Capital Asset Pricing & Asset Growth

Capital Asset Pricing Model & Asset Growth

Capital Asset Pricing Model &

Asset Growth

Submitted to

Sir Hidayat Ali Khan

Mam Syeda Faiza Arooj

Presented by

Muhammad Irfan


Contents Capital Asset Pricing Model & Asset Growth .............. 3

Abstract ........................................................................... 4

Introduction: ................................................................... 5

Literature Review: .......................................................... 6

Purpose & Methodology: ............................................... 8

RULE # 1: ...................................................................... 8

RULE # 2: ...................................................................... 8

Findings & interpretation: ............................................. 9

Analysis: ........................................................................ 9

Regression Table: ....................................................... 9

Returns Table: .......................................................... 11

Conclusion: .................................................................... 13

References: .................................................................... 14


Capital Asset Pricing Model

& Asset Growth


Abstract

Recent studies suggest that the conditional CAPM might hold, period-by-period, and that time-

varying betas can explain the failures of the simple, unconditional CAPM. We argue, that

significant betas are affecting the returns of firm. Capital Assets Pricing Model (CAPM) is the

widely tested, accepted and rejected model of asset pricing. In this study we tested the CAPM with

Addition of Asset Growth on Oil & Gass Industry of Pakistan selected from KSE-100 index. After

testing the CAPM with Addition of Asset Growth we suggested that CAPM is may be useful to

forecast the required return but many other factors are there which are important to include and

study. When we assume that all other factors are constant than we calculate the required return but

these results are not 100% accurate may be some important things are miss here. This study

suggested that asset growth have negative impact on required return either excess market return

have positive impact of required return. During (July, 2009 – December, 2103) asset growth in Oil

& Gass Industry Pakistan is not supported, & this affecting on required return negatively which is

caused of less required return.

Key word:

Beta, Required Return, Actual Return, Risk Free Rate, Market Return, Capital Asset Pricing

Model, Asset Growth. Etc.


Introduction:

The unconditional CAPM does not describe the cross section of average stock returns. Most

prominently, the CAPM does not explain why, over the last few years, small stocks outperform

large stocks, why stocks with high returns during the past year continue to outperform those with

low past returns (momentum), or why high asset growth firm can’t perform well than low asset

growth firms. In this paper, our main goal is to understand and clarify the whether a conditional

version of the CAPM might explain these patterns.

CAPM is a model that describes the relationship between risk and expected return and which is

used in the pricing of risky securities. In CAPM investors need to be compensated in two ways

time value of money and risk. The time value of money is represented by the risk-free rate (Rfr)

in the formula and compensates the investors for placing money in any investment over a period

of time. The other half of the formula represents risk and calculates the amount of compensation

the investor needs for taking on additional risk. This is calculated by taking a risk measure (beta)

that compares the returns of the asset to the market over a period of time and to the market premium

(Rm-Rfr). CAPM says that the expected return of a security or a portfolio equals the rate on a risk-

free security plus a risk premium. If this expected return does not meet or beat the required return,

then the investment should not be undertaken. The security market line plots the results of the

CAPM for all different risks (betas). The Capital Asset Pricing Model (CAPM) of William Sharpe

(1964) and john Lintner (1965) marks the birth of asset pricing theory (resulting in a Nobel Prize

for Sharpe in 1990). Four decades later, the CAPM is still widely used in applications, such as

estimating the cost of capital for firms and evaluating the performance of managed portfolios.

Theoretically, it is well known that the CAPM model could be perfect, but actually there are many

other factors which are important to study and need to add in this model. Because, this model is

not 100% perfect to use for calculate the required rate of returns in the basis of Market return (Rm)

and Risk free Rate (Rfr). This is very important to study more factors and add them if any

necessary.

This research explores the asset pricing implications of changes in firm asset levels. Variously

referred to as an “investment effect” and tied to capital investment activity or an “asset growth

effect” and tied more broadly to changes in total assets, the underlying regularity is a negative

correlation between growth in assets and subsequent returns. The return pattern may have a

traditional systematic risk-based explanation- that firms with relatively higher asset growth are

associated with relatively low risk and there is some evidence consistent with this explanation.

However, there is also evidence that this effect may be related to mispricing by investors. Given

the ease of executing a long-short strategy based on asset growth, any mispricing in this effect

would be related to costly arbitrage. In this paper, we provide evidence that the asset growth effect

is closely linked to the existence of arbitrage costs, suggesting that mispricing is an important

determinant of these return patterns.


Literature Review:

Generally agreed that investors demand a higher expected return for investing in risky securities.

