Multistyle Rotation StrategiesThe benefits are considerable.

Parvez Ahmed, Larry J. Lockwood, and Sudhir Nanda

PARVEZ AHMED is an assis-

tant professor of finance atThe Pennsylvania State Uni-versity ' Harrisburg in Mid-dletown (PA 17057).psal3@psu.edu

LARRY J. LOCKWOOD is the

C.R. Williams professor offinancial services at TexasChnstian University in FortWorth {TX7612y).l.lockwood@tcu.edu

SUDHIR NANDA is an analyst

at T. Rovv'e Price in Balti-more (MD 21202).snanda@troweprice.coni

Since the inid-1980s, many institutional investorshave pursued focused investment strategies v«thspecific market capitalization and growth require-ments. In 1987, Wilshire Asset Management

introduced its equity style indexes, investment accountswere soon designed specifically to capture performancedifferentials across market capitalization and growthdimensions.

Differences in performance have been especiallydramatic in recent years. For example, the Wilshire LargeCompany Growth Index returned 42% in 1998, 36% iti1999, and -25% in 2000. This is a stark contrast with theWilshire Small Company Value Index, which returnedin those years -7%, - 1 % , and 23%.

We show how terminal wealth improves by formingportfolios based on multiple investment styles. Multifactormodels for portfolio fortnation have become increasinglyimportant as evidenced in Christopherson [1995J, Trzcinka[1995]. Christopherson and WiUiams [1997], Gallo andLockwood [1997], Fabozzi [1998], Jones [1998], and Maand Mallet [1998], among others. Bernstein [1995] andCoggin, Fabozzi, and Arnott [1997] provide excellentgeneral discussions of equity style investing. -

The results of our tests show that performance rank-ings of stocks classified by market capitalization and growthfactors change significantly over titne. This lack of per-formance consistency might lead investors to dismiss theitnportance of style classification, but we sbow that thereare benefits to conditioning portfolios on multiple factors.

We also show that astute investors can irnprove port-

2{M)2 THE JOURNAL OF PORTFOUO MANAGEMENT 17

EXHIBIT 1MARKET CAPITALIZATION AND E/P PREMIUMS

Differences in returns between small versus large (S-L) and between higheamin^i-lo-pri(e (value) versus low eamings-to-price (growth)firms (V-C).

folio pertormance significantly by incorporating style shiftsinto their asset allocation strategies. Active asset allocationstrategies that exploit the variability of multistyle premiunxsare far superior to passive and active strategies that investin stocks of a single investment style.

HISTORICAL PERSPECTIVE

It was not that long ago that small-cap value invest-ing was all the rage. For instance, the geometric meanannual returns over 1967-1983 were 8.7% for large firmsand 15.U% for small firms. Many studies examined thesmall-firm effect (see Basu [1977). Banz [1981], Rein-ganum [1982], and Keim [1983]), and funds were formedto exploit the small-firm premium. Then, over the next

17-year period 1984-2000, large firms dominated—thegeometric mean annual returns were 16.0% for Iargefirms and 11.8% for small firms.'

Consider the dramatic difference in performancebetv 'een value and growth firms illustrated in Exhibit 1.While there are various ways to classify value and growthfirms, we define value firms as firms with earnings-to-priceratios above the median; growth firms have E/P ratiosbelow the median. For early studies of the E/P effect, seeBasu [1977, 1983] and Cook and RozefT [1984). Inter-national evidence of value effects is provided by Capaul,Rowley, and Sharpe [1993], Arshanapalli, Coggin, andDoukas [1998], and Fama and French [1998].

As demonstrated in Exhibit 1, high E/P (value) firmsoutperformed low E/P (growth) firms in 12 of the 16 years.The mean difference is above 4% per year in favor ofvalue stocks. On a cumulative basis over 1981-1997, largeoutperformed small by approximately 20%, and valuetrounced growth by a whopping 95% {see Exhibit 2).

