal form:

=−=900

0512

.

..T .0778

Since it is a comparative (relative) measure, just like Sharpe, you can use either

whole numbers or decimals in your calculations as long as you are consistent.

You would compare the Treynor ratio of one fund with other funds you may be

considering, and the higher the number the better. Remember, though, that since

Treynor uses beta there has to be a high enough level of systematic risk (R-

squared of 70 or higher) in order for beta to be reliable enough to use Treynor.

Information Ratio (IR)

The information ratio has just recently been added to the CFP Board exam sheet,

and is determined as follows:

A

BP RR IR

σ= −

where

PR = Return of the portfolio

BR = Return of the benchmark index

Aσ = Standard deviation of only the excess return

The information ratio is an extension of the Sharpe ratio; however, instead of

subtracting the risk-free rate from the portfolio return, the benchmark return is

subtracted in the numerator. This means that you are looking at what excess

return (if any) the fund manager achieved over the benchmark. This excess

return, or alpha, can be positive or negative depending on the performance of the

manager. Another difference is that the denominator is not the standard deviation

of the portfolio; instead, it is the standard deviation of the difference between the

returns on the portfolio and the returns on the benchmark—generally called the

tracking error or active risk.


Managers taking on higher levels of risk are expected to achieve higher rates of

return, and this can be measured by the IR. The higher the IR, the more likely it

is that the portfolio manager was able to capitalize on opportunities in the

marketplace. An IR of 0.50 or higher would mean that the fund manager has an

excess return (or alpha) that is about half of the volatility of the alpha (the

tracking error).

Example. You have two funds, both with a return of 12%. The return of the

benchmark is 10%. Fund X has active risk (tracking error) of 4%, and Fund Y

has active risk of 8%.

Fund X: 4

1012 −= IR = .50

Fund Y: 8

1012 −= IR = .25

You would choose Fund X, with the higher information ratio. Managers with IRs

of 0.50 or higher are often in the top quartile of their asset class.



Determining the Market Rate

Investors want to know how their specific investments are performing. They can

use the performance measures previously discussed to determine how each of

their investments is performing relative to its risk level. Each of the performance

measurement methods involves knowing how “the market” did. Defining “the

market” is not an easy matter.


Index Characteristics

The International Guide to Securities Market Indices contains information on

400 of the world’s leading securities market indexes. Among the characteristics

that are preferred in an index are the following:

1. The index should be relevant and appropriate. It should track the relevant

markets, market segments, instruments, individual securities, and investment

styles.

2. The index should be comprehensive, or broad based, incorporating, to the

extent appropriate, the markets, security types, and individual securities that

reflect the investment opportunities available to investors.

3. An investor should be able to invest in the index, and market participants

should be able to replicate it.

4. The index should be constructed so that each security’s return is weighted

according to its market value at the beginning of the period that the return is

measured.

Benchmark Principles

Two indexes are well known to all investors: the Dow Jones Industrial Average

and the Standard & Poor’s 500 Index. Many investors judge how well their

securities and portfolios have performed by comparing them to one or both of

these indexes. This method may have been adequate as recently as the 1960s,

when investors’ portfolios consisted primarily of large companies headquartered

in the United States. Investors’ portfolios today, however, consist of far more.

Financial advisors invest their clients’ portfolios in a combination of asset classes

that typically include the following:

1. equities:

U.S. stocks: large-cap, mid-cap, and small-cap stocks

international stocks: developed countries and emerging markets


2. fixed income:

U.S. government, U.S. intermediate-term, U.S. high-yield, and municipal

bonds

foreign debt

3. real assets (securitized)

REITs

4. cash equivalents

money market funds

Advisors may use asset classes other than the ones listed here, but these classes

are among the ones most commonly used in client portfolios.

Performance Index

A performance index for each asset class helps investors properly measure the

performance of their stocks or funds against other similar securities. For example,

U.S. large-cap stocks and funds led the investment hit parade during the mid-to-late

1990s. U.S. small-cap stocks and funds performed less spectacularly during the

same period. An investor should measure the performance of a small-cap fund in

his or her portfolio against the small-cap index, not against the large-cap index.

The fund could be an outstanding performer in the small-cap asset class, but its

performance could look anemic compared to that of the large-cap index.

Index Mutual Fund

Some advisors prefer to use one of the many index mutual funds as the index

instead of one of the indexes described in the tables that follow. These indexes

cannot be replicated precisely by an investor’s portfolio because the index reports

gross total returns, whereas an investor generally has transaction costs and (with

mutual funds or privately managed accounts) investment management fees

subtracted from total returns. Therefore, an index fund is a better indicator of

what an investor might expect from a passive approach because the index fund

return is net of transaction costs and management fees.


Weighted Indexes

Measuring the performance of an entire portfolio against a single performance

measure is difficult. No single index is so comprehensive as to include even the

short list of asset classes identified previously. Several world indexes do exist in

the stock and bond asset classes that could be used, but even a comparison

against these indexes might not be realistic. A more realistic approach might be

to create a dollar-weighted portfolio index using the indexes against which each

asset class is being measured. A consistent method of measuring each asset class

and the entire portfolio would then be available.

The vast majority of market indexes are capitalization weighted (also called

value weighted), which means that whatever percentage of market capitalization

you have relative to the market capitalization of the entire index is the amount of

weight you will be given in that index. For example, if your market capitalization

is $10 billion, and the market capitalization of the entire index is $100 billion,

you will account for 10% of that index, and for 10% of the price movement of

the index. Capitalization weighted indexes are used in modern portfolio theory,

since they most accurately reflect what is happening in the market.

There are two notable exceptions to the capitalization weighted indexes, and

these are the Dow Jones Industrial Average, and the Value Line Composite

Index. The DJIA is a “price-weighted” index, and the Value Line is an “equal

weighted” index.

Dow Jones Industrial Average

The Dow Jones Industrial Average results from adding together the prices of all

30 stocks in the index, and then dividing by a “divisor.” The divisor adjusts for

stock splits and company changes that have occurred over time. The net effect of

this is that higher priced stocks will generally have more of an impact on the

average than lower priced stocks, regardless of the market capitalization of the

stocks. For example, a company trading at $80 per share with a market cap of

$10 billion would have more impact than a company trading at $25 per share

with a market cap of $20 billion. Another way to look at it is that a 5% change on


a $100 stock ($5.00) will have more of an impact on the average than a 5%

change on a $50 stock ($2.50). Despite these shortcomings, the DJIA is the most

widely followed stock market indicator for the U.S. markets. But because it is not

capitalization (value) weighted, it is not used in modern portfolio theory analysis.

You will not find the DJIA used as a benchmark by Morningstar.

Value Line Index

The Value Line Index is the other notable exception to capitalization weighted

indexes. The Value Line is an equally weighted index, giving the same weight to

each of the approximately 1,700 stocks in the index. This is done by considering

only the percentage change in each of the stocks. Market price and market

capitalization are not relevant.

Asset Class Benchmarks

Advisors have a wide range of potential benchmarks that they may use for each

asset class. Table 4 identifies some of the more popular benchmarks used by

investment advisors for some of the asset classes listed earlier.

Table 4: Asset Class Benchmarks


U.S. large-cap stocks S&P 500 S&P 100

U.S. mid-cap stocks S&P Mid-Cap 400

U.S. small-cap stocks Russell 2000 S&P Small-Cap 600

International developed markets MSCI EAFE

International emerging markets S&P/IFC Investable MSCI Emerging Markets Free Global

U.S. intermediate-term bonds Barclays Capital Aggregate Bond



U.S. high-yield bonds Bank of America—Merrill Lynch U.S. High Yield

Municipal bonds Bank of America—Merrill Lynch Municipal Master

Equity REITs Wilshire Real Estate Securities

A synopsis of these indexes is shown in Table 5.

Table 5: Descriptions of Popular Benchmarks

Benchmark Synopsis

S&P 500 Tracks performances of 500 of the largest companies listed on the NYSE, the AMEX, and the Nasdaq system, accounting for approximately 64% of the market value of stocks listed on the exchanges

S&P 100 Tracks performances of 100 of the largest stocks in the S&P 500 index.

S&P Mid-Cap 400 Tracks performances of stocks listed on the NYSE that have a market capitalization between $200 million and $5 billion

Russell 2000 Tracks performances of the smallest 2,000 stocks in the Russell 3000 index, which have a market capitalization between $9 million and $2 billion and account for approximately 8% of the U.S. market capitalization

S&P Small-Cap 600 Tracks performances of 600 companies that have an average market value range of $80 million to $600 million and are in market sectors representative of the sectors typical in the small company universe

MSCI EAFE The most common benchmark for foreign stocks in 21 developed countries in Europe, Australia, and the Far East (no U.S. or Canada)

Barclays Capital Municipal Bond

Comprised of about 8,000 municipal bonds that are all investment grade, fixed-rate, and long-term maturities.


Benchmark Synopsis

S&P/IFC Investable Tracks performances of 30 developing countries in Europe, the Middle East, Africa, and Latin America that are available for purchase by foreign institutional investors

MSCI Emerging Markets Free Global

Tracks performances of stocks in 25 developing countries that are open to foreign investment

Barclays Capital Aggregate Bond

Tracks performances of U.S. investment grade bonds, including government, government agency, corporate and mortgage-backed securities between one and ten years

Wilshire Real Estate Securities

Tracks the performance of publicly traded equity REITs, real estate operating companies, and master limited partnerships

BofA Merrill Lynch Bond Indices

Bank of America Merrill Lynch has numerous bond indices that represent various bond markets and bond sectors

Note that you should strive to make as accurate a comparison as possible when comparing a portfolio against a benchmark. This normally entails coming up with a “blended” benchmark. For example, if 30% of a client’s portfolio is in U.S. large-cap stocks, then 30% of the client’s benchmark could be the S&P 500. If 10% were in U.S. small-cap stocks then 10% of the client’s benchmark could be the Russell 2000. You would do this for each of the major asset classes, until you reach 100%. You could then compare the client’s portfolio against a blended benchmark that truly reflects how the client is invested. It makes no sense to compare a client’s entire portfolio return against just the S&P 500 return if only 30% of the portfolio is invested in U.S. large-cap stocks.

Long-Term Market Statistics

Long-term data helps financial advisors and investors keep their perspective about the long-term returns and correlations of major asset classes and about the relative relationships of long-term returns and long-term risk levels. For example, Ibbotson data shows that the return on intermediate-term U.S. Treasury bonds (5.4%) is only slightly lower than the return on long-term U.S. Treasury bonds (5.7%); yet the risk level, as measured by standard deviation, is 5.7% for intermediate term Treasury bonds, and 9.8% for long-term Treasury bonds. In other words, for 30 basis points (1% = 100 basis points) more of yield, investors


have taken on about 71% more risk. This fact may help explain why many investors like intermediate-term bonds more than long-term bonds.

