athanassakos, g. 2011. do value investors add value. journal of investing, 20(2), 86-100

Do Value Investors Add Value?GEORGE ATHANASSAKOS

GEORGEATHANASSAKOSholds Ben Graham Chairin Value Investing at theRichard Ivey School ofBusiness at the Universityof Western Ontario inLondon, ON, [email protected]

Alarge body of academic researchhas shown that value stocks (i.e.,low price-to-earnings ratio, orP/E, or price-to-book-value ratio,

P/BV, stocks) tend to have higher averagereturns than growth stocks (i.e., high P/Eor high P/BV stocks). Basu [1977] was thefirst to confirm the existence of a value pre-mium, namely, that value stocks outperformgrowth stocks. More recently, Chan, Hamao,and Lakonishok [1991], Fama and French[1992, 1993, 1996], Lakonishok, Shleifer, andVishny [1994], Chan and Lakonishok [2004]and Athanassakos [2009, 2011] have foundevidence consistent with a positive valuepremium in markets around the globe usingnot only P/E-based classifications of stocksinto value and growth but also other searchcriteria that value investors have traditionallyused to divide stocks into value and growth,such as P/BV and dividend yield.

Although academic papers such asthose mentioned claim to examine value andgrowth strategies and their performance, suchclaims are only partly correct. The problemwith the academic classification of stocks intovalue and growth is that such a stock selectionapproach is only part of what value investorsdo. Value investors screen for low P/E or lowP/BV stocks to identify possibly undervaluedstocks. But this is not all they do—it is just thefirst step they take in stock selection. Once the

possibly undervalued stocks are screened in,value investors then proceed to the second stepof their analysis—identifying the stocks thatare truly undervalued by valuing individuallyeach stock and arriving at their investmentdecision using the concept of the "margin ofsafety."

Unfortunately, academics do not andcannot know which stocks value investorseventually choose to invest in and so they onlylook at the first step of value investors' stockselection process. After all, academics knowthat it is from this group of low P/E or lowP/BV stocks that value investors tend to selectstocks to invest in. Consequently, academicstend to call the low P/E (or P/BV) stocksvalue stocks and the high P/E (or P/BV)stocks growth stocks, as this latter group ofstocks is not the group of stocks from whichvalue investors typically tend to select stocksto invest in. The first step of stock selection,and the one the academics have examined, is anaive process and entirely mechanical. Anyonecan run such a stock screening selection pro-cess to identify possibly undervalued stocks.The value that value investors add, however, iswith regards to their second step of stock selec-tion, namely, valuing each stock individuallyand using the concept of "margin of safety" inorder to identify the truly undervalued stocks.And it is this step in particular that previousacademic research has not examined.

8 6 Do VALUE INVESTORS ADD VALUE? SUMMER 2011

This study uses Canadian data for two distinctlydifferent subperiods, 1985-1999 and 1999-2007,' toconfirm that a value premium exists in our sample usinga search process (i.e., the first step of stock selection) thatconsists of cross-sorting stocks by both P/E and P/BVratios. Our hypothesis is that we expect (potentially)value stocks (i.e., low P/E, low P/BV) to beat growthstocks (i.e., high P/E, high P/BV).^ The second goalof this study is to examine whether the second step ofvaluation and stock selection that value investors followadds any value. In this regard, our hypothesis is that ifvalue investors really add any value, stocks found to betruly undervalued (i.e., true value stocks), on average,beat stocks selected naively via the first step of stockselection (i.e., potential value stocks).^ The key objectiveof this article, and the article's main contribution, is withregards to testing the second hypothesis and answeringthe related question: Do value investors add value? Pre-vious academic research has said nothing about the valueof value investors. To our knowledge, this is the firststudy to examine both steps of the value investing deci-sion-making approach and explore whether value inves-tors add value to the strictly mechanical search process.

We find that a strong and pervasive value premiumexists in Canada over our sample subperiods that persistsin bull and bear markets and during recessions/recov-eries. Furthermore, this article demonstrates that valueinvestors do add value, in the sense that their process ofselecting truly undervalued stocks, via in-depth secu-rity valuation of the possibly undervalued stocks andarriving at their investment decision using the conceptof "margin of safety," produces positive excess returnsover and above a naive approach of simply selecting lowP/E or P/BV ratio stocks.