Investors predict the risk of securities with the help of different models. CAPM is used by the

investors in finding the risk of the investment and to predict the expected return of the stock

(Jagannathan & Wang, 1993). The CAPM, like any other models is based on certain Assumptions;

(Van Horne, 2006). Unsystematic risk can be avoided by the portfolio diversification; investors

are to be rewarded for the systematic risk of security which cannot be diversified; higher the

systematic risk higher will be the return investors expect (Lau & Quay, 1974). Beta is the measure

of systematic risk having positive correlation with return. Investors need to be rewarded in two

ways: firstly for time value of money and secondly risk associated with the security. First half of

equation represents risks free return (RFr) that compensates the investors for placing money in any

investment over a period of time. The other half of the formula represents [β (Rm-Rfr)] risk

premium for bearing additional risk. CAPM is the mostly used model for finding the investors

return. Number of studies conducted for testing the validity of the CAMP. This model is based on

certain assumptions like any other model which provided ground for criticism. The assumptions

of CAPM are; Investors hold diversified portfolios, Single period transaction horizon; Investors

can borrow and lend at the risk-free rate; perfect capital market; (Tony Head, 2008). These

assumptions are the weakness of this model.

CAPM is tested in various countries by different authors. In 1974, Lau & quay applied CAPM on

Tokyo stock market and concluded that the Model is applicable to the Tokyo stock market and

gives the accurate results; the investors in stock market were compensated for bearing systematic

risk. The study covered the period of five years (1964-69) with sample size of 100 companies.

Bjorn and hordahl, (1998) in their paper examine the relationship between expected return and

time varying risk on the Swedish stock market covering fourteen years period (1977-90) with the

sample size of 80 firms. Results of CAPM were also compared with the results of traditional

(GARCH) model. They concluded that their results are very different from international evidence

of CAPM, where the traditional CAPM very often is rejected in favour of assets pricing models

that rely on more general measures of risk. The study conducted on the validity of CAPM by

Huang, (2000) covers period of eight years (1986-93) with sample size of 93 firms. It was applied

on the two different sets a high risk and the other was low risk set. He found that the high risk sets

are conflicting with CAPM whereas data from the low-risk set is consistent with CAPM. He

concluded that the results of CAPM are not valid; the return calculated by the model does not

interpret the actual position and could not be relied upon.

There are some findings which support the argument that returns were not just based on the single

risk factor. The study of Scheicher, (2000) covers period of twenty three years on a sample of

twelve companies with 276 observations. The result of the study documents that the result of the

GARCH or other multi risk factor models simply out performs the CAPM results. The research

conducted by Gomez and zapatro, (2003) covering period (1973-98) with sample size of 220 US

securities from S&P 500 index. They use two risk factors one was standardized market systematic

risk factor; and other was active management risk. The interpretation of these results is evidence

of the two Beta model. The same study conducted in UK stock market with sample of 64 securities


gave the results in favour of this model because of the similarities in the market structure of UK

and US. Fraser and Hamelink, (2004) documented that in early researches the findings conclude

that the results of CAPM are accurate and correct but as the time passes the more accurate tools

like APT outperforms the CAPM. Their study covered twenty two years period (1975-96) and the

sample size was 7 sectors. The research conducted on the London stock exchange and results of

CAPM were compared with the conditional GARCH model. The risk and return calculated by the

GARCH model are correct that are negative in nature but when calculated through CAPM the

finding didn’t match the actual situation which is correctly measured by the GARCH model.

The same study conducted in the Australian stock market covering six years period (1988-93) with

sample size of 8 sectors, gave the same results. They concluded that the results of GARCH model

and Arbitrage Pricing Theory (APT) model are same but the findings of the CAPM are different,

hence, decisions taken on the basis of CAPM might be misleading (Groenewold and

Fraser, 1997).

The Asymmetric approach says it focuses on the single equation specification or single Beta which

was corrected and explained in the research of the Quo and Perron, (2005). They conducted

research covering period of twenty seven years (1978-2004) with the sample size of 50 securities

on US stock market and concluded that the CAPM only identify single equation factor which leads

to the wrong estimation of the results. The literature also contains some of the researches that show

CAPM takes into account two important features found in most time series, namely, nonlinearity

and structural instability (asymmetry). The research conducted by hung and Wu, (2005) covering

81 years (1924-2004).

Another study conducted by Grigoris and Stavros, (2006) on Greek stock market covering five

years period (1998-2000) with sample size of 100 securities listed on Athens Stock Exchange. The

main finding of this study does not support basic statement like high risk and high level of return.