Haugen [1997] provides a behavioral explanation,consistent with the value effect, in which investors over-react to recent news, both good and bad.- Thus, firms withrecent negative abnormal profits (value stocks) tend tobecome underpriced now, and firms with recent positiveabnormal profits (growth stocks) tend to become over-priced now. As subsequent abnormal profits for the twogroups merge, the previously defined growth stocks willlag the value stocks.

Haugen also contends that stocks with undiscoveredabnormal profit selling at reasonable prices (growth at areasonable price, or GARP) can be expected to outper-form. Ahmed and Nanda [2001] perform tests showingthat GARP stocks, defined as stocks of firms with high

EXHIBIT 2TERMINAL WEALTH FROM $1 INVESTMENT IN SINGLE-STYLE STRATEGIES—1981-1997

14

12.30

Year

18 MULTISTYLE ROTATION STRATEGIES SPRING 2002

EXHIBIT 3 -ANISnJAL RETURNS TO SMALL GROWTH, LARGE GROWTH, SMALL VALUE,AND LARGE VALUE PORTFOLIOS—1981-1997

Year1981-19821982-1983

1983-19841984-1985

1985-1986

1986-1987

1987-1988

1988-1989

1989-1990

1990-1991

1991-1992

1992-19931993-1994

1994-1995

1995-1996

1996-1997

AverageExcl. January

Cumulative

SmallGrowth-23.0 (4)103.7(1)

-21.0(4)

12.0(4)

24.6(4)

7.4 (4)

-7.7(4)

10.4(4)

7.6 (2)

-0.6 (4)

7.2 (4)26.0(1)

5.1 (2)26.9(1)

26.0(1)

10,9(4)

13.5(4)9.8 (4)

429 (4)

SmallValue-5.0(1)94.7 (2)

-3,1 (2)29.2 (2)

38.0(1)

13.8(3)0.4(1)

17.6(2)

4.6 (4)

3.5 (3)

15.1 (2)25.4 (2)

7.6(1)14.7 (4)

22,0 (2)21.3(2)

18.7(1)15.0(2)

1126(1)

LargeGrowth-20.7 (3)73.3 (3)

-14.7(3)

20.6 (3)

35.3 (3)

24,2(1)

-5.5 (3)

15.9(3)

20.3(1)

7.9 (2)9.2 (3)

14.7 (4)

0.5 (3)

26.8 (2)

20.9 (3)15.8(3)

15.3(3)13.1 (3)

674 (3)

LargeValue-7.3 (2)62.0 (4)

-1,5(1)

37.0(1)

37.1 (2)

21.7(2)

0.0 (2)

18.8(1)

7.2 (3)9.0(1)

15.7(1)

20.8 (3)

-0.8 (4)

24.3 (3)

20.3 (4)

24.7(1)

18.1 (2)15.3(1)

1116(2)

Value-Growth

15.73-10.12

15.56

16.79

7.66

1.87

6.78

5.08

-8.00

2.59

7.21

2.79

0.62

-7.32

-2.30

9.63

4.03

Small-Large-0.0431.52

-3.93

-8.22

-4.91

-12.36

-0.86

-3.35

-7.67

-7.03

-1.247.96

6.51

-4.75

3.39

-4.16

-0.57

Numbers in parentheses refer to investment style ranking. Final two columns report the differences in retum between value and growth stocks and between smalland lar;ge stocks.

earnings growth but with reasonable price-to-earningsratios, outperform other classes of stocks.

Additional insight is gained by analyzing returns forportfolios conditioned on multiple factors. We compute12-month returns to small growth, small value, largegrowth, and large value portfolios. These results are pro-vided in Exhibit 3.

Over the entire time period, small value tops all cat-egories, but the rankings are anything but consistent dur-ing the period. The average correlation of consecutive-yearrankings is only 0.11, indicating that only about 1%(R^ = 0.012) of the variability in this years rankingscould have been predicted by last year's rankings. Stellarperformers of the recent past may be laggards in the nearfuture. For example, in 1982-1983, small growth is thetop performer, and large value is the laggard. In 1983-1984, small growth finishes last and large value first.