DATA AND METHODOLOGY

This article uses data from Compustat from whichearnings per share (E), book value per share (BV), sharesoutstanding, stock prices, and dividends paid are obtainedand from which trailing P/E and P/BV and market-capinfo are derived. For the trailing P/E and P/BV, the price(P) is as of the end of April of year t, and E and BV are,respectively, the December (t - 1) fully diluted annualearnings per share and book value per share for compa-nies with fiscal year-end December (t - 1), as reportedin Compustat. Market cap is derived by multiplying

price per share times shares outstanding at the end ofApril of year t. Annual total stock returns for the secondsubperiod are calculated as the price change plus thedividend from April of year t to April of year t + 1 overthe price in April of year t, using Compustat. For thefirst subperiod, due to data unavailability, annual totalreturns were calculated as just described, but data for thecalculation were obtained from the Canadian FinancialMarkets Research Center (CFMRC) database.

Our sample includes all December fiscal yearend non-financial services companies that trade on theToronto Stock Exchange (TSX).''Based on this, we startedwith Compustat's industrial 4,443 year-firm observations(data) belonging to 1,263 companies for the period 1985-1999, and 4,503 year-firm observations (data) belongingto 1,081 companies for the period 1999-2007. We carriedout a number of screenings of the data. We eliminatedany companies that were income trusts. Companies wererequired to have return data available for the year fol-lowing the determination of P/E and P/BV, unless acompany was acquired, in which case the stock returnfor the remaining annual period was assumed to be theCanadian T-bill six-month rate obtained from the Bankof Canada database. To prevent problems arising fromincluding negative or extremely positive P/E and P/BVfirms and to eliminate likely data errors,' we excludednegative P/E and P/BV, as well as P/E in excess of 150and P/BV in excess of 20. Firms had to have botb P/Eand P/BV within the aforementioned boundaries to beincluded in the sample. Finally, to be included in oursample a stock had to have a price over $1.^-'

Our data, which are adjusted for stock splits andstock dividends, are for each year over two distinctlydifferent subperiods, 1985-1999 and 1999-2007.'* Afterall aforementioned screenings, we end up with 2139, in1985-1999, and 1301, in 1999-2007, cross sectional-timeseries (firm-year) observations belonging to a cumulativenumber of 406 and 377 unique companies, respectively,over tbe two sample subperiods. Appendix A reports thetotal number of observations (companies examined) peryear for each subperiod.

For the end of April of every year t, starting eitherin 1985 or in 1999, firms are ranked based on trailingP/E from low to high, and the ranked firms are dividedinto four groups of equal size. Each P/E-based quartile isthen subdivided into four quartiles based on P/BV fromlow to high. This process is repeated for each year of

SUMMER 2011 THEJOURNAL OP INVESTING 8 7

our sample. Membership in a quartile changes each yearbecause multiples change from year to year. Inclusionin a quartile depends on a stock's multiple in relation toother stocks' multiples. Because P/E and P/BV changeover time, an arbitrary measure across time for all stocksin our sample would be inappropriate. The range ofP/E-P/BV per year for the low P/E-low P/BV basket(Ql) and the high P/E-high P/BV basket (Q16), persubperiod, are reported in Appendix B.

In the first subperiod, we end up with 140 observa-tions in both the low and high P/E-P/BV baskets (Ql andQ16). In the second subperiod, we end up with 81 obser-vations in the low P/E-low P/BV basket (Ql) and 85observations in the high P/E-high P/BV basket (Q16).'

For each stock within each portfolio, returns areobtained for the following year (starting in May 1, 1985or 1999, and ending April 30, 1999 or 2007, for eachsubperiod) and equally weighted mean (and median)returns for each portfolio (basket) are derived.'" Basket 1(Ql) is the lowest P/E-lowest P/BV portfolio or thevalue stocks, while Basket 16 (Q16) is the highest P/E-highest P/BV portfolio or the growth stocks." For eachsubperiod, the number of observations for each basketper year is reported in Appendix C. The 140 overallobservations for the first subperiod belong to 78 uniquecompanies for Ql and 75 unique companies for Q16.The 81 overall observations in Ql and 85 observationsin Q16 for subperiod 1999-2007 correspond to 48 and59 unique companies, respectively.