They documented that CAPM provides better results for some years but overall it did not support

the model. Hui and Christopher, (2008) conducted a study, covering eleven years (1996-2006)

with sample size of 95 companies in United States and Japan institutional frame work, shows that

CAPM fails to explain the exact return when applied to Japan and US stock markets. It

significantly gives negative return which occurs as a result of the volatility. Volatility does

influence stock returns. However, the volatility of the Japan and US stock prices predicts the time

series of stock returns and is priced in the cross-section of stock returns. The returns calculated

using the rates eventually give returns which do not show the accurate results on a particular time

series.

In Pakistan a study conducted by Eatzaz and Attiya, (2008) on Karachi stock market with the

sample size of 49 stocks covering period of twelve years (1993-2004). They applied CAPM and

matched their results with the conditional multi risk factors model taking macroeconomic factors

as an evidence of the risk. They concluded that the traditional CAPM performs well in explaining

the risk and return relationship but the results are only convincing for few stocks and only for few

years. They supported conditional multifactor model over the traditional single factor model for

decision making. The exploration power of the CAPM is low because it is using market return for


the calculation of returns and only single Beta for the decision making and compensation for the

risk. According to Raei and Mohammadi, (2008), covering twelve years period (1994-2005) with

sample size of 70 companies from NASDAQ concluded that CAPM is used for pricing, calculating

cost of capital. However, estimation methods frequently have been changed. CAPM model always

give way to very low return values. The low clarifying power of the CAPM is due to the

economical specification, which uses market returns as the only independent variable, it neglects

other variables that are used in different estimation models (e.g. APT) for giving accurate results.

The results generated by Shafer and Vovk’s (2008), covering six years period(2000-2005) with a

sample size of 50 companies, also gives the same results when applied in actual practice the

conclusion of their research also say that the CAPM is using single independent variable which

could not be used for estimating return. CAPM relies on single measure of risk (Beta) and ignores

the other factors contributing in risk of a security. The basic risk return relationship is not rejected.

Model retains its place in literature and can be a helping hand to investors with certain

modifications especially inclusion of more risk factors as suggested in APT.

Purpose & Methodology:

The research problem is “Dose CAPM with Addition of Asset Growth provides accurate results

when applied to Karachi Stock market and assist the investors in pricing the securities”? The

purpose of the research is addition new factor in CAPM and validation of Capital Asset Pricing

Model. The important area of the research is to focus upon the calculation of Beta of Oil and Gass

Industry during July, 2009 to December, 2013 and also calculating the Asset Growth of Industry

to Estimate the required returns to compare with actual returns in order to form an opinion about

the validity of CAPM. The data collected from Karachi Stock Exchange website related to Oil and

Gass Industry of Pakistan. We made 2 rules to check the validity of CAPM after addition of Asset

Growth.

RULE # 1: After taken the data of each company from Karachi Stocks Exchange website

calculating the Returns (Ri) of each company and also calculate the market return (Rm), after

calculating of returns take risk free rate (Rfr) from T Bills and make an equation and draw an

regression equation to calculate the Beta, the Equation is drawn as it:

Ri = Rfr + β (Rm – Rfr)

This is the actual equation of CAPM, this equation calculate the Required Rate of Return of

Organization as well as Industry. This is useful if you ignore all other factors, or you assume all

other factors are constant.

RULE # 2: This rule is about adding asset growth (AG) in the equation of CAPM to calculate the

required rate of return of an Industry or a Firm. After adding this new factor in CAPM we also

check the impact of Asset growth (AG) on Expected return. After addition of Asset Growth (AG)

the CAPM equation changed and have a new shape that is:

Ri = Rfr + β1 (Rm – Rfr) + β2 (AG)


This equation give us the new required rate of return of an Industry or a firm. This equation is

called multivariate equation that provide us the results. We apply this equation on Oil & Gass

Industry of Pakistan to calculate the required rate of return and compare them with actual returns.

After using this equation we get results and calculate the required returns. These returns help us to

take decision related to investment.

In this Equation we use some symbols these are:

Ri: Required rate on security,

Rfr: is Risk free rate of return,

β: is Beta of Security of i

Rm: is market return of portfolio.

& AG: is Asset Growth,

These are symbols used in equation to determine the required return.

Findings & interpretation:

Regression Analysis suggested that for the period of July 2009 to December 2013 of Oil & Gass

Industry Pakistan have a positive and highly significant R square that is 0.772758027 which shows

that in this period Oil & Gass Industry of Pakistan is significant to invest and have positive returns

in each period. This figure shows the industry significant level and inform the investors to returns.

We used 2 independent variables and 1 dependent variable. Independent variables are (Excess

Market Return and Asset growth) & Dependent variable is (Required return).