Here are return and risk numbers from the 2013 Ibbotson Stocks, Bonds, Bills, and Inflation Classic Yearbook, which we have already looked at in a previous module. This time, compare these long-term numbers to the annual returns by decade, found in Table 7.

Table 6: Risk and Return, 1926 to 2012

Geometric Mean

Arithmetic Mean

Standard Deviation

Large Company Stocks 9.8% 11.8% 20.2%

Small Company Stocks 11.9% 16.5% 32.3%

Long-Term Corporate Bonds 6.1% 6.4% 8.3%

Long-Term Government 5.7% 6.1% 9.7%

Intermediate-Term Government 5.4% 5.5% 5.6%

U.S. Treasury Bills 3.5% 3.6% 3.1%

Inflation 3.0% 3.1% 4.1%

Source: Ibbotson SBBI 2013 Classic Yearbook

Table 7: Compound Annual Rates of Return by Decade

1920s* 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s

Large Co.

19.2% -0.1% 9.2% 19.4% 7.8% 5.9% 17.5% 18.2% -0.9%

Small Co.

-4.5% 1.4% 20.7% 16.9% 15.5% 11.5% 15.8% 15.1% 6.3%

LT Corp. 5.2% 6.9% 2.7% 1.0% 1.7% 6.2% 13.0% 8.4% 7.6%

LT Gov’t 5.0% 4.9% 3.2% -0.1% 1.4% 5.5% 12.6% 8.8% 7.7%

IntTerm Gov’t

4.2% 4.6% 1.8% 1.3% 3.5% 7.0% 11.9% 7.2% 6.2%

T-Bills 3.7% 0.6% 0.4% 1.9% 3.9% 6.3% 8.9% 4.9% 2.8%

Inflation -1.1% -2.0% 5.4% 2.2% 2.5% 7.4% 5.1% 2.9% 2.5%

*based on the period 1926–1929

Source: Ibbotson SBBI 2013 Classic Yearbook

You will notice that there can be a fairly substantial difference between the

historical long-term rate of return, and the annual return by decade. For example,


the long-term return for large company stocks is 9.8%. In the 1990s the

compound annual return was 18.2%, over 8% a year better! Then take a look at

the return for 2000 decade and the annual return is -0.9%! These are major

differences and they cover what many would consider a fairly long period of

time—a decade. This is why it is generally recommended by many advisors that

any funds needed within the next five years should not be invested in the stock

market. Looking at the returns we have had since 2000, perhaps this time period

should even be longer. It is important when using long-term returns that advisors

and investors understand that these are long-term averages, calculated over long

periods of time that have seen some pretty wide variability, both up and down.

The average long-term return might be 9.8%, but an investor might not see that

return for years, even decades.


4–9 Evaluate the risk-adjusted performances of alternative investment

securities or portfolios to recommend the most appropriate selection

for a given client situation.

Risk-Adjusted Performance

Investors use many approaches to select investments and combinations of

investments for portfolios. The principles of portfolio selection focus on selecting

investments that have low correlation coefficients with each other. The asset classes

discussed earlier have correlation coefficients that are sufficiently distant from each

other so that a portfolio consisting of those asset classes would have a relatively low

portfolio standard deviation.

All the asset classes mentioned do not have to be used for a portfolio to be diversified sufficiently. Academic research has demonstrated that a minimum of four asset classes is necessary for adequate diversification, but increasing the number to more than seven or eight asset classes results in minimal marginal benefit.


Selection of individual securities or mutual funds focuses on risk-adjusted returns. If an investor has decided to invest in the large-cap asset class, he or she needs to select a specific fund from that asset class. Investors who believe that markets are completely efficient may select index funds for each asset class. Investors who believe in active portfolio management will select non-index funds.

Even within an asset class, individual funds will differ in the individual securities held, the diversification among industry groups, and the risk level taken. Therefore, some method of standardizing the returns relative to the risk taken will help investors make better decisions about selection of individual funds and/or stocks.

Computing a Risk-Adjusted Return

The portfolio performance methods shown in this module are ideal for this step in the portfolio management and design process. The Sharpe index can be used to compare any two securities with each other. It is best used to compare securities within the same asset class, such as large-cap funds. Even within the large-cap asset class, a further breakdown into large-cap value and large-cap growth is advisable. Value securities and growth securities frequently are on different cycles. Comparing like-kind securities with each other yields results that are superior to those derived from comparing securities with different characteristics.

The Jensen index (alpha) can be used with most securities and funds, especially when the relevant market index is the same for each security. Morningstar simplifies this process for mutual funds by providing a “best-fit index” for each fund that it analyzes. Sometimes even the best fit may not be most appropriate because Morningstar uses only the indexes that it maintains in its database. Some funds are difficult to fit into any one of the Morningstar databases. Because beta is used in the Jensen index, the beta must be relevant for the index to be useful.

The Treynor index is more difficult to use in practice. Perhaps this is why Morningstar makes no attempt to provide a Treynor index in its reports. To use the Treynor index, which uses beta in the denominator, the security or fund being analyzed must be part of a fully diversified portfolio. It is difficult to know when this fact can be relied upon for MPT purposes. Therefore, the Treynor index is


seldom used in practice. A Treynor index can be computed using the best-fit index and be relevant relative to other funds that are compared to that same index.

Other methods of computing risk-adjusted returns include (1) dividing the total return by the beta or standard deviation of the security or portfolio and (2) computing the coefficient of variation, which is the standard deviation divided by the total return. In general, no single method should be used alone; the results of more than one method can be compared to see if the results are similar or different.

Mutual Fund Comparison

The following mutual funds were selected, using historical data, to help demonstrate several of the concepts we have now covered. We will then compare this data to more recent data later in this chapter.

Morningstar Exercise: Table A (2007)

Fund Mean Return

Standard Deviation

Sharpe Ratio

Vanguard 500 Index 13.00% 7.52% 1.11

Davis NY Venture A 14.12% 6.75% 1.38

RiverSource Large Value A 12.72% 7.64% 1.06

First Eagle Gold A 21.43% 24.21% 0.75

Fidelity Real Estate 18.16% 15.60% 0.88


Morningstar Exercise: Table B (2007)

Name R-squared (R2 ) Benchmark Beta Alpha

Vanguard 500 Index 100 S&P 500 1.00 –0.12

Davis NY Venture A 87 S&P 500 0.84 2.19

89 Russell 1000 Value 0.82 0.84

RiverSource Large Value A

93 S&P 500 0.98 –0.16

96 Russell 1000 Value 0.95 –1.78



First Eagle Gold A 45 MSCI EAFE 1.71 –11.45

95 AMEX Gold Miners 0.79 3.89

Fidelity Real Estate 39 S&P 500 1.30 2.80

98 Wilshire REIT 0.94 –0.51


(Note that Morningstar is using just three years of data when calculating return

and risk measurements for these mutual funds, and quoting the mean return and

standard deviation on an annualized basis. For our example we are using data

from 2004 to 2007.)

Vanguard 500 Index. Refer first to the Vanguard 500 Index fund in Morningstar

Exercise: Table A. Note that its R2 with the market (the S&P 500 Index) is 100,

meaning 100% of the price movement of the Vanguard 500 Index fund is

explained by the S&P 500 Index (100% systematic risk). This of course makes

sense since it is an index fund. Note that the beta is 1.00, which also makes sense.

The Vanguard fund is just as volatile as the index itself, since it is the index.

Alpha, however, is slightly negative (-0.12), and this is because of the fees. If

there were no fees the alpha would be 0.

Davis NY Venture A. Now let’s take a look at the next fund, Davis NY Venture

A. Note that its R2 with the S&P 500 is 87. This means that 87% of the price

movement of the fund is explained by the S&P 500 (systematic risk), and the

other 13% would then be unsystematic risk. Remember that we are looking for an

R2 of 70 or higher in order to consider beta to be reliable, so we are above that

threshold. This means we can use both Treynor and alpha, which use beta in their

formulas. Note that there is a very respectable alpha of 2.19, meaning the

portfolio manager has achieved 2.19% more for investors than required based on

the amount of risk taken.

Russell 1000 Value. There is an index that is even more highly correlated with

the Davis NY Venture A, and that is the Russell 1000 Value. Note that the R2

with the Russell 1000 Value is 89, giving us 89% systematic risk, 11%

unsystematic. The beta is 0.82, and we still have a positive alpha, although lower,


of 0.84. Based on both of these comparisons we can see that the Davis NY

Venture fund has lower volatility than the market (as shown by the betas lower

than 1.00), and has provided a return greater than required for the amount of risk

taken (as shown by the positive alphas).

RiverSource Large Value A. Our next fund is also a large-cap value fund: the

RiverSource Large Value A. Note that its R2 with the S&P 500 is 93, giving us

93% systematic risk, and 7% unsystematic. The beta is 0.98, and it has a negative

alpha of -0.16. It has an even higher correlation with the Russell 1000 Value, an

R2 of 96, a beta of 0.95, and a negative alpha of -1.78. This means that the fund

has not delivered the amount of return it should have given the amount of risk

that was taken, falling 1.78% short of the required return. One other item to note,

with an R2 of 96 this fund is very close to being a pure index fund. An investor

might consider just purchasing a Russell 1000 value index fund, which would

have lower fees while closely mirroring the index.

First Eagle Gold A. The next fund is the First Eagle Gold A, which is obviously

a gold and metals fund. Its R2 with the MSCI EAFE is just 45, giving us 45%

systematic risk and 55% unsystematic risk. The low R2 means that this fund

would be a very good diversifier because of its low correlation with the MSCI

EAFE. (Note: Remember how you take the square root of R2 to come up with the

correlation coefficient?)

HP-10BII+: .45, SHIFT, x (minus key) = .6708

HP-12C: .45, ENTER, g, x (yx key) = .6708

An R2 of 45 means that beta is not reliable since it is below 70. This means that

the beta shown of 1.71, and the alpha of -11.45 should not be used. Now look at

the First Eagle Gold compared to the AMEX Gold Miners index. The R2 is 95,

giving us a very high level of systematic risk, and thus beta reliability. Note the

low beta of 0.79, and a high positive alpha of +3.89. So comparing this gold fund

against a benchmark of gold funds, we have lower volatility than the benchmark

(low beta), and a higher risk-adjusted return (positive alpha). One caveat:


Remember that beta is a relative measure, telling you how volatile one

investment is relative to another (usually a benchmark); it does not necessarily

mean an investment is not volatile. If you look at Morningstar Exercise: Table A

you will see that The First Eagle Gold fund has a standard deviation of 24.21%—

much higher than the Vanguard 500 standard deviation of 7.52%—talk about a

bumpy ride!