A time series of non-overlapping annual returns areobtained for each stock within the Ql and Q16 portfo-lios (and for each portfolio) from May 1, 1985 (1999),to April 30, 1999 (2007). Summary statistics of variablesof interest (i.e., value and growth stock returns, valuepremium, market cap) for the various stocks and port-folios are calculated and univariate analysis is conductedto look at value and growth stock performance and thevalue premium. If a stock stopped trading due to anacquisition, then the remaining year returns for this stockwere estimated as being the Canadian Six-month T-billrate of return from the Bank of Canada database.'^

Once a value premium is established, we go on todetermine whether the second step of the value investingprocess, namely, valuing each stock and determiningwhether it is truly undervalued to buy, will beat thenaively determined value stocks. To determine the trulyundervalued stocks, the naively chosen stocks from Ql

were individually valued. The annual reports of thecompanies in question were obtained from Sedar.com.

For each stock in Ql, two valuations were carriedout. First, the net replacement value of each company'sassets (net asset value) was estimated using an approachsimilar to the one described in Greenwald et al. [20011.Second, a free-cash-flow (FCF) based valuation for eachcompany was produced (called earnings power value),by normalizing FCFs and discounting them to infinityusing a perpetuity formula. The discount rate was theweighted average costs of capital (WACC), using thecost of equity obtained from the bond plus risk pre-mium approach described by Athanassakos [1998] andthe cost of debt obtained from the company's ratingand the YTM of similarly rated companies obtainedfrom Canadian Bond Rating Service and Scotia CapitalMarkets for 1985-1999 and Moody's and Bloomberg for1999-2007. The weights in the WACC formula werethe company's target capital structure weights.

Value investors believe that in the long run, in afree-entry market, the return on invested capital (ROIC)will be equal to WACC, and so for the majority of com-panies the discounted cash flow (DCF) model becomesone of perpetuity. However, if a company has a sustain-able competitive advantage, a (real) growth assumptionis incorporated in the DCF model and the value withgrowth (Vg) is derived.

Consequently, two values were derived for eachcompany. One was the net asset value (NAV) and theother the earnings power value (EPV). Where exactlythe company's intrinsic value lay depended on strategicanalysis and the probabilities of possible outcomes. Ifthe NAV exceeded the EPV, a catalyst was assumeddepending on the probability of a takeover or the prob-ability of management change given public informa-tion available in the financial press. In this case, thecompany's intrinsic value was between NAV and EPV.Whether the intrinsic value was closer to NAV than EPVdepended on how high or low the probability of theaforementioned changes was. If EPV was above NAV,then an analysis of the company's competitive environ-ment was made to determine whether the company hada sustainable competitive advantage. If that was the case,then the company's intrinsic value was its EPV; if not,the company's intrinsic value was between EPV andNAV. How close to EPV or NAV the intrinsic valuewas depended on how strong we felt, given available

8 8 Do VALUE INVESTORS ADO VALUE? SUMMER 2011

information and our strategic analysis of the industry andcompany, the probability of sustainability of competitiveadvantage was. The lower this probability, the closer toNAV the intrinsic value was and vice versa. If a (real)growth assumption was necessary, then the value withgrowth was estimated (Vg), which for obvious reasonsexceeded EPV (no growth valuation to perpetuity). Inthis case, the company's intrinsic value was Vg.

We found 87 cases in the first subperiod and 54cases in the second subperiod in which NAV was aboveEPV; 2 and 18 cases, respectively for which EPV wasabove NAV; and no case and only 1 case, respectively,for which a growth assumption was necessary, that is,when Vg was higher than EPV.''' Once, the intrinsicvalue was estimated, the entry price was calculated as2/3 of the intrinsic value. This allowed for 1/3 marginof safety. The entry price in the growth case was thelower of EPV or 2/3 of Vg.

If a stock's current price was below the entry price,a decision was made to invest in this stock; the stockwas truly undervalued. Otherwise, a decision was madenot to invest in the stock in the following 12-nionthperiod. At the end of each 12-month period, stocks wereliquidated and annual returns were calculated for thisperiod. At the beginning of the next 12-month period,new intrinsic values and entry prices were re-estimated.Stocks whose current price was below their re-estimatedentry price were invested in the new sophisticated port-folio for the following 12 months, and the process con-tinued for every subsequent 12-month period. That is,at the beginning of each 12-month period, every stockin the sophisticated portfolio needed to have met thecondition of having a price less than its entry price tojustify its position in the following year's sophisticatedportfolio.