The data in Exhibit 3 highlight the importance ofconditioning portfolios on multiple factors. In 1985-1986, large beat small, but small value topped all categories.The negative size premium is due mainly to the under-performance of small growth stocks. In 1993-1994, smallvalue outperformed all groups, while large value finished

SPRING 2D02

last, primarily because of a large positive size effect dur-ing the period.

These results raise critical questions about the ben-efits of asset allocation across multiple investment styles.For instance, can the variability in size and growth pre-miums be used to improve portfolio performance? Whatis the probability of target wealth shortfall associated withdifferent single-style and multistyle strategies? How greatis the improvement in performance moving from a sin-gle-style to a multistyle portfolio? How great is the poten-tial improvement in performance of perfect-foresighttactical style portfohos versus constant-niix porttolios?How much of a tactical deviation fix)m the constant mixis required to add significantly to performance?

We attempt to address many of these questions inthis study.

BENEFITS OF SINGLE-STYLEASSET ALLOCATION STRATEGIES

Reinganuni [1999] provides important insights intothe economic benefits of managing market capitalizationexposure. He argues that variability in small-cap premi-

TH£ JOUIUVAL OF PORTFOUO MANAGEME rr 1 9

unis can be used to improve returns. Comparing passivebuy-and-hold and rebalanced fixed-weight strategiesagainst tactical asset allocatioti strategies, he shows thatreturn differentials are highly significant and economicallymeaningful. For example, over 1926-1998, the com-pound atinual return for annually rebalanced portfolios was13% for 65/35 large/small allocation, and 16% for a tac-tical allocation deviating up to 30 percentage points in anygiven year from the 65/35 fixed weights, depending onthe most favorable allocadon for that year. Thus, managerswith superior tactical skills could produce significantly bet-ter pertormance if given the flexibility to shift their mar-ket capitalization exposure.

Levis and Liodakis [1999] examine strategies thatrotate between value and growth styles, and bet^veensmall- and large-cap stocks, in the United Kingdom forthe period 1968-1997. They show that an investor whocould perfectly predict the direction of the size spreadwould have earned an average annual return of 34%,which exceeded the return of the Financial Times AllShares Index by 17 percentage points. A forecasting accu-racy of 60%-70% would be sutficient to outperform thesmall-cap-only buy-and-hold portfolio. In the case ofvalue/growth rotation, perfect foresight would have pro-vided a return of 29%. A value-only buy-and-hold port-folio would have returned 24% (and growth-only returnwas 12%). At least an 80% forecastitig accuracy of thedirection of the spread each month would be required tobeat the value-index portfolio.

Kao atid Shuniaker [1999] develop tactical assetallocation strategies by testing a model to explain therelationships between macroeconomic variables and thesubsequent year's performance of value versus growthstocks. They document tnany significant relationships.Therefore, investors who successfiilly manage their styleexposures according to different market conditions likelywould significantly outperform investors who do notalter style exposures.

BENEFITS OF MULTISTYLEASSET ALLOCATION STRATEGIES

We contend that significant benefits can accrue tomtiltistyle strategies versus single-style strategies. Our objec-tive is to tneasure and examine the benefits of asset alloca-tion across multiple-style portfolios. We examine allnon-financial fimis listed on the New York Stock Exchange,the American Stock Exchange, and the Nasdaq returnfiles usitig the monthly Center for Research in Security

Prices database and the annual Compustat database. To bein the sample, firms must be listed on both CRSP andCompustat sometitiie during the 1979-1997 period.

To ensure that investors would have all the dataneeded to form the portfolios, we require at least a six-month lag fixjm the reporting date of the accounting data.The portfolios are held fi-otiijuly of year t through June ofyear t + 1. For instance, the earnings-to-price (E/P) ratioused to delineate value and growth firtns is calculated byusing the earnings for fiscal year t - 1 and stock price atthe end of December year t - 1 . Size is measured by thetnarket value of equity in June of year t. Only non-nega-tive E/P firms are included in the study. Firms that aredelisted during the year are included for the time periodduritig which they traded.