Fidelity Real Estate. Finally, take a look at the Fidelity Real Estate. Compared

with the S&P 500 its R2 is just 39, making it a great diversifier with the S&P 500,

but beta is not reliable. When it is compared with the Wilshire REIT index we

have an R2 of 98, making beta very reliable. In fact, with such a high R2 an

investor might consider a Wilshire REIT index fund, since this fund is in fact

almost mirroring the index, and with a negative alpha (-0.51) there is no risk-

adjusted value being added.

You should also take a look at Morningstar Exercise: Table A, which gives you

additional data on these funds, including their Sharpe ratios. For example, the

Sharpe ratios for our two large-cap value funds that we discussed above are:

Davis NY Venture A 1.38

RiverSource Large Value A 1.06

Based on this relative measure, we would choose the Davis NY Venture fund

because of the higher Sharpe ratio.

Another calculation you could do with the information given in Morningstar

Exercise: Table A is the coefficient of variation—dividing the standard deviation

by the mean return.

If we were to do that for our two large-cap funds the results would be:

Davis NY Venture A 6.75/14.12 = .4780

RiverSource Large Value A 7.64/12.72 = .6006


With coefficient of variation the lower the better, so based on this measurement we would also choose the Davis NY Venture fund.

Bear in mind that when we look at Morningstar or other sources we are looking at past history. Correlations change, variability and volatility change, and performance numbers change, as we will see next. We do our best with the tools we have, but there are, of course, no guarantees.

What a Difference a Year or Two Makes

The previous exercise was using Morningstar 3-year annualized return statistics from 9/2004 –9/2007:

Morningstar Exercise: Table C (2007)

Fund Mean Return Standard Deviation Sharpe Ratio

Vanguard 500 Index 13.00% 7.52% 1.11


RiverSource Large Value A 12.72% 7.64% 1.06




Let’s take a look at the same five funds, but use data from a year later, using

returns from 9/2005–9/2008:

Morningstar Exercise: Table D (2008)


Vanguard 500 Index 2.74% 10.06% –0.09


RiverSource Large Value A –2.95% 12.27% –0.52





And here again are these same five funds, but using data now from 9/2006-

9/2009:

Morningstar Exercise: Table E (2009)


Vanguard 500 Index –5.83% 19.60% –0.34 Davis NY Venture A –6.35% 21.97% –0.31 RiverSource Equity Value A* –6.04% 21.10% –0.32 First Eagle Gold A 14.83% 33.96% 0.50 Fidelity Real Estate –15.06% 41.02% –0.25


*RiverSource Large Cap Value was merged into the RiverSource Equity Value A on 9/11/2009

You can see quite a dramatic change caused by the market sell-off in 2008 and 2009. Note that the mean returns have gone down, and the standard deviations have risen dramatically. The standard deviation for the Vanguard 500 more than doubled during this time period—it was 7.52% in 9/2007, 10.06% in 9/2008, and 19.60% in 9/2009. The standard deviation for the Fidelity Real Estate fund jumped from 15.60% in 9/2007 to 41.02% in 9/2009. Investors were handed the worst of both worlds during this time period: lower, often negative returns, accompanied with higher standard deviations.

Here is the second table, first the one from 2007 we used previously, and updated tables for 2008 and 2009:

Morningstar Exercise: Table F (2007)


Vanguard 500 Index 100 S&P 500 1.00 –0.12 Davis NY Venture A 87 S&P 500 0.84 2.19 89 Russell 1000 Value 0.82 0.84 RiverSource Large Value A 93 S&P 500 0.98 –0.16 96 Russell 1000 Value 0.95 –1.78 First Eagle Gold A 45 MSCI EAFE 1.71 –11.45 95 AMEX Gold Miners 0.79 3.89 Fidelity Real Estate 39 S&P 500 1.30 2.80

98 Wilshire REIT 0.94 –0.51 Source: Morningstar Principia Pro, September 2007


Morningstar Exercise: Table G (2008)




93 Russell 1000 Value 0.98 0.00

RiverSource Large Value A 96 S&P 500 1.06 –2.93

97 Russell 1000 Value 1.05 –2.83

First Eagle Gold A 1 MSCI EAFE 8.65 12.50

96 AMEX Gold Miners 0.81 5.60


98 Wilshire REIT 0.96 –1.70


Morningstar Exercise: Table H (2009)




97 S&P 500 1.11 0.60

RiverSource Equity Value A* 98 S&P 500 1.07 0.50

98 Russell 1000 1.04 0.10

First Eagle Gold A 1 ML USD LIBOR

5.67 9.60

97 AMEX Gold Miners

0.72 5.02


99 DJ Real Estate

1.00 –0.10


*RiverSource Large Cap Value was merged into the RiverSource Equity Value A on 9/11/2009


Again, changes can be observed. For example, notice that the First Eagle Gold

fund had a correlation of 45 with the MSCI EAFE index in 9/2007, and this

dropped to a correlation of just 1 in 9/2008. Notice how the correlation for the

Fidelity Real Estate fund has risen; in 9/2007 its correlation with EAFE was just

39, and in 9/2009 it has risen to 64. Remember that we discussed how

correlations change over time in Module 2, and how there can sometimes be

dramatic changes in correlation, especially over short time periods.

Since Morningstar is using only three years of data for these return and risk

measurements, an advisor needs to be careful to not read too much into them. If

one looks at the 9/2007 numbers (with the Vanguard 500 Index fund having a

mean return of 13% and a standard deviation of 7.52%) it is easy to get an overly

optimistic picture of the market. However, fast-forward just two years to 9/2009

(with the Vanguard 500 Index fund having a mean return of –5.83% and a

standard deviation of 19.60%), and the picture looks fairly bleak given the

tremendous amount of risk (standard deviation) for a negative return, and it is

easy to get an overly pessimistic picture of the market. It is important that

advisors have a clear understanding of what they are looking at, and be able to

objectively evaluate any data and performance measurements they may come

across in their research. As one can see it can be naïve, even dangerous, to just

look at one set of numbers and make too many assumptions from just those

numbers.

Summary 75 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Summary any investors rely on dividend income for part of their retirement

income. Dividend reinvestment plans are an important means of

building investor net worth. Dividends are a key component of the

dividend growth model, which is used to determine a security’s intrinsic value.

Investors can use several valuation methods, including ratio analysis, to

determine if a security is undervalued or overvalued. New investors should learn

these various approaches to avoid the trap of relying on only one technique,

which may lead an investor to make a bad decision regarding which stock to buy

or sell.

A good start in constructing and monitoring client portfolios is to draft an

Investment Policy Statement (IPS). Some method of performance evaluation

(that may be addressed in the IPS) is necessary to determine how the absolute

and risk-adjusted returns compare to like-kind investments.

Three performance measures—the Sharpe, Treynor, and Jensen (alpha)

indexes—are used to compute risk-adjusted performance. Beta needs to be a

reliable number (R-squared of 70 or higher) in order to use Treynor or alpha.

Investors must measure their asset class returns against the indexes for each asset

class in which they are invested. It is important, though, to always keep in mind

that statistics, such as those provided by Morningstar, are always backward-

looking and investors should not get an overly optimistic or overly pessimistic

outlook based on any of these numbers. The examples in the text showed how

dramatically those numbers could change in just a short period of time. Finally,

the overall portfolio performance must be measured against a weighted-average

index or a performance measure that closely reflects the components of the actual

portfolio.

M


Having read the material in this module you should be able to:







valuation models.


(IPS).









Module Review 77 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Module Review

Questions



1. Explain each of the following terms that are associated with the payment of common stock dividends.

a. regular cash dividend

Go to answer.

b. payout ratio

Go to answer.

c. retained earnings

Go to answer.

d. ex-dividend date

Go to answer.

e. date of record

Go to answer.

f. stock dividend

Go to answer.

g. dilution

Go to answer.

h. special dividend

Go to answer.

2. Assume that a corporation announces on April 10 (the declaration date) that a dividend will be paid on May 15 and that the date of record will be Friday, May 5. Your client purchases 100 shares of the stock on May 2 and then sells the shares on May 4. Will your client receive the dividend? Explain your response.

Go to answer.


3. Assume ABC Company announces that a stock dividend of 4%—rather than a cash dividend—will be paid on its common stock. Your client owns 500 shares of ABC Company, and the current price is $30 per share.

a. What is your client’s dollar ownership before the stock dividend?

Go to answer.

b. How many additional shares will your client receive as a result of the stock dividend?

Go to answer.

c. What is your client’s dollar ownership after the stock dividend, assuming there have been no other changes due to trading in the stock?

Go to answer.

d. Does the stock dividend change the firm’s assets or liabilities? Explain your answer.

Go to answer.

4. List the primary advantage and the primary disadvantage of a stock dividend.

Go to answer.

5. What is the most common reason for a company to declare a stock split, and how does a stock split accomplish the company’s purpose?

Go to answer.

6. Describe the impact of a stock split on each of the following.

a. the firm’s balance sheet

Go to answer.

b. the value of the stock

Go to answer.


7. Your client owns 2,000 shares of QRX common stock before the company issues a 3-for-1 stock split. The market price of QRX before the split was $60 per share.

a. What would your client’s total investment in QRX be worth immediately before the split?

Go to answer.

b. What would the market price of your client’s holdings in QRX be immediately after the split?

Go to answer.

8. What is a reverse stock split, and what is its purpose?

Go to answer.

9. Answer each of the following questions about dividend reinvestment plans.

a. What are the two ways in which a company can obtain and deliver shares if an investor has opted for a dividend reinvestment plan?

Go to answer.

b. What are the advantages for an investor who participates in a dividend reinvestment plan?

Go to answer.

c. What are the advantages for a firm when an investor participates in a dividend reinvestment plan?

Go to answer.

d. How are reinvested dividends taxed?

Go to answer.

10. Why do firms sometimes repurchase their stock?

Go to answer.

11. Identify the two sources of return that are available to an investor in common stock, and briefly explain the taxation of each.

Go to answer.


12. What is the impact on a shareholder who does not participate in a company’s dividend reinvestment plan?

Go to answer.

13. What is the impact on an investor when a company chooses to repurchase stock instead of increasing the dividends paid?

Go to answer.


14. Answer the following questions about estimating dividend growth rates. (Note: For this question, use only the process for estimating dividend growth; you will be asked to use the growth rate in the dividend growth model in subsequent questions.)

a. If a company decides to raise its dividend payout ratio (and its future return on equity [ROE] is projected to remain constant), how would the decision to raise the dividend payout ratio affect its dividend growth rate?

Go to answer.

b. How would the company’s stock price be affected if the company raises the payout ratio?