While this portfolio rebalancing may not beentirely true for all value investors many of whom maystill be invested in the stock as long as it hasn't reachedits intrinsic value, the fact that a stock moved up overthe previous year and was now above its new entry pricemay mean that much of the upside on the stock hasbeen realized and better investment opportunities mayexist in other stocks with price less than entry price thatwere worth investing in with higher upside. Besides, ourobjective was to compare the returns of the sophisticatedportfolio to those of the naive Ql portfolio, and to dothis accurately and consistently, we needed to derive

annual total returns for both portfolios. Because theassumption of once-a-year rebalancing applied to Ql,the same assumption was also made for the sophisti-cated portfolio. The final number of stocks per year inthe invested "sophisticated" portfolio (QIS) is shown inAppendix D. The total number of stocks purchased inthe sophisticated portfolio corresponds to 44 companies(30 unique companies) in the first subperiod and 33companies (24 unique companies) in the second subpe-riod. That is, a few companies were repeat members ofthe sophisticated portfolio as, year after year, they metthe price-less-than-entry-price condition.

EMPIRICAL RESULTS

Step 1: The Search Process—Is There a ValuePremium?

Exhibit 1 reports the mean and median annualreturns of P/E-P/BV sorted value (Ql) and growth(Q16) portfolios and the value premium (Ql minus Q16)per year and overall. Exhibit 1 also reports the varianceof returns of tbe value and growth portfolios and theirSharpe ratio performance metrics for the two subperiodsexamined.

It is quite apparent from this exhibit that a valuepremium exists and that it is quite impressive for its sizeand consistency, particularly for the 1999—2007 subpe-riod. The mean value premium per year in Exhibit 1 ismostly positive. In the years when the value premiumis negative, the size of the value premium is relativelysmall, when compared with the years when the valuepremium is positive. All median annual value pre-miums are positive. For 1985—1999, the mean (median)annual value premium (Q1-Q16) is 2.4% (3.7%). For1999—2007, the mean (median) annual value premium is16.60% (16.00%). For comparative purposes, using onlyP/E sorting, Athanassakos [2009] finds that the meanvalue premium in Canada for the period 1985-2005 is6.30%, whereas Athanassakos |2011|, using again P/Esorting, finds that the mean value premium in the U.S. is6.24%, 11.40%, and 6.00% for AMEX, NASDAQ, andNYSE stocks, respectively, for the period 1986-2006.

Exhibit 1 also allows us a glimpse into the behaviorof the value premium during recessions and/or bear mar-kets. For example, TheDowTheory.com reports years2000 and 2002 as bear market years and years 1991 and

SUMMER 2011 THE JOURNAL OF INVESTING 89

E X H I B I T 1

Mean and Median Annual (%) Returns to P/E-P/BV-Based Value (Ql) and Growth (Q16) Strategies by Year

Panel A: 1985-1999

Year

19851986198719881989199019911992199319941995199619971998

1985-1999

Variance

Risk-free rate

SHARPE ratio*

Mean

Q112.4%81.8%-2.2%15.0%

-13.8%1.1%

-10.8%9.4%

36.3%3.8%7.1%

20.6%54.1%

-16.3%

14.2%

7.4%

7.8%

0.24

ReturnQ16

-3.4%47.3%

-12.3%-7.2%

8.9%19.3%-4.5%98.1%

3.0%-9.2%16.1%-1.2%

9.7%1.0%

11.8%

8.5%

7.8%

0.14

Value Premium

Q1-Q16

15.8%34.6%10.1%22.2%

-22.7%-18.2%

-6.3%-88.7%

33.4%13.0%-9.0%21.8%44.4%

-17.3%

2.4%

Median

Q19.3%

60.9%-7.3%

1.6%-23.8%

2.1%-3.5%19.1%21.4%-1.5%12.9%15.8%33.6%

-26.9%

5.7%

ReturnQ16

-17.9%34.9%

-25.2%-5.2%

1.4%14.8%

-15.4%107.8%

9.4%-13.8%

20.4%-25.1%

11.6%2.7%

2.1%

Value Premium

Q1-Q16

27.2%26.0%17.9%6.7%

-25.2%-12.7%

11.9%-88.7%

12.0%12.3%-7.5%40.9%21.9%

-29.6%

3.7%

Panel B:1999-2007

Year

19992000200120022003200420052006

1999-2007

Variance

Risk-free rate

SHARPE ratio**

Mean

Q15.7%1.5%

45.4%-4.6%92.8%32.5%84.8%17.8%

34.5%

14.0%

3.6%

0.83

ReturnQ16

10.9%4.8%9.7%

-4.2%29.7%33.4%53.2%

5.6%

17.9% .