We first form portfolios on the basis of market cap-italization. In June of each year, firms are classified intomarket capitalization deciles. Market capitalization decilebreakpoints are determined from NYSE and AMEXsecurities (to avoid biasing the decile breakpoints bysmaller firms listed on the Nasdaq). Firms are furtherclassified into E/P deciles within each market capitaliza-tion decile. The E/P decile breakpoints use all the NYSE,AMEX, and Nasdaq firms.

Thus, a total of 100 portfolios are created. Tbesmall growth portfolio in all exhibits consists of stocks clas-sified in the five smallest E/P deciles withiti each of thefive smallest-firm deciles. Small value consists of the fivelargest E/P deciles within each of the five smallest-firtndeciles. Analogous definitions pertain to the large firmstyles.

Simulation Results WithoutAllocation Consideration

For most itwestors, the standard deviation of a port-folio's time series returns is far less important than vari-ability in end-of-period wealth (see Kritzman [1994]).Instead, we assess style risk by examining various per-centiles of terminal wealth from the simulated portfolios{also see Radcliffe [1994]). The results will provide insightinto the probabilities and shortfalls of underperfbrmingspecific terminal wealth targets, lending themselves wellto value at risk analysis.

To simulate termitial wealth for tnultistyle portfo-lios, we randotnly select 5 portfolios fixim the 25 portfo-lios in each style class. This process is repeated 1,000times. The terminal wealth for each multistyle portfolioreported in the exhibits is the arithmetic mean of the ter-

20 MULTISTYLE ROTATION STRATEGIES SPRING 2002

EXHIBIT 4TERMINAL WEALTH FOR MULTISTYLE STRATEGIES—1981-1997

Portfolio Style

Panel A. Multistyle

Small Growth

Small Value

Large Growth

Large Value

MeanTerminalWealth

5.12

12.23

7.6!

12.19

Panel B. Single Style

Growth

Value

Large

Small

6.32

12.30

9.74

8.07

Terminal Wealth

S'"

4.10

9.98

5.66

10.37

5.24

10.82

8.21

6.87

25'"

4.31

10.28

5.98

10.66

5.47

11.10

8.52

7.10

Percentile Values

75'"

5.56

13.23

8.43

13.04

6.74

12.94

10.86

9.04

95'"

6.36

15.33

9.46

14.28

7.47

13.98

1!.15

9.38

EXHIBIT 5TERMINAL WEALTH FROM $1 INVESTMENT IN MULTISTYLE STRATEGIES—1981-1997

14

Year

minal wealth for the five randomly selected portfohos."*Exhibit 4 reports results for the four multistyle port-

folios over the 1981-1997 period. For each style, wereport mean terminal wealth and terminal wealth associ-ated with the 5th, 25th, 75th, and 95th percentiles. Themetric is the terminal wealth fi-om investing $\ in July1981, and rebalancing each July. For comparison, single-style results are reported in the second panel of the exhibit.

Exhibit 5 plots results for multistyle small value,small growth, large value, and large growth strategies.

The small value and large value strategies provide thehighest terminal wealth (S12.23 and $12.19, respecdvely).

The terminal wealth for all firms included in the sampleis S8.91. Thus, the value strategies outperform the indexby approximately 37% on a cumulative basis over thesample period.

It is virtually certain tbat a bigh E/P manager wouldhave outperformed the broad index during the sampleperiod; the 5th percentiles for the high E/P strategies arefar above the index. Without abnormal (stock selection)performance, there is also virtually no chance that a small-cap low E/P manager could have outperformed the broadindex during the sample period {the 95th percentile is$6.36), and there would have been about a 15% chance

Si'RiNC 2002 THE JOURNAL OF PORTFOUO MANAGEMENT 2 1

EXHIBIT 6TERMINAL WEALTH FOR SINGLE-STYLE CONSTANT-WEIGHT STRATEGIES—1981-1997

MeanTerminal

Wealth

A. Market Capitalization StrategiesLarge0.900.100.650.350.550.450.750.25

Small0.100.900.350.650.450.550.250.75

9.598.259.208.699.038.879.368.52

B. Value/Growlh StrategiesValue0.900.100.650.350.550.450.750.25

Growth0.100.900.350.650.450.550.250.75

11.566.799.858.079.238.63

10.517.54

Terminal

5'-

8.227.168.117.718.017.898.187.51

10,255.728.827.068.237.649.406.50

Weallh

25"-

9.077.778.778.308.628.468.888.09

10.946.369.427.678.828.24

10.007.51

PercentMe Values

75*^

10.128.729.649.069.449.239.828.92

12.107.21

10.288.449.619.02

10.977.94

95*

10.899.48

10.249.79

10.069.92

10.469,69

13.037.88

10.929.12

10.269.68

11.728.52

that a large-cap low E/P manager could have outper-formed the broad index during the period.