Go to answer.

c. When estimating the dividend growth rate, what impact do fluctuating earnings have on the computation?

Go to answer.

15. Briefly define each of the following terms.

a. expected rate of return

Go to answer.

b. required rate of return

Go to answer.


c. intrinsic value of a stock

Go to answer.

d. risk-free return

Go to answer.

16. Why is present value analysis used to calculate intrinsic value under the dividend growth model?

Go to answer.

17. Under the dividend growth model, what are the three factors on which a stock’s intrinsic value is based?

Go to answer.

18. If a company does not pay a dividend, how can the intrinsic value of its stock be determined?

Go to answer.



19. An investor is considering purchase of a $2.50 series A preferred stock. His required return is 10%. Should he purchase this stock if it is selling for $27 per share?

Go to answer.

20. Perform the following calculations to compute the intrinsic value of a stock.

a. Assume that the risk-free rate of return is 8.5%, that the expected rate of return of the market is 13%, and that the stock has a beta coefficient of 1.2. What is the investor’s required rate of return for the stock?

Go to answer.


b. The current dividend is $2.20 annually, and it is expected to grow at 5% per year. What is the intrinsic value of the stock using the DDM?

Go to answer.

21. Stock BLQ pays an annual dividend of $2.45; its dividends are expected to increase at 4% annually. The stock has a beta coefficient of .72; the risk-free rate is 6.9%; and the market rate of return is 14%. The current market price of stock BLQ is $35 per share.

a. What should be an investor’s required rate of return for stock BLQ?

Go to answer.

b. What is the intrinsic value of stock BLQ?

Go to answer.

c. What is the expected rate of return on stock BLQ?

Go to answer.

22. An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for stock CMR.

a. intrinsic value using the DDM

Go to answer.

b. expected return

Go to answer.

c. P/E ratio

Go to answer.

d. PSR

Go to answer.

e. P/B ratio

Go to answer.


23. Assume that Zeus Industries has the following financial statistics.

Zeus Industries Value

Dividend None

Book value per share $2.16

Sales per share $4.24

EPS (current year) $.57

EPS (next year) $.72

Current stock price per share $30.00

Compute the following financial information for Zeus Industries


Go to answer.

b. P/E ratio (current year’s earnings)

Go to answer.

c. P/E ratio (next year’s earnings)

Go to answer.

d. P/B ratio

Go to answer.

e. PSR

Go to answer.


valuation models.

24. How can an investor use intrinsic value in deciding what action to take concerning a security?

Go to answer.


25. Assume the stock in Question 20 is selling for $30 per share. Is the stock overvalued or undervalued, and is its expected return less than or more than its required return?

Go to answer.

26. Assume that stock BLQ in Question 21 sells for $35 per share.

a. According to the dividend growth model, is stock BLQ overvalued or undervalued for this investor? Why?

Go to answer.

b. Does the expected rate of return for this stock meet the investor’s required rate of return?

Go to answer.

27. Refer to the answers for Question 22 regarding stock CMR. Assume that the following statistics about the market and the industry for stock CMR apply.

Stock CMR Value

Market P/E ratio 21

Industry P/E ratio 16

Market PSR 1.62

Market P/B ratio 3.4

Would you advise the investor to purchase the stock? Why or why not?

Go to answer.


28. Refer to the answers for Question 23 regarding Zeus Industries. Assume the following ratios are reported for Zeus Industries, the industry, and the market.


PEG ratio for Zeus Industries 1.68

Industry PEG ratio 1.8

S&P 500 PEG ratio 3.29

S&P 500 P/E ratio (current-year earnings) 27.8

S&P 500 P/B ratio 6.0

Would you advise an investor to purchase the stock of Zeus Industries? Why or why not?

Go to answer.

29. Jon Allen is a retired widower who wants extra income. He has $5,000 available to invest in the stock market, but he is not sure which of the following two stocks he should purchase. His required rate of return is 13%.

Stock 1 Stock 2

Current dividend $1.84 $2.36

Dividend growth rate 3% 6%

Current market price $20/share $32/share

Current yield 9.2% 7.4%

a. According to the dividend valuation method, is Stock 1 currently overvalued or undervalued using Jon’s required rate of return?

Go to answer.

b. Does Stock 1 meet Jon’s required rate of return?

Go to answer.

c. According to the dividend growth method, is Stock 2 currently overvalued or undervalued using Jon’s required rate of return?

Go to answer.


d. Does Stock 2 meet Jon’s required rate of return?

Go to answer.

e. Which stock is more appropriate for Jon? Justify your response.

Go to answer.

30. A growth company paid a dividend of $0.50 per share in the last fiscal year. They estimate increasing the dividend by 15% per year for the next three years, after which it is expected to grow at a constant rate of 8%. The investor’s required return is 12%. What is the intrinsic value of the stock?

Go to answer.

31. Larry Jones, a recent college graduate, has a good job, and he feels secure enough about his future to be speculative in his investments. Larry’s required rate of return is 17%. He has been considering the following two issues.

Stock 1 Stock 2



Current market price $20/share $24.50/share

a. Which stock is more appropriate for Larry? Justify your response.

Go to answer.

b. If interest rates decrease, causing the risk-free rate to fall by 3%—therefore causing Larry’s required rate of return to decrease to 14%—would you make the same selection? Why?

Go to answer.

32. Two stocks have been presented for your consideration. The beta of Stock A is 1.3, while the beta of Stock B is 0.7. The annual growth rates of dividends are 11% and 6%, respectively. The dividend yields are 5% and 7%, respectively.

a. Since Stock A offers higher potential growth, should it be purchased? Why?

Go to answer.


b. Since Stock B offers a higher dividend yield, should it be purchased? Why?

Go to answer.

33. Assume that the estimated earnings per share for a stock have been forecast to be $3. The stock’s P/E ratio has ranged from 9 to 12.

a. From the information given, what is the possible price range for the stock?

Go to answer.

b. If the stock is currently selling for $28.50 and the estimated earnings are $3, what do these values indicate?

Go to answer.

c. If the appropriate P/E ratio is believed to be 11, is the stock underpriced or overpriced in terms of future earnings? Explain your answer.

Go to answer.


(IPS).

34. What is the objective of performance evaluation?

Go to answer.

35. Investment policy statements (IPS) have now become mainstream in financial planning practices.

a. What are the four basic purposes of an IPS?

Go to answer.

b. What are the major content areas that should be covered in an IPS?

Go to answer.




36. The capital asset pricing model is the basis for the Jensen, Treynor, and Sharpe performance indexes. What does the CAPM specify about the required return on an investment?

Go to answer.

37. Answer each of the following questions on the Jensen performance index.

a. What information does the Jensen index provide about a specific investment or portfolio?

Go to answer.

b. The Jensen equation can be expressed as follows:

( )[ ]β−+−= fmfp RRRRa

Why is this form of the equation useful in performance evaluation?

Go to answer.

c. What does a positive alpha indicate about a portfolio manager’s performance? What does a negative alpha indicate?

Go to answer.

d. The Jensen index measures the risk premium in terms of beta. On what assumption is this risk measure based?

Go to answer.

38. Answer each of the following questions on the Treynor performance index.

a. What limitations are associated with the Treynor index?

Go to answer.

b. How can these limitations be overcome?

Go to answer.


39. Answer each of the following questions on the Sharpe performance index.

a. In what one way does the Sharpe index formula differ from the Treynor index formula?

Go to answer.

b. Of what significance is this difference?

Go to answer.

c. The Sharpe index has a limitation that is the same as a limitation of the Treynor index. What is this limitation, and how is it overcome?

Go to answer.

40. Is one of the three performance indexes (Jensen, Sharpe, or Treynor) better than the others?

Go to answer.



41. Your client has found a mutual fund that she likes. Performance and risk characteristics of the fund and the market are as shown in the following table. Compute the Treynor index for the fund and for the market, and determine if the fund outperformed the market.

Characteristic Client Fund Market

Excess return (portfolio return minus risk-free rate)

13% 11%

Beta 1.4 1.0

R-squared with market 88% N/A

Treynor index

Go to answer.


42. Using both the Sharpe and Treynor performance indexes, indicate which of the two funds shown in the following table has the best risk-adjusted performance. (The risk-free rate is 6%.)

a. Assume that the R2 for Fund A is 85% and that it is 89% for Fund B.

Fund A Fund B

Return 18% 16%

Beta 1.3 1.1

Standard deviation 24 30

Go to answer.

b. Assume that the R2 for Fund A is 46% and that it is 89% for Fund B. What impact does Fund A’s lower R2 have on the calculations?

GoGo to answer. to answer.

43. Your client wants you to analyze the funds in the following table based on the information given. Use all three performance evaluation methods. (The risk-free rate is 6%.)

Fund X Fund Y

Market Index

Realized return 17% 20% 18%

Beta .72 1.2 1.0

Standard deviation 9 16 15

R2 with market 87 81 N/A

Go to answer.


44. List the four attributes that preferred indexes should have.

Go to answer.


45. The S&P 500 Average and the Dow Jones Industrial Average are the two most popular averages reported in the financial press and on financial programs on radio and television. Why might the returns on these averages be inappropriate for measuring the performance of an investment portfolio?

Go to answer.

46. Using Table 6 in this module, list the six asset classes in order of decreasing risk (highest risk first), and note any exceptions to the usual risk/return trade-off.

Go to answer.

47. How should historical returns be used in investment planning?

Go to answer.

48. Explain how the Dow Jones Industrial Average (DJIA) differs from each of the following indexes.

a. Standard & Poor’s 500 Index (S&P 500)

Go to answer.

b. NYSE Composite Index

Go to answer.

c. Value Line Index

Go to answer.

49. What observations can you make about inflation and various asset classes using the data shown in Table 6 (Summary Statistics of Annual Total Returns)?

Go to answer.




50. Assume that you have another fund to recommend to the client in Question 41. Over the same period as the period of the fund that the client likes, the new fund’s excess return was 12% and its beta was 0.95. Would you recommend that your client purchase the fund you like or purchase a market index fund?

Go to answer.


51. You have narrowed your choices down to the following three funds.

Fund A Fund B Fund C

Sharpe 0.23 0.55 0.69

Treynor 0.44 0.67 0.51

Jensen (alpha) 1.24 0.96 –0.23

Beta 0.92 0.97 1.02

R-squared 87 82 93

a. Which fund would you choose and why?

Go to answer.

b. If the R-squared for all three funds was below 70, what fund would you then choose and why?

Go to answer.

52. In the past, Grant Walker, age 37, has invested in individual stocks without much success. He wants to take a moderate risk and hopes to have a moderate return that is above that of CDs. He is considering the following two funds.