Excess market return have positive beta that is 1.118656717 this figure shows that excess market

return have positive impact on required return and that is caused of increasing the required return

of a firm or as well as Industry. That’s why this variable is more important in calculate the required

return. Even Asset Growth have negative beta that is -0.274172063 this figure shows that asset

growth have negative relation with required return and this factor is not important to study and

take as a main variable to calculate the required return of a firm or an Industry.

The t values of Excess market return and asset growth shows the significant level of both variables

both have different figure these are:

Excess market return have 12.54206161 t test value this figure shows that this variable is significant

to estimate the required return of a firm and another side asset growth have -0.424410925 t test

value this figure shows that asset growth is not significant to estimation of required return these

figure taken from the excel sheet that have data of Oil & Gass Industry of Pakistan during July,

2009 to December, 2013 and after applying the regression test we get the results in sense of these

figure which are mentioned above.

Analysis:

Regression Table:


SUMMARY OUTPUT

Regression Statistics

Multiple R 0.879066566

R Square 0.772758027

Adjusted R Square 0.763846577

Standard Error 0.034670564

Observations 54

ANOVA

df SS MS F Significance

F

Regression 2 0.208471625 0.104235813 86.71518491 3.89456E-17

Residual 51 0.061304447 0.001202048

Total 53 0.269776072

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 0.002956671 0.010842513 0.272692406 0.786190791 -

0.018810583 0.024723925 -

0.018810583 0.024723925

X Variable 1 1.118656717 0.089192411 12.54206161 3.31645E-17 0.93959548 1.297717955 0.93959548 1.297717955

X Variable 2 -

0.274172063 0.646006139 -

0.424410925 0.673051206 -

1.571083502 1.022739377 -

1.571083502 1.022739377


Asset growth calculated annual basis of each firm and then take an average of all these companies

to run the test in excel and calculate the values of Beta, R Square, & t test etc. after calculating the

average of all firms we divided the figures on 12 to get monthly growth rate. Ri in this paper used

is average Ri of all firms.

Required return and actual return is shown in table which is given below:

Returns Table:

Month Actual Return Rm Rfr Asset Growth

Beta 1 Beta 2 Required Returns

Jul-09 0.089197808 0.078014 0.113847 0.01159 1.118657 -0.27417 0.07058

Aug-09 0.118217851 0.123656 0.124425 0.01159 1.118657 -0.27417 0.12039

Sep-09 0.05793786 0.07769 0.125801 0.01159 1.118657 -0.27417 0.06880

Oct-09 -0.114976635 -0.02038 0.12584 0.01159 1.118657 -0.27417 -0.04090

Nov-09 0.027311748 0.005135 0.12437 0.01159 1.118657 -0.27417 -0.01219

Dec-09 -0.000348687 0.019629 0.121569 0.01159 1.118657 -0.27417 0.00436

Jan-10 0.00878856 0.024211 0.119627 0.018037 1.118657 -0.27417 0.00794

Feb-10 -0.010244211 0.004535 0.121173 0.018037 1.118657 -0.27417 -0.01425

Mar-10 0.039133635 0.053909 0.123178 0.018037 1.118657 -0.27417 0.04074

Apr-10 -7.44243E-05 0.024531 0.122515 0.018037 1.118657 -0.27417 0.00796

May-10 -0.115100735 -0.10565 0.121108 0.018037 1.118657 -0.27417 -0.13750

Jun-10 0.004691796 0.042405 0.122189 0.018037 1.118657 -0.27417 0.02799

Jul-10 0.094773111 0.081991 0.123253 0.018037 1.118657 -0.27417 0.07215

Aug-10 -0.082655308 -0.06711 0.126502 0.018037 1.118657 -0.27417 -0.09503

Sep-10 -0.000292036 0.020408 0.127563 0.018037 1.118657 -0.27417 0.00275

Oct-10 0.047204991 0.058431 0.130752 0.018037 1.118657 -0.27417 0.04490

Nov-10 0.123622392 0.060043 0.131466 0.018037 1.118657 -0.27417 0.04662

Dec-10 0.031591772 0.070113 0.133887 0.018037 1.118657 -0.27417 0.05760

Jan-11 0.052697522 0.028023 0.135575 0.014522 1.118657 -0.27417 0.01128

Feb-11 -0.121454472 -0.08658 0.136651 0.014522 1.118657 -0.27417 -0.11705

Mar-11 0.07404061 0.046089 0.136269 0.014522 1.118657 -0.27417 0.03141

Apr-11 0.025110911 0.021 0.13633 0.014522 1.118657 -0.27417 0.00333

May-11 0.027755899 0.005441 0.134975 0.014522 1.118657 -0.27417 -0.01391

Jun-11 -0.014771676 0.030758 0.136976 0.014522 1.118657 -0.27417 0.01417

Jul-11 -0.00857398 -0.02446 0.137515 0.014522 1.118657 -0.27417 -0.04766

Aug-11 -0.069553799 -0.09186 0.132631 0.014522 1.118657 -0.27417 -0.12248

Sep-11 0.061480954 0.062453 0.132369 0.014522 1.118657 -0.27417 0.05018

Oct-11 -0.023132257 0.009089 0.123201 0.014522 1.118657 -0.27417 -0.00843

Nov-11 -0.031231563 -0.02831 0.117534 0.014522 1.118657 -0.27417 -0.04960

Dec-11 -0.049054378 -0.01606 0.117534 0.014522 1.118657 -0.27417 -0.03589

Jan-12 0.061059691 0.046462 0.117038 0.018964 1.118657 -0.27417 0.03289

Feb-12 0.028272652 0.084463 0.117896 0.018964 1.118657 -0.27417 0.07530


Mar-12 -0.001709493 0.068636 0.118679 0.018964 1.118657 -0.27417 0.05750

Apr-12 -0.028618461 0.016613 0.119347 0.018964 1.118657 -0.27417 -0.00078

May-12 0.003148967 -0.01456 0.119415 0.018964 1.118657 -0.27417 -0.03566

Jun-12 -0.022385819 0.001073 0.119393 0.018964 1.118657 -0.27417 -0.01817

Jul-12 0.024855785 0.056196 0.118795 0.018964 1.118657 -0.27417 0.04357

Aug-12 0.065055446 0.055881 0.109604 0.018964 1.118657 -0.27417 0.04431

Sep-12 -0.044239647 0.003459 0.102544 0.018964 1.118657 -0.27417 -0.01350

Oct-12 0.010119975 0.030126 0.095375 0.018964 1.118657 -0.27417 0.01718

Nov-12 0.028844219 0.041719 0.092723 0.018964 1.118657 -0.27417 0.03047

Dec-12 0.006627017 0.02 0.09284 0.018964 1.118657 -0.27417 0.00616

Jan-13 -0.00530276 0.019959 0.091685 -0.00101 1.118657 -0.27417 0.01173

Feb-13 0.052196633 0.05399 0.092436 -0.00101 1.118657 -0.27417 0.04971

Mar-13 -0.020906693 -0.00717 0.094115 -0.00101 1.118657 -0.27417 -0.01891

Apr-13 0.009243598 0.052048 0.094235 -0.00101 1.118657 -0.27417 0.04732

May-13 0.200298011 0.149645 0.093727 -0.00101 1.118657 -0.27417 0.15656

Jun-13 -0.037356969 -0.03745 0.090718 -0.00101 1.118657 -0.27417 -0.05238

Jul-13 0.179010097 0.109832 0.089521 -0.00101 1.118657 -0.27417 0.11252

Aug-13 -0.062015603 -0.04941 0.089863 -0.00101 1.118657 -0.27417 -0.06566

Sep-13 -0.142385295 -0.01481 0.0945 -0.00101 1.118657 -0.27417 -0.02750

Oct-13 0.038816656 0.0432 0.09457 -0.00101 1.118657 -0.27417 0.03738

Nov-13 0.10662957 0.067016 0.09464 -0.00101 1.118657 -0.27417 0.06402

Dec-13 0.043185002 0.039459 0.099791 -0.00101 1.118657 -0.27417 0.03258


Conclusion:

The study examine that the CAPM model is not completed and there is a need of addition other

factors which are important and affecting the returns of firm, like Size of an firm and value of an

firm etc. The application of the CAPM with addition of asset growth on Oil & Gass Industry of

Pakistan to form an opinion about its validity and reliable application in local institutional

framework. For the analysis of Pakistan Oil and Gass Industry is selected from KSE-100 index

covering 4 and half year period (July, 2009 – December, 2013). After comparing the results that

we calculated and get from the CAPM equation we seen that the actual returns are higher than the

required returns. This equation is not perfect to forecast the future on the basis of CAPM because

there are many other variables which affect the required returns and have positive impact on it.

Our factor asset growth is not powerful to change in required return and it is less important than

excess market return.

Asset growth have negative impact on required return this is not factor that is reason of increase

in required return. May be other research take it good and seen that this is helpful in increasing in

required return but as per this study asset growth during (July, 2009 – December, 2013) is not

perform better as per our expectations.


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Capital Asset Pricing & Asset Growth

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