T.,

Simulation Results withAsset Allocation Consideration

Exhibit 6, Panel A, summarizes terminal wealthresults for a constant-mix allocation for various marketcapitalization strategies. Cumulative terminal wealththrough the sample period is plotted in Exhibit 7.

The constant-mix portfolio rebalances the portfolioeach July to maintain the target mix. We should note thatour results do not include transaction costs or any possi-ble leverage effects. Transaction costs could materiallyaffect the simulation results, especially if individual stocksare used to form the portfolios rather than style index fiinds.

The weights are presented in the first two columns.As expected, portfolios with high allocations to largefirms provided higher terminal wealth during the sampleperiod. The probability of beating the broad index wasnearly 80% using the 90/10 large/small allocation andabout 67% using the 65/35 large/small mix. As evidentthroughout this study, the market capitalization effects wereslight during the sample period.

More dramatic results are presented in Pane! B ofExhibit 6 for constant-mix strategies between high E/P(value) and low E/P (growth) stocks in the portfolio.Exhibit 8 plots the cumulative effects of the variousvalue/growth allocations on terminal wealth.

As expected, during the sample period, a portfoliooverweighting high E/P stocks would have providedhigher terminal wealth. The chance of beating the broadindex with even a moderate 65/35 allocadon is over 90%.

The deviation from equal weighting need not havebeen large. Even a 55/45 allocation had nearly a 70%chance of beating the broad index.

Simulation Results with TacticalAsset Allocation Consideration

More striking differences are observed for tacticalasset allocation. Exhibit 9 reports findings for portfoliosthat allocate to winning/losing sectors. The perfect-fore-sight test is helpful merely to measure the maximum his-torical benefit from tactical asset allocation and to reportthe extent of return contribution from model estimation.^

As explained by Ma and Mallet [1998], the idealempirical approach is to consider only the economic

22 MULTISTYLE ROTATION STRATEGIES SPRING 2002

EXHIBIT 7TERMINAL WEALTH FROM $1 INVESTMENT IN CONST ANT-WEIGHTMARKET CAPITALIZATION STRATEGIES—1981-1997

II

Year

EXHIBIT 8TERMINAL WEALTH FROM $1 INVESTMENT IN CONSTANT-WEIGHT E/P STRATEGIES—1981-1997

Wea

l

12

10

8

6

4

<

982 r n T t w i N O f - - O O O N O —

O C O O O C O O O O O O O O O N O NO* ON ON ^ ^ ON O - CT- CT*

Year

' ^ • N

^ - ^ - ^

r-j mON ONCT- O-

4

y

994

ON OON CT-

/

997

12.30

9.85

8.918.07

6.32

65-35

*—35-65

»—- Index

SPUING 2002 THEJOURNAL OF PORTFOLIO MANAGEMENT 2 3

EXHIBIT 9TERMINAL WEALTH FOR TACTICAL STRATEGIES—1981-1997

Weight inWinningPortfolio

Weightin LosingPortfolio

MeanTerminalWealth

Panel A. Market Capitalization

0.90O.IO0.650.350.550.450.750.25

Panel B. E/P

0.900.100.650.350.550.450.750.25

0.100.900.350.650.450.550.250.75

0.100.900.350.650.450.550.250.75

12.936.12

10.291.119.388.54

11.287.07

14.025.61

10.617.539.488.45

11.876.70

Terminal Wealth

5"-

11.145.299.096.868.307.589.896.19

12.254.779.506.598.437.48

10.585.82

25'"