Mutual Fund 1 Mutual Fund 2

Type of fund International S&P 500 index


Five-year compound appreciation 18.4% 12.2%

Beta (S&P 500 index) 1.14 1.00


R2 with S&P 500 37% 99%

Which one of the two funds is most appropriate for Grant to invest in at this time? Go to answer.

53. Should most portfolios be measured against just one benchmark? Why or why not?

Go to answer.


Answers



1. Explain each of the terms listed in the following table that are associated with the payment of common stock dividends.

a. regular cash dividend

Most American firms distribute their regular cash dividends on a

quarterly basis. The amount is decided upon by the board of

directors according to company dividend policy.

Return to question.

b. payout ratio

The payout ratio is the amount of dividends paid, divided by the

earnings of the corporation.

Return to question.

c. retained earnings

Retained earnings is that part of earnings not paid out as

dividends. Most firms retain some of their earnings to finance

future growth.

Return to question.

d. ex-dividend date

The ex-dividend date is the second business day preceding the

date of record that was fixed by the corporation. On that date, the

stock trades exclusive of any right to the next dividend payment.

An investor who purchases the stock on or after the ex-dividend

date will not receive the next dividend payment.

Return to question.

e. date of record

The date of record is the second business day after the ex-

dividend date. On the record date, trades are settled and reflected

on the corporation’s books. To have a right to a dividend, an

investor must purchase stock before the ex-dividend date. For

example, assume that Monday, April 6, is the ex-dividend date.


Therefore, the record date is Wednesday, April 8. The investor

must have purchased the stock on or before Friday, April 3, in

order to receive the next dividend.

Return to question.

f. stock dividend

A stock dividend is a noncash dividend that is paid by issuing

additional stock to a current stockholder in proportion to the

number of shares he or she owns. It is considered a

recapitalization to the corporation—neither increasing nor

decreasing assets or liabilities.

Return to question.

g. dilution

Dilution occurs when a company issues a stock dividend in place

of a cash dividend (when stock options, convertibles, and other

options to purchase stock also exist). The market price of the

stock and the earnings per share are reduced to reflect the fact

that more shares are outstanding. (With a stock dividend, each

shareholder ends up with the same percentage of the company

that he or she originally had. When other securities are converted

into new shares, a true dilution occurs for those owners who did

not have anything to exchange for new shares. These owners now

own a smaller percentage of the company than they did before.)

Return to question.

h. special dividend

Sometimes a company will pay a dividend beyond their regular

dividend, called a special dividend; if they have had especially

strong earnings in a year. This is usually accompanied with a

buildup of corporate cash, and the board decides this is an

appropriate way to share the company’s success with the

commons stockholders.

Return to question.


2. Assume that a corporation announces on April 10 (the declaration date) that a dividend will be paid on May 15 and that the date of record will be Friday, May 5. Your client purchases 100 shares of the stock on May 2 and then sells the shares on May 4. Will your client receive the dividend? Explain your response.

The client will receive the dividend because she purchased the stock

one business day before the ex-dividend date (May 3), which is two

days prior to the record date. When she sold the shares on May 4 (the

trade date), the sale was not recorded on the company’s books until

three business days later. Therefore, she was listed as a shareholder

on the company’s books on the record date of May 5.

Return to question.

3. Assume ABC Company announces that a stock dividend of 4%—rather than a cash dividend—will be paid on its common stock. Your client owns 500 shares of ABC Company, and the current price is $30 per share.

a. What is your client’s dollar ownership before the stock dividend?

The client’s investment is worth $15,000 ($30 × 500 shares).

Return to question.

b. How many additional shares will your client receive as a result of the stock dividend?

Stock dividends are expressed as a percentage and are paid as

shares of stock in proportion to the shares already owned. The

client will receive 20 additional shares (.04 × 500), bringing the

total owned to 520 shares.

Return to question.

c. What is your client’s dollar ownership after the stock dividend, assuming there have been no other changes due to trading in the stock?

The client’s investment is still worth $15,000. The value of a

stockholder’s investment is not increased by a stock dividend.

Only the number of shares held by the stockholder is increased.

As the old shares are diluted, the price per share changes to

reflect the dilution—in this case, down to $28.85 ($30 ÷ 1.04 or

$15,000 ÷ 520).

Return to question.


d. Does the stock dividend change the firm’s assets or liabilities? Explain your answer.

Stock dividends are a form of recapitalization and do not affect the

assets or liabilities of the firm; only the entries in the equity section

of the firm’s balance sheet are affected. A stock dividend transfers

an amount equal to the market price of the shares from retained

earnings to common stock and additional paid-in capital. Although

there has been an increase in the number of shares outstanding,

there has not been an increase in the firm’s cash.

Return to question.

4. List the primary advantage and the primary disadvantage of a stock dividend.

The primary disadvantage is the expense. Among the costs are those

related to issuing new certificates, paying taxes or listing fees on the

new shares, and revising the firm’s stockholder records. A primary

advantage is that it brings to the current stockholders’ attention the

fact that the firm is retaining its cash in order to grow (i.e., a stock

dividend is issued instead of a cash dividend). The stockholders

eventually may be rewarded through the firm’s retention of assets and

its increased earning capacity.

Return to question.

5. What is the most common reason for a company to declare a stock split, and how does a stock split accomplish the company’s purpose?

A corporation usually uses a stock split to bring the market price of its

stock back into a range that is perceived by investors as attractive.

With a stock split, book value per share changes, but the dollar book

value of the firm remains the same. For example, a 2-for-1 split

means that, if there are 100,000 shares outstanding, 100,000 new

shares will be issued, for a total of 200,000 shares outstanding.

Although the dollar book value of the firm does not change, the book

value per share is reduced by half. The market price of the shares is

also reduced by half.

Return to question.


6. Describe the impact of a stock split on each of the following.

a. the firm’s balance sheet

Like a stock dividend, a stock split is a recapitalization, and as

such it does not affect the assets or liabilities of the firm. In a 2-for-

1 split, for example, the number of shares doubles, but each new

share has a par value that is equal to one-half of the par value of

each old share.

Return to question.

b. the value of the stock

The wealth of a stockholder is not immediately affected; however,

if other investors prefer the lower-priced shares after a split, then

demand for this stock could increase and its market value would

rise.

Return to question.

7. Your client owns 2,000 shares of QRX common stock before the company issues a 3-for-1 stock split. The market price of QRX before the split was $60 per share.

a. What would your client’s total investment in QRX be worth immediately before the split?

Before the split, the client’s holdings in QRX would have a value of

$120,000 (2,000 × $60).

Return to question.

b. What would the market price of your client’s holdings in QRX be immediately after the split?

After the 3-for-1 split, the client would own 6,000 shares of QRX,

and the market price of each share would be $20. The value of the

client’s total holdings of QRX would not change because of the

stock split (6,000 × $20 = $120,000).

Return to question.

8. What is a reverse stock split, and what is its purpose?

A reverse stock split reduces the number of shares and raises the

price of the stock. The purpose of such a split is to “add respectability”

to the stock if it is perceived that investors will not buy the stock at a


low price. Sometimes a reverse stock split is used immediately prior to

an initial public offering so that the offering price is raised into a range

that the underwriter believes makes the stock more marketable.

Return to question.

9. Answer each of the following questions about dividend reinvestment plans.

a. What are the two ways in which a company can obtain and deliver shares if an investor has opted for a dividend reinvestment plan?

Firms may either purchase shares of stock on the open market or

use authorized, but unissued, shares as a way to obtain shares to

use for DRIPs. In both types of reinvestment programs, investors

may also have the option of making additional cash contributions.

Return to question.

b. What are the advantages for an investor who participates in a dividend reinvestment plan?

Dividend reinvestment plans offer the investor an automatic

savings plan, the benefits of dollar cost averaging, and reduced

commission costs.

Return to question.

c. What are the advantages for a firm when an investor participates in a dividend reinvestment plan?

Firms benefit from dividend reinvestment plans because they can

save on the costs associated with sending dividend checks, they

have a method of selling shares (i.e., unissued shares) to

investors without going through a broker, and they have a source

of equity capital.

Return to question.

d. How are reinvested dividends taxed?

Dividends that are directly invested through a dividend

reinvestment plan are taxed at the same rate as dividends paid in

cash.

Return to question.


10. Why do firms sometimes repurchase their stock?

A firm with excess cash may repurchase some of its outstanding

shares of stock as an alternative to paying cash dividends. Of course,

stockholders do not have to sell their shares. A firm may repurchase

shares to reduce the number of shares outstanding, which would

result in an increase in earnings per share. (This strategy can be an

effective way to avoid a takeover attempt by another company.

Excess cash is distributed to current shareholders, and the stock price

frequently rises as earnings per share increases. The rising share

price keeps the stock from becoming undervalued and therefore also

keeps it from becoming a target for takeover attempts.)

Return to question.

11. Identify the two sources of return that are available to an investor in common stock, and briefly explain the taxation of each.

An investor in common stock anticipates a total return in the form of

dividend income and price appreciation. Dividends are taxable when

earned, and capital gains (from price appreciation) are subject to

taxation when realized.

Return to question.

12. What is the impact on a shareholder who does not participate in a company’s dividend reinvestment plan?

When a company offers a dividend reinvestment plan (DRIP) and a

shareholder declines to participate in the plan, that shareholder

experiences a dilution of his or her ownership in the company. The

percentage of the company’s shares owned by the nonparticipating

shareholder decreases slowly but surely as other shareholders who

are participants in the plan purchase fractional shares each quarter.

The sale of additional shares also affects the company’s earnings per

share since the number of shares over which the earnings must be

spread is greater as a result of the DRIP. (This assumes that the

company issues new shares instead of buying shares in the open

market.)

Return to question.


13. What is the impact on an investor when a company chooses to repurchase stock instead of increasing the dividends paid?

Investors in high tax brackets receive no tax benefit, since the capital

gains tax rate is the same as the rate on dividends. Also, the

corporate earnings will be distributed over a smaller share base, thus

increasing the earnings per share. If the intended purpose of the stock

repurchase program is to raise the value of the stock to prevent it from

becoming undervalued, then shareholders will benefit from that. The

stock price will rise, increasing their total return on investment.

Return to question.


14. Answer the following questions about estimating dividend growth rates. (Note: For this question, use only the process for estimating dividend growth; you will be asked to use the growth rate in the dividend growth model in subsequent questions.)

a. If a company decides to raise its dividend payout ratio (and its future return on equity [ROE] is projected to remain constant), how would the decision to raise the dividend payout ratio affect its dividend growth rate?

The dividend growth rate will be lower because the company will

retain less of its earnings to finance its future growth. Should the

company need additional funds for future expansion, it will have to

seek those funds through a stock or debt offering because the

shareholders will have already received a portion of the money

that could have been used to internally finance growth.