3.6%

3.6%

0.75

Value PremiumQ1-Q16

-5.2%-3.3%35.7%-0.4%63.1%-0.9%31.6%12.2%

16.6%

Median

Q11.4%0.6%

20.1%1.8%

89.4%28.6%42.1%22.9%

21.5%

ReturnQ16

-4.8%-17.7%

8.4%-8.8%26.0%16.2%34.4%2.5%

5.5%

Value PremiumQ1-Q16

6.2%18.3%11.6%10.7%63.4%12.4%7.7%

20.4%

16.0%

*The p-value of the difference between the Sharpe ratios of the two portfolios is 0.09.

**The p-value of the difference between the Sharpe ratios of the two portfolios is 0.03.

2001 as recessionary years.''' With the exception of themean value premium in 1991, which is negative. Exhibit 1shows that irrespective of the state of the world, the valuestrategy normally beats the growth strategy. As far as tbemean returns are concerned. Exhibit 1, Panel A showsthat in 1991, a recessionary year, tbe growth strategy

beats the value strategy by 6.3%. Exhibit 1, Panel B,however, shows that in the bear market years value andgrowth portfolios experience about the same return,whereas in 2001, the year of recession, value clearly beatsgrowth. As far as the median returns are concerned.Exhibit 1, Panel A shows tbat the value premium ispositive in 1991, the recessionary year. In Exhibit 1,

90 Do VALUE INVESTORS ADD VALUE? SUMMER 2011

Panel B all value premiums are positive in both bearmarkets years (2000 and 2002) and the recessionary year(2001). It can also be easily inferred from Exhibit 1 thatvalue premiums in adverse states of the world are mostlycomparable to the value premiums in favorable statesof the world over our two sample periods, particularlythe 1999—2007 subperiod. These findings are consis-tent with Athanassakos [2009, 2011] and Kwag and Lee[2006], who, similar to our findings, show that valuestocks in Canada and the U.S., on average, outperformgrowth stocks throughout the business cycle.

How do the variance and firm-size of the valuestocks compare to those of the growth stocks? Exhibit 1reports the variance of the annual returns of the valueand growth portfolios, while Exhibit 2 reports the

E X H I B I T 2Mean and Median Market Capitalization(in $ millions) for P/E-P/BV-Based Value(Ql) and Growth (Q16) Strategies hy Year

Pane

Year19851986198719881989199019911992199319941995199619971998

A:1985-1999Q1 (Value)

Avg Mcap

101.7642.97260.3190.33260.38283.73132.87151.88130.93127.8689.244.499.1157.84

Mdn Mcap78.1126.3375.77115.7979.58147.7246.56145.752.8750.0363.826.5752.161.27

Q16 (Growth)

Avg Mcap

724.011025.22378.181156.651350.272589.37916.321038.441746.46822.513751.482544.41248.043762.14

Mdn Mcap

398.43536.23930.34711.441017.32748.48730.6421.76362.57330.841199.71385.61211.931558.34

Pane

Year19992000200120022003200420052006

B:1999-2007Q1 (Value)

Avg Mcap44.5591.2997.1495.01143.94187.83262.97316.75

Mdn Mcap

26.8573.3247.0165.56147.6944.9171.8987.59

Q16 (Growth)

Avg Mcap1233.52772.04

2957.894734.21024.621022.131007.461306.94

Mdn Mcap116.8142.5791.89907.98348.26630.71320.12800.85

market capitalization of the value and growth portfoliosper year over our two subperiods. These exhibits showthat value stocks tend to be smaller than growth stocksand that while the value portfolio has higher annualvariance of returns than the growth portfolio in thesecond subperiod, the opposite is the case in the firstsubperiod. The smaller size of Ql vs. Q16 may implythat the outperformance of value over growth stocks isdriven by risk, as normally one would expect smallerstocks to have higher risk than larger stocks. However,if risk drove the findings, one would expect to find1) consistently higher variance in the returns of valueversus growth stocks and 2) that the higher risk of valuestocks is manifested more vividly during adverse statesof the world (such as recessions and bear markets), atwhich time growth would beat value strategies. As this isnot the case, one cannot attribute the return differencesbetween value and growth stocks to possible higher riskof value stocks.''