12.135.769.807.408.958.15

10.706.71

13.225.24

10.167.169.068.07

11.306.34

Percentile Values

75""

13.626.46

10.748.129.788.92

11.837.43

14.745.95

11.087.889.898.81

12.407.03

Panel C. Allocate Across Both Market Capitalization and E/P Sectors

0.900.100.650.350.550.450.750.25

0.100.900.350.650.450.550.250.75

22.957.14

16.0910.3913.9312.0418.578.95

19.366.29

13.939.19

12.1510.6115.937.95

21.286.80

15.159.90

13.2011.4517.388.55

24.397.46

16.9610.8314.6412.5819.649.32

95'"

14.896.99

11.568.70

10.499.52

12.827.93

15.996.58

11.848.50

10.569.47

13.337.65

26.938.0]

18.3611.6015.7713.5221.35

9.98

Trading rules assume perfect foresight.

variables that are suggested by the underlying theorybeing tested (e.g., value and growth variables used toproxy financial distress). While it is usually impossible forex post results not to influence a research design, carefulresearchers will revise the theory when confronted withanomalous empirical results rather than make ad hocchanges to their experiments.

Panel A of Exhibit 9 shows results for an investorwho manages market capitalization weights without regardfor E/P dimensions {also see Exhibit 10). For instance, ter-minal wealth jumped from $9.20 for a 65/35 large/smallconstant-mix portfolio (see Panel A of Exhibit 6) to $10.29for a portfolio that invested 65% in the outperformingmarket capitalization sector, to $12.93 for a portfolio thatinvested 90% in the outperforming market capitalizationsector each year, and to $14.15 for perfect market capi-talization forecasting {abo see Exhibit 10). For less of a devi-

ation from a 65/35 large/small "nornial policy" constantmix, terminal wealth rises from $9.20 to $11.28 for a port-folio that invests 75% in the outperforming market cap-italization sector each year. Therefore, by permitting justa 10 percentage point deviation from the 65/35 constantweights, the manager who correctly forecasts the out-performing market capitalization sector would add morethan $2 to terminal wealth per $1 initial investment overthe sample period.

In Panel B of Exhibit 9, we show results for a port-folio that allocates between high E/P and low E/P stockswithout regard to market capitalization (also see Exhibit 11).Terminal wealth rises from $9.85 using the 65/35 con-stant-mix high/low E/P portfolio {Exhibit 6, Panel B) to$10.61 from investing 65% each year in the outperform-ing sector and to $14.02 from investing 90% in the out-performing E/P sector.

24 MULTISTYLE ROTATION STIIATEGTES 2tK)2

EXHIBIT 10TERMINAL WEALTH FROM SI INVESTMENT IN SINGLE-STYLEMARKET CAPITALIZATION TACTICAL ASSET ALLOCATION STRATEGIES—1981-1997

65-35

35-65

tOO-0

0-100

Index

Year

A 10 percentage point deviation (75/25) from a65/35 high/low "normal policy" constant mix would haveproduced terminal wealth of $11.87, a $2 increase for everySI invested versus the 65/35 constant mix ($9.85). Thisresult matches the findings for the market capitalizationstrategies. For perfect E/P style forecasting, terminalwealth climbs to $15.65 per dollar initial dollar investment{Exhibit 11).

As expected, the most impressive potential improve-ment is observed by rotating across the four multistyleportfolios {small value, small growth, large value, andlarge growth). These results are provided in Panel C ofExhibit 9. Cumulative effects on terminal wealth are plot-ted in Exhibit 12.

Results show that the mean terminal wealth isS22.95 for the portfolio that invests 90% in the best-per-forming of the four portfolios and 10% distributed equallyacross the remaining three portfolios. This allocationimproves on the perfect forecast 90/10 market capital-ization (value/growth) rotation allocation presented inPanel A (Panel B) of Exhibit 9 by approximately 77%(64%). And, it more than doubles the best constant-mix65/35 single-style strategies reported in Exhibit 6.