Return to question.

b. How would the company’s stock price be affected if the company raises the payout ratio?

The price could rise or fall; it is not possible to determine the

impact on the stock based solely on this decision.

Return to question.


c. When estimating the dividend growth rate, what impact do fluctuating earnings have on the computation?

Fluctuating earnings could result in a dividend growth rate that is

much lower or higher than is realistic, especially if one or two

recent years are not typical. To counter this tendency, analysts

could use a longer time period and/or eliminate the atypical years.

Return to question.

15. Briefly define each of the following terms.

a. expected rate of return

The expected rate of return is the anticipated return on an

investment. It is the sum of interest or dividend income and capital

gains.

Return to question.

b. required rate of return

The required rate of return is the minimum return the investor

wants to receive to compensate for the risk associated with

investing in a particular security. It is computed using the formula

for the security market line (also known as CAPM)—the sum of a

risk-free rate and a risk premium based on the market return and

the security’s beta.

Return to question.

c. intrinsic value of a stock

Intrinsic value, which is the underlying or inherent value of a stock,

is a function of the stock’s current dividend, the anticipated growth

rate in dividends, and the investor’s required rate of return.

Return to question.

d. risk-free return

The risk-free return is the nominal rate of return that an investor

could earn on a risk-free security (e.g., a U.S. Treasury bill).

Return to question.


16. Why is present value analysis used to calculate intrinsic value under the dividend growth model?

Present value analysis is used because the value of any security can

be determined by discounting the future stream of economic benefits

(cash flows—generally dividends) that the investor expects to receive.

Return to question.

17. Under the dividend growth model, what are the three factors on which a stock’s intrinsic value is based?

Intrinsic value is based on (1) the current dividend, (2) the expected

future growth in earnings and dividends, and (3) the required rate of

return.

Return to question.

18. If a company does not pay a dividend, how can the intrinsic value of its stock be determined?

The intrinsic value can be computed using the P/E ratio, the price-to-

sales ratio, the price-to-book ratio, and the PEG ratio. Even if the

company pays a cash dividend, it is wise to estimate intrinsic value

using all of these techniques to determine if the various approaches

validate each other.

Return to question.



19. An investor is considering purchase of a $2.50 series A preferred stock. His required return is 10%. Should he purchase this stock if it is selling for $27 per share?

2510

502 =.

.

According to the zero growth model, the maximum price to pay would

be $25. Since the stock is currently selling at $27, it would be

considered overvalued and should not be purchased.

Return to question.


20. Perform the following calculations to compute the intrinsic value of a stock.

a. Assume that the risk-free rate of return is 8.5%, that the expected rate of return of the market is 13%, and that the stock has a beta coefficient of 1.2. What is the investor’s required rate of return for the stock?

The investor’s required rate of return is 13.9%.

Return to question.

b. The current dividend is $2.20 annually, and it is expected to grow at 5% per year. What is the intrinsic value of the stock using the DDM?

The intrinsic value is $25.96

962505139

05120210 .$..

).(.

gr

)g(DV =

−+

=−

+=

Return to question.

21. Stock BLQ pays an annual dividend of $2.45; its dividends are expected to increase at 4% annually. The stock has a beta coefficient of .72; the risk-free rate is 6.9%; and the market rate of return is 14%. The current market price of stock BLQ is $35 per share.

a. What should be an investor’s required rate of return for stock BLQ?

r = 6.9 + (14 – 6.9) .72 =

6.9 + (7.1) .72 =

6.9 + 5.1 = 12%

Return to question.

%...).(..r

)rr(rr

s

fmfi

9131392108513085 ==−+=β−+=


b. What is the intrinsic value of stock BLQ?

85310412

04145210 .$..

).(.

gr

)g(DV =

−=

−+

=

Return to question.

c. What is the expected rate of return on stock BLQ?

%...).(.

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)g(D)r(E 2811112804

35

04145210 ==+=++=

Return to question.

22. An investor’s required rate of return is 10%. Stock CMR sells for $26 per share and pays an annual dividend of $.85; its dividends are expected to increase by 7% annually. CMR’s earnings per share are $1.40, its sales per share are $29, and its book value is $14 per share. Compute the following financial statistics for stock CMR.


32300710

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).(.

gr

)g(DV =

−+

=−

+=

Return to question.

b. expected return

%...).(.

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)g(D)r(E 5010105007

26

0718510 ==+=++=

Return to question.

c. P/E ratio

5718401

26.

.$

$E/P ==

Return to question.


d. PSR

90029

26.

$

$PSR ==

Return to question.

e. P/B ratio

86114

26.

$

$B/P ==

Return to question.

23. Assume that Zeus Industries has the following financial statistics.


Dividend None

Book value per share $2.16

Sales per share $4.24

EPS (current year) $.57

EPS (next year) $.72

Current stock price per share $30.00

Compute the following financial information for Zeus Industries


The DDM cannot be used because Zeus Industries does not pay

dividends.

Return to question.

b. P/E ratio (current year’s earnings)

652570

30.

.$

$ =

Return to question.


c. P/E ratio (next year’s earnings)

7.4172.0$

30$ =

Return to question.

d. P/B ratio

9.1316.2$30$ =

Return to question.

e. PSR

1.724.4$30$ =

Return to question.


valuation models.

24. How can an investor use intrinsic value in deciding what action to take concerning a security?

The intrinsic value of a security is compared to the security’s current

market price to determine if the security is undervalued (i.e., the

market price is less than the intrinsic value) or overvalued (i.e., the

market price is greater than the intrinsic value). If an asset is

undervalued, the asset may be an attractive investment. If an asset is

overvalued, the asset may be less attractive as an investment.

Return to question.


25. Assume the stock in Question 20 is selling for $30 per share. Is the stock overvalued or undervalued, and is its expected return less than or more than its required return?

The stock is overvalued at $30 since its intrinsic value is $25.96.

When a stock is overvalued, its expected return is less than the

required return, which in this case is 13.90%.

Return to question.

26. Assume that stock BLQ in Question 21 sells for $35 per share.

a. According to the dividend growth model, is stock BLQ overvalued or undervalued for this investor? Why?

Stock BLQ is overvalued because the market price is greater than

the intrinsic value calculated using the investor’s required rate of

return for BLQ stock.

Return to question.

b. Does the expected rate of return for this stock meet the investor’s required rate of return?

No, the expected rate of return E(r) for BLQ stock is 11.28%, and

the investor’s required rate of return is 12%. An overvalued stock

will always have an expected return that is lower than the required

return.

Return to question.

27. Refer to the answers for Question 22 regarding stock CMR. Assume that the following statistics about the market and the industry for stock CMR apply.

Stock CMR Value

Market P/E ratio 21

Industry P/E ratio 16

Market PSR 1.62

Market P/B ratio 3.4

Would you advise the investor to purchase the stock? Why or why not?

Yes. The intrinsic value, as computed by the DDM, is higher than the

current market price; therefore, the expected return is higher than the

investor’s required return. The P/E ratio is higher than the industry P/E

ratio, but this could mean the company is one of the superior


companies in the industry; the company P/E ratio is lower than the

market P/E ratio, which is further evidence of an undervalued

company. The PSR and P/B ratio also indicate an undervalued

company, compared to the market ratios.

Return to question.

28. Refer to the answers for Question 23 regarding Zeus Industries. Assume the following ratios are reported for Zeus Industries, the industry, and the market.


PEG ratio for Zeus Industries 1.68

Industry PEG ratio 1.8

S&P 500 PEG ratio 3.29

S&P 500 P/E ratio (current-year earnings) 27.8

S&P 500 P/B ratio 6.0

Would you advise an investor to purchase the stock of Zeus Industries? Why or why not?

No. The P/E ratio is substantially above the market’s ratio, even when

using projected earnings for the next year. The stock sells for 13

times book value, which is more than twice the ratio of the market.

And finally, the PSR is more than twice the level at which many would

consider a security to be overvalued. The PEG ratio seems

reasonable, compared to the industry and market levels; however,

given the extreme levels of the other ratios, the PEG ratio alone does

not appear to invalidate the conclusion suggested by the other ratios.

Return to question.


29. Jon Allen is a retired widower who wants extra income. He has $5,000 available to invest in the stock market, but he is not sure which of the following two stocks he should purchase. His required rate of return is 13%.

Stock 1 Stock 2


Dividend growth rate

3% 6%

Current market price

$20/share $32/share


a. According to the dividend valuation method, is Stock 1 currently overvalued or undervalued using Jon’s required rate of return?

Stock 1 is overvalued for Jon at the current stock market price of

$20 because, using Jon’s required rate of return, its intrinsic value

is only $18.95.

95180313

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gr

)g(DV =

−+

=−

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Return to question.

b. Does Stock 1 meet Jon’s required rate of return?

No. Stock 1 has an expected return of 12.48%, which is less than

Jon’s required rate of return of 13%.

%...).(.

gP

)g(D)r(E 4812124803

20

03184110 ==+=++=

Return to question.


c. According to the dividend growth method, is Stock 2 currently overvalued or undervalued using Jon’s required rate of return?

Stock 2 is currently undervalued using Jon’s required rate of

return because its intrinsic value is more than the current stock

market price.

74350613

06136210 .$..

).(.

gr

)g(DV =

−+

=−

+=

Return to question.

d. Does Stock 2 meet Jon’s required rate of return?

Yes. Stock 2 has an expected return of 13.82%, which is greater

than Jon’s required rate of return of 13%.

%...).(.

gP

)g(D)r(E 8213138206

32

06136210 ==+=++=

Return to question.

e. Which stock is more appropriate for Jon? Justify your response.

Stock 2 is more appropriate because it is undervalued and it

exceeds Jon’s required rate of return. Without the intrinsic value

analysis, Stock 1 might have been chosen because of its higher

current yield.

Return to question.

30. A growth company paid a dividend of $0.50 per share in the last fiscal year. They estimate increasing the dividend by 15% per year for the next three years, after which it is expected to grow at a constant rate of 8%. The investor’s required return is 12%. What is the intrinsic value of the stock?

Step 1

Year 1 dividend .50 × 1.15 = .575

Year 2 dividend .575 × 1.15 = .6613

Year 3 dividend .6613 × 1.15 = .7604


Step 2

53200812

0817604.

..

).(. =−

Step 3

Calculator keystrokes

12 I

0 CF0

.575 CF1

.6613 CF2

.7604 +

20.53

CF3

SHIFT NPV 16.19

Return to question.

31. Larry Jones, a recent college graduate, has a good job, and he feels secure enough about his future to be speculative in his investments. Larry’s required rate of return is 17%. He has been considering the following two issues.

Stock 1 Stock 2




a. Which stock is more appropriate for Larry? Justify your response.