For a less dramatic tactical allocation assumption, aperfect forecast 75/25 allocation would have provided ter-

minal wealth of $18.57, which beats the perfect forecast75/25 single-style market capitalization (value/growth)rotation strategies by 64%i (56%). For perfect forecasting(100% in the winning style), mean terminal wealth soarsto $26.40 as shown in Exhibit 12.

Overall Benefits

To summarize, for single-style market capitaliza-tion strategies, a $10,000 initial investment would haverisen from $92,000 for a 65/35 large/small "normal pol-icy" mix {Exhibit 6, Panel A)to%\ 12,800 for a 75/25 win-ner/loser allocation {Exhibit 9, Panel A), and to $141,500for perfect forecast allocation {Exhibit 10).

For E/P strategies, a $10,000 initial investment wouldhave risen from $98,500 with a 65/35 high/low E/P nor-mal policy mix {Exhibit 6, Panel B) to $118,700 for a75/25 winner/loser allocation {Exhibit 9, Panel B), and to$156,650 for a perfect forecast allocation {Exhibit 11).

For multistyle strategies, terminal wealth cHmbs to$185,700 for a 75/25 winner/loser allocation {Exhibit 9,Panel C) and soars to $264,000 for perfect forecast allo-cation {Exhibit 12). These results demonstrate that the ben-efits of multistyle asset allocation are highly significant andmeaningful.

Sl'KING 2(H)2 THE JOURNAL OF PORTFOLIO MANAtiEMENr 2 5

EXHIBIT 11TERMINAL WEALTH FROM SI INVESTMENT IN SINGLE-STYLE E/PTACTICAL ASSET ALLOCATION STRATEGIES—1981-1997

16

14-

12

10

2 •

15.65

10.61

- 4,98

oo 00 oo\OOO

r-.ooON

•000ON

OK

aoON o ON O N O N O N

Year

EXHIBIT 12TERMINAL WEALTH FROM $1 INVESTMENT IN MULTISTYLETACTICAL ASSET ALLOCATION STRATEGIES—1981-1997

Wea

lth $

24

21

18 '

15

12

9

6

3

0

1

1

r.

— ^ ^

fS r'l ^ V> 'O00 00 00 00 00^ o^ ^ ^ O

r-- 00 ON o — (si moo oo 00 Ov ON <7- ON( ^ ^ o ^ * o

Year

y 26.40

/

// y 16.10

y ^ 10.39_ X ^ J(^\^ 8-91

^:^^>^ ^ ^ 6.12

— » ; — 35-65

0-100

——• Index

TT tn -o r-O^ ON Os O*

26 MULTISTYLE ROTATION STRATEGIES i 2002

SUMMARY AND CONCLUSIONS

We have shown that manitaining style consistencyfor the overall fund may produce portfolios that seriouslyunderperform portfolios formed using astute style rota-tion strategies. We show that even moderate multistylerotation gives a portfolio an excellent chance of outper-forming the market index over the sample period. More-over, the potential enhancement in performance is highlysignificant and meaningful.

First, we show slight dominance of large versussmall firms during the sample period. Value clearly dom-inates growth. We find that low E/P growth managers,especially those targeting small firms, were destined tounderperform the broad index during the sample period.

Second, we show that value/growth strategies thatoverweighted high E/P stocks did not need to be extreme.For instance, we show that a 55/45 high/low E/P blendwould have had a 70% chance of beating the broad indexduring the period.

Third, we calculate the potential benefits of tacti-cal asset allocation for single-style strategies. We show bypermitting just a 10 percentage point deviation fix)m the65/35 constant mix that the manager who correctly fore-casts the outperforming market sector (either market cap-italization or value/growth) would have added more than$2 to terminal wealth per $1 initial investment over thesample period.

Finally, we show the benefits of tactical asset allo-cation across small value, small growth, large value, andlarge growth multiple-styles. Performance is enhancedgreatly by moving from single-style to multistyle strate-gies. For example, we show that terminal wealth for a$10,000 initial investment in 1981 would have grown by1997 to $92,000 with a single-style market capitalizationportfoho investing 65% in large stocks and 35% in smallstocks. A tactical portfolio of investing in the best-per-forming multistyle class would have soared to $264,000over the same period.