Stock 2 is more appropriate because it is undervalued and it

exceeds Larry’s required rate of return of 17%.

Stock 1 Stock 2

Intrinsic value $15.71 $28

Expected return 15.5% 17.71%


Required return 17% 17% Return to question.


b. If interest rates decrease, causing the risk-free rate to fall by 3%—therefore causing Larry’s required rate of return to decrease to 14%—would you make the same selection? Why?

Yes, Stock 2 would still be more appropriate because it is even

more undervalued in this case. A relatively small difference in

expected growth rates can have a dramatic effect on valuations in

an environment of declining interest rates.

Stock 1: 50271014

10100110 .$..

).(.

gr

)g(DV =

−+

=−

+=

Stock 2: 701214

12125110 $..

).(.

gr

)g(DV =

−+

=−

+=

Return to question.

32. Two stocks have been presented for your consideration. The beta of stock A is 1.3, while the beta of stock B is 0.7. The annual growth rates of dividends are 11% and 6%, respectively. The dividend yields are 5% and 7%, respectively.

a. Since stock A offers higher potential growth, should it be purchased? Why?

Just because stock A offers higher potential growth is not a

sufficient reason to buy it. Additional information that would be

required before a purchase is made would include the investor’s

required return, the stock’s intrinsic value, and the stock’s current

market price. In accordance with the efficient market hypothesis,

the higher growth expectations may already be reflected in the

current market price.

Return to question.

b. Since stock B offers a higher dividend yield, should it be purchased? Why?

Just because stock B offers a higher dividend yield is not a

sufficient reason to buy it. Additional information that would be

required before a purchase is made would include the investor’s

required return, the stock’s intrinsic value, and the stock’s current


market price. Stock B’s current yield may be higher, but its lower

expected growth rate may make it a less attractive alternative.

Return to question.

33. Assume that the estimated earnings per share for a stock have been forecast to be $3. The stock’s P/E ratio has ranged from 9 to 12.

a. From the information given, what is the possible price range for the stock?

The possible price range is $27 to $36.

Low: $3 × 9 = $27

High: $3 × 12 = $36

Return to question.

b. If the stock is currently selling for $28.50 and the estimated earnings are $3, what do these values indicate?

The resulting P/E of 9.5 suggests that the stock is selling at a

price that is near its historic low. It may indicate that the stock is a

good buy, provided that earnings continue to grow and the

company’s financial position remains strong.

Return to question.

59.$3

$28.50P/E ==

Return to question.

c. If the appropriate P/E ratio is believed to be 11, is the stock underpriced or overpriced in terms of future earnings? Explain your answer.

If the appropriate P/E ratio is believed to be 11, the stock is

underpriced in terms of future earnings. As those future earnings

are achieved, the price should rise from $28.50 to $33. The stock

should be purchased.

Return to question.



(IPS).

34. What is the objective of performance evaluation?

The objective of performance evaluation is to provide an opportunity

to alter an investment strategy to improve portfolio performance.

Performance evaluation measures are used to judge the managers of

portfolios. They also can be used by individual investors to measure

the success of their investment approaches.

Return to question.

35. Investment policy statements (IPS) have now become mainstream in financial planning practices.

a. What are the four basic purposes of an IPS?

Setting objectives—includes risk tolerance and return objectives

Defining the asset allocation policy—includes the asset classes to be used and how diversification will be achieved

Establishing management procedures—guide for selecting and monitoring the investments as well as evaluating the performance

Determining communication procedures—make sure all parties are aware of the process and objectives, and who is responsible for implementation Return to question.

b. What are the major content areas that should be covered in an IPS?

Return requirement

Risk tolerance

Liquidity

Time horizon

Laws and regulations

Taxes


Unique preferences and circumstances

Permitted and excluded investments Return to question.



36. The capital asset pricing model is the basis for the Jensen, Treynor, and Sharpe performance indexes. What does the CAPM specify about the required return on an investment?

The CAPM specifies that the required return on an investment

depends on (1) the return an investor may earn on a risk-free asset

and (2) a risk premium. This is important in performance

measurement because all three approaches measure whether the

portfolio is achieving the risk premium anticipated.

Return to question.

37. Answer each of the following questions on the Jensen performance index.

a. What information does the Jensen index provide about a specific investment or portfolio?

The Jensen performance index determines by how much the

realized return differs from the return required by the CAPM.

Return to question.

b. The Jensen equation can be expressed as follows:

( )[ ]β−+−= fmfp RRRRa

Why is this form of the equation useful in performance evaluation?

This form of the equation is useful because it measures alpha,

which is the difference between the realized return and the risk-

adjusted required return. A portfolio manager’s performance can

be judged relative to the security market line. The numerical value

of a in the equation indicates a superior or inferior performance.


The absolute numerical values of alpha allow for the ranking of

relative performance, with higher scores indicating better

performances.

Return to question.

c. What does a positive alpha indicate about a portfolio manager’s performance? What does a negative alpha indicate?

A positive alpha indicates that a portfolio manager consistently

does better than the CAPM projections (i.e., the manager

outperformed the market on a risk-adjusted basis). If the

performance is inferior, the alpha is negative. A zero alpha means

that the performance matches the market on a risk-adjusted basis.

Return to question.

d. The Jensen index measures the risk premium in terms of beta. On what assumption is this risk measure based?

Measuring the risk premium in terms of beta is based on an

assumption that the portfolio is well diversified. (A well-diversified

portfolio’s total risk is primarily its systematic risk.) If a portfolio were

not sufficiently diversified, the portfolio’s risk would include both

unsystematic and systematic risk, and the standard deviation of the

portfolio’s returns would be a more appropriate measure of risk.

Return to question.

38. Answer each of the following questions on the Treynor performance index.

a. What limitations are associated with the Treynor index?

The Treynor index does not indicate whether a given portfolio

manager outperformed or underperformed the market. Also, as

with the Jensen index, the Treynor index assumes that the

portfolio is part of a fully diversified portfolio.

Return to question.

b. How can these limitations be overcome?

The Treynor index can be computed for the market to determine

whether the portfolio manager outperformed the market. If the


portfolio in question is not a part of a diversified portfolio

containing other asset classes, then the Sharpe index can be

used instead of the Treynor index.

Return to question.

39. Answer each of the following questions on the Sharpe performance index.

a. In what one way does the Sharpe index formula differ from the Treynor index formula?

The Sharpe performance index formula uses the standard deviation

of the portfolio rather than its beta in the denominator of the equation.

Return to question.

b. Of what significance is this difference?

The significance is that the Sharpe index does not assume that

the portfolio is well diversified.

Return to question.

c. The Sharpe index has a limitation that is the same as a limitation of the Treynor index. What is this limitation, and how is it overcome?

Both the Sharpe and Treynor indexes do not indicate whether a

given portfolio manager outperformed or underperformed the

market. The limitation is overcome by computing the Sharpe index

for the market and comparing the Sharpe index of the portfolio to

that of the market.

Return to question.

40. Is one of the three performance indexes (Jensen, Sharpe, or Treynor) better than the others?

Whether an index is preferred by an investor depends on the

investments being evaluated. The Sharpe performance index

encompasses total risk, and it would seem to be more appropriate if

an investor’s total portfolio is not well diversified. If an investor is

concerned with evaluating the performance of a mutual fund, for

example, and the fund represents the investor’s total risk, the Sharpe

index would be preferred. If the goal is to evaluate how the portfolio

performed relative to the market (alpha) and/or to other portfolios, the

Jensen index would be used. If the investor’s entire portfolio is well


diversified, then the Treynor index would be appropriate.

Return to question.



41. Your client has found a mutual fund that she likes. Performance and risk characteristics of the fund and the market are as shown in the following table. Compute the Treynor index for the fund and for the market, and determine if the fund outperformed the market.

Characteristic Client Fund Market

Excess return (portfolio return minus risk-free rate)

13% 11%

Beta 1.4 1.0

R-squared with market 88% N/A

Treynor index 9.29 11.00

The client’s fund did not outperform the market. The Treynor index for

the market is greater than that same index for the fund.

29941

13.

.

rrT fp

f ==β−

= 001101

11.

.

rrT

fpm ==

β−

=

Return to question.

42. Using both the Sharpe and Treynor performance indexes, indicate which of the two funds shown in the following table has the best risk-adjusted performance. (The risk-free rate is 6%.)

a. Assume that the R2 for Fund A is 85% and that it is 89% for Fund B.

Fund A Fund B

Return 18% 16%

Beta 1.3 1.1



Fund A has the best risk-adjusted performance as computed by

both the Sharpe and Treynor indexes. The Treynor index can be

used because both funds have a high R2 (greater than 70%).

Return to question.

23931

12.

.

rrT fp

a ==β−

= 09911

10.

.

rrT

fpb ==

β−

=

5024

12.

rrS

a

fpa ==

σ−

= 3330

10.

rrS

b

fpb ==

σ−

=

b. Assume that the R2 for Fund A is 46% and that it is 89% for Fund B. What impact does Fund A’s lower R2 have on the calculations?

The Treynor index cannot be used because the Fund A beta may

be unreliable due to the low R2. Therefore the only index that can

be used in this case is the Sharpe index. Fund A has the best risk-

adjusted performance if the Sharpe index is used.

Return to question.

43. Your client wants you to analyze the funds in the following table based on the information given. Use all three performance evaluation methods. (The risk-free rate is 6%.)

Fund X Fund Y Market Index

Realized return 17% 20% 18%

Beta .72 1.2 1.0

Standard deviation 9 16 15

R2 with market 87 81 N/A

Fund X has better performance statistics than either Fund Y or the

market. Its Sharpe and Treynor indexes are the highest of the three,

and it has a positive alpha.

Return to question.


Fund X Fund Y Market Index

Sharpe 1.22 .88 .80 Treynor 15.28 11.67 12.00 Jensen (alpha) +2.36 –.40 0.00

2219

11.

rrS

x

fpx ==

σ−

= 281572

11.

.

rrT

fpx ==

β−

=

8816

14.

rrS

y

fpy ==

σ−

= 671121

14.

.

rrT

fpy ==

β−

=

8015

12.

rrS

m

fpm ==

σ−

= 001201

12.

.

rrT

fpm ==

β−

=

[ ] 362641417 ..)rr(rra fmfpx +=−=β−+−=

[ ] 40042020 ..)rr(rra fmfpy −=−=β−+−=


44. List the four attributes that preferred indexes should have.

a. relevant and appropriate

b. comprehensive and broad-based

c. investable and capable of being replicated

d. value-weighted (capitalization weighted)

Return to question.


45. The S&P 500 Average and the Dow Jones Industrial Average are the two most popular averages reported in the financial press and on financial programs on radio and television. Why might the returns on these averages be inappropriate for measuring the performance of an investment portfolio?

These two indexes are most appropriate for measuring the returns of

the large-cap asset class, but they are not appropriate for measuring

the return of a portfolio that may consist of many additional asset

classes. The other asset classes generally will have performance

characteristics that are different from those of large-cap stocks, even if

stocks, in general, are trending in the same direction. Some classes,

such as real estate, foreign securities, and bonds, may be in a totally

different cycle than that of U.S. large-cap stocks. Each asset class

should be measured against an index that is appropriate for that class.

The entire portfolio should be measured on the basis of a weighted

average of the returns for each class. The Dow Jones Industrial

Average is also a price-weighted index; value-weighted indexes are

more appropriate, as noted in the comments about preferred indexes in

the “Benchmark Principles” section of the module.

Return to question.

46. Using Table 6 in this module, list the six asset classes in order of decreasing risk (highest risk first), and note any exceptions to the usual risk/return trade-off.

From highest risk to lowest risk, based on standard deviation, the six

asset classes are as follows:

Small-cap stocks

Large-cap stocks

Long-term government bonds

Aaa corporate bonds

Intermediate-term government bonds

U.S. Treasury bills

Note that, based on standard deviation, long-term government bonds are more risky than Aaa corporate bonds. Yet most investors consider


corporate bonds more risky than government bonds because they have some degree of credit risk. Return to question.

Return to question.

47. How should historical returns be used in investment planning?

Historical returns may help determine what rates of return are reasonable for use in projecting future returns. Straight-line projections of historical returns into the future can result in unrealistic expectations about future returns. Frequently, asset classes that outperform the historical average in one time period underperform the historical average in the subsequent time period. Return to question.

48. Explain how the Dow Jones Industrial Average (DJIA) differs from each of the following indexes.

a. Standard & Poor’s 500 Index (S&P 500)

The DJIA is a simple average (price-weighted), while the S&P 500 is a value-weighted index. In a price-weighted indicator, the market value of stock is based on the value of one share, regardless of the number of shares outstanding; in a value-weighted index, stocks with higher prices and more shares outstanding have a greater impact on the index’s value. The DJIA includes only the prices of 30 industrial companies; the S&P 500 has a broad base of 500 stocks that reflect broad sectors of the market, including smaller capitalization stocks as well as blue chips. The DJIA is an absolute number; the S&P 500 is expressed as an index relative to a base year. Return to question.

b. NYSE Composite Index

The DJIA differs from the NYSE Composite Index in the following ways: DJIA is a price-weighted (simple average) indicator, while NYSE is a value-weighted index; there are 30 DJIA industrial stocks versus all the stocks listed on the NYSE; DJIA is an absolute number versus NYSE being an index. Return to question.


c. Value Line Index

The DJIA differs from the Value Line Index in the following ways: DJIA is a price-weighted (simple average) indicator, while Value Line is a geometric average; there are 30 DJIA industrial stocks versus 1,700 stocks representing the NYSE, the American Stock Exchange, and the over-the-counter (OTC) market in the Value Line index. Return to question.

49. What observations can you make about inflation and various asset classes using the data shown in Table 6 (Summary Statistics of Annual Total Returns)?

With long-term inflation at 3.0%, the 3.6% yield on U.S. Treasury bills does not keep the investor much ahead of inflation. U.S. Treasury bonds provide a higher return of almost twice the inflation rate. However, in order to provide substantially better returns than the inflation rate, investing in stocks would have been necessary. The highest return was in small-cap stocks with an 11.9% return; around 9% greater than the inflation rate. The standard deviation, however, on small-cap stocks is 32.5%, about 60% greater than that of large-cap stocks. Large-cap stocks had a return of 9.8%, nearly 7% greater than the inflation rate. Return to question.




50. Assume that you have another fund to recommend to the client in Question 41. Over the same period as the period of the fund that the client likes, the new fund’s excess return was 12% and its beta was 0.95. Would you recommend that your client purchase the fund you like or purchase a market index fund?

631295

12.

.

rrT fp

f ==β−

=


Your fund’s Treynor index exceeds the Treynor indexes of the client’s

fund and the market. You should recommend that the client purchase

your fund instead of an index fund because your fund’s performance,

as measured by the Treynor index, is superior.

Return to question.

51. You have narrowed your choices down to the following three funds.

Fund A Fund B Fund C

Sharpe 0.23 0.55 0.69

Treynor 0.44 0.67 0.51

Jensen (alpha) 1.24 0.96 –0.23

Beta 0.92 0.97 1.02

R-squared 87 82 93

a. Which fund would you choose and why?

Since R-squared is given, this should be looked at first to

determine whether beta is a reliable number. Since the R-

squareds are 70 or higher we can use beta and any formulas that

use beta. This means we can use alpha, which is our first choice

since it is an absolute measure of return. Fund A has the highest

alpha, so we would choose Fund A. If the alphas had not been

given we could then use Treynor, and the fund with the highest

Treynor ratio is Fund B.

Return to question.

b. If the R-squared for all three funds was below 70, what fund would you then choose and why?

If the R-squareds were below 70, that would mean that the betas

given are not reliable, and so formulas using beta would also not

be reliable. This would mean that alpha and Treynor cannot be

used, which leaves Sharpe. The fund with the highest Sharpe ratio

is Fund C, so this is the fund that should be chosen.

Return to question.

52. In the past, Grant Walker, age 37, has invested in individual stocks without much success. He wants to take a moderate risk and hopes to have a


moderate return that is above that of CDs. He is considering the following two funds.

Mutual Fund 1 Mutual Fund 2

Type of fund International S&P 500 index


Five-year compound appreciation

18.4% 12.2%

Beta (S&P 500 index) 1.14 1.00


R2 with S&P 500 37% 99%

Which one of the two funds is most appropriate for Grant to invest in at this time?

Fund 2 is more appropriate because Grant wants to achieve a

moderate return with moderate risk. This fund has a lower standard

deviation than fund 1. International funds tend to be very unstable,

whereas index funds generate predictable returns with predictable

risk. The beta of fund 1 cannot be compared directly to the beta of

fund 2 because the coefficient of determination of fund 1 is so low with

respect to that of the S&P 500. Therefore, standard deviation is a

better measure of relative risk of the two funds. Dividing the standard

deviation by the total return to determine the coefficient of variation

yields a CV for fund 1 of 1.31 (26/19.8) and a CV for fund 2 of 1.24

(18/14.5). Select the fund with the lowest CV. Note that the total return

for each fund includes the dividend (current yield). This must be

added to the five-year appreciation to arrive at the figure for the

denominator.

Return to question.

53. Should most portfolios be measured against just one benchmark? Why or why not?

Most portfolios should be measured against a blended, and not just

one, benchmark. Unless a portfolio is composed of just one asset

class (such as entirely in U.S. large-cap stocks) then comparing a


portfolio comprised of various asset classes against a benchmark

representing just one class does not make sense. The percentages

should be weighted so that the benchmark percentage used matches

the percentage found in the client’s portfolio. For example, if a client’s

portfolio is composed of 25% in U.S. large-cap stocks, then only 25%

of the benchmark being constructed for comparison purposes should

be represented by the S&P 500.

Return to question.

About the Author 127 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

About the Author Jason G. Hovde, CIMA®, CFP®, APMA® is the Senior

Director of Certification and Designation Programs as well

as an Associate Professor of Investments at the College for

Financial Planning. Prior to joining the College, Jason had a

financial planning/investment advisory practice and was a

branch manager for one of the largest independent broker-

dealers in the country. Additionally, he spent several years

with another independent broker-dealer, first as a trader and options principal,

and then as a member of the senior management team. Jason holds two

bachelor’s degrees, one in accounting and the other in behavioral science from

Metropolitan State University of Denver, as well as an MBA in finance and

accounting from Regis University. You can contact Jason at

[email protected].


References BIRR Portfolio Analysis Inc. <www.birr.com> (December 2006).

Boone, Norman M., and Linda S. Lubitz. Creating an Investment Policy

Statement: San Francisco: FPA Press, 2004.

Dalton, Michael A., James Dalton, Randal R. Cangelosi, et al. Personal

Financial Planning, Theory and Practice. Kaplan Publishing, 2005.

Dow Jones & Company Inc. “Dividends Do Matter.” <http://djindexes.com>

(December 2006).

DRIP Advisor. <www.dripcentral.com> (December 2010).

Gitman, Lawrence J., and Michael D. Joehnke. Fundamentals of Investing.

Boston: Pearson, Addison Valley, 2005.

Hammond, Brett, Leo Kamp, Douglas Fore. “What’s Your Risk-Adjusted Return

Ratio?” TIAA-CREF Asset Management Market Monitor. October 2006.

Ibbotson SBBI 2012 Classic Yearbook. Chicago: Morningstar Inc., 2012.

Ibbotson SBBI 2013 Classic Yearbook. Chicago: Morningstar Inc., 2013.

Mayo, Herbert B. Investments: An Introduction, 9th edition. Mason, OH: South-

Western, 2008.

Morningstar, Inc. Principia Pro. Chicago: Morningstar Inc. September 2007,

2008, 2009.

SmartMoney. <www.smartmoney.com> (November 2009).

Wilson, Jack, and Charles Jones. North Carolina State University, 2007.

Index 129 © 1983, 1986, 1989, 1996, 2002–2015, College for Financial Planning, all rights reserved.

Index A master index covering all modules of this course can be found in the Self-Study

Examination book.

Benchmarks, 61

popular, 62

Dividend discount model (DDM), 14

Dividend growth valuation models, 17

calculation, 19

constant growth, 18

non-constant growth, 25

zero growth, 17

Dividends, 5

basics, 6

distribution dates, 7

importance of, 5

reinvestment plans (DRIPs), 10

reverse split, 10

special, 7

stock dividends, 8

stock repurchases, 12

stock split, 9

Equity valuation, 13

Information ratio (IR), 56

Intrinsic value, 13

Investment policy statement (IPS), 38

minimum content areas, 39

purposes of, 39

Jensen index (alpha), 50, 66

Market indexes, 58

asset class benchmarks, 61

benchmark principles, 58

characteristics of, 58

long-term market statistics, 63

Mutual funds, 67

P/B (price-to-book) ratio, 16

P/E ratio, 15

growth-adjusted (PEG), 15

Portfolio performance evaluation

information ratio (IR), 56

Jensen index (alpha), 50

Sharpe index, 52

Treynor index, 55

PSR (price-to-sales ratio), 15

Return

expected return, 13

required return, 13

Risk and return, 64

Risk-adjusted performance, 65

computing, 66

Securities

performance evaluation, 45

Sharpe index, 52, 66

SWOT analysis, 43

Treynor index, 55, 66

Common Stock Valuation & Performance Measurement

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