Clearly, the more volatile the sector performancebecomes, the greater the benefit fi'om accurate tacticaldecisions. A number of researchers have asked whether thevariability in returns of small- and large-cap stocks andvalue and growth stocks is predictable.''Coggin [1998]finds that U.S. equity style indexes and style return spreadsfollow a random walk. He therefore suggests that stylereturns and style return spreads should be conditionedupon macroeconomic variables using multiple-time seriesmodels. •, :

Others have examined the relationship betweenadditional variables and style index returns. Some exam-ples are earnings-yield gap, P/E, dividend yield, moneysupply, term structure, estimated GDP growth, and cal-endar regularities. Jensen,Johnson, and Mercer [1998], forexample, showed that the value premium in U.S. stocksis higher and significant in an expansionary monetarypolicy enviroiunent.

Our findings demonstrate that the potential bene-fits of exploiting the variability in market capitalization andvalue/growth premiums are dramatic. Most important, ourfindings highlight the importance of asset allocation acrossmultiple investment styles. The key question, of course,is the degree to which style spreads can be predicted. Theresearch holds promise documenting the predictabilityofthe direction of style spreads based on economic activ-ity factors.

ENDNOTES ' •' - ' . j •

The authors thank Christopher Barry, John Gallo. andMauricio Rodriguez for their insights. They especially thank DanCoggin for many helpful suggestions and recommendadons.

'We calculate the geometric retums for small and largefimis using the Fama-French small and large benchmark port-folios {see Fama and French [1993]). The updated data are fromProfessor French's website. The breakpoint for sniaU versus lar^efimis is the midpoint ofthe NYSE fimis.

^ e end the study in 1997 to match a similar study onU.K. markets by Levis and Liodakis |1999|. We define small asfimis below the median size and large as fimis above the mediansize. We define 12-month annual periods from July of year t toJune of year t + 1 for two reasons. First, we want to avoid cre-ating market-capitalization portfolios using market capitalizationfrom December when there are end-of-year market capitaliza-tion effects (also see Fama and French [1992]}. Second, we repli-cate our tests using markct-to-book value ratio to see if thevalue/growth results are robust to definition of value and growth.Therefore, we impose at least a six-month lag for forming themarket-to-book portfolios to allow for a lag in the release oftheaccounting data. Results of the market-to-book tests show nomaterial difFereiice from our E/P results. Last, we use a six-monthlag to match the lag used in Fama and French [1992].

^Also see Scott, Stumpp, and Xu [1999].''Simulations for the four multistyle portfolios (large value,

large growth, small value, and small growth) randomly select5 portfolios from the 25 classified in each style category. Thesimulations for the two single-style strategies (market capital-ization and value/growth) randomly select 5 portfolios from the50 classified in each style category (large/small or value/growth).

SPRING 2002 THE JOURNAL OF PORTFOUO MANAGEMENT 2 7

Note that the terminal wealth for single-style portfohosmay not equal the average ofthe teniiin^il wealth for the multi-style portfolios {e.g., average temiinal wealth for the valueportfolio might not equal the average tenninal wealth for thesmall value and large value portfolios). The differences areshght, and are attributable to the separate simulations we useto derive the single-style and multistyle portfolios.

"As a caveat, statistically significant historical excess returnsdo not guarantee or even imply future excess returns. Asexplained by Ma and Mallet [1998], statistical significance is anartifact of the statistical model and the empirical data. Eco-nomically meaningful results, however, depend not on statis-tical significance but on the power ofthe model to identify profitopportunities. Other studies using perfect foresight includeKester [1990], Hammer [1991[, Case and Cusimano [1995].Philips, Rogers, and Capaldi [1996], Anderson [1997], Cog-gin [1998], Kao and Shumaker [1999|. Levis and Liodakis[1999], and Reinganum [1999].

'•See De Bondt and Thaler [1985, 1987], Fama andFrench [1988], Reinganum [1992], Jegadeesh and Titman[1993], Lakonishok, Shieifer, and Vishny [1994], Chan,Jegadeesh, and Lakonishok [1996], and Sias and Starks [1997]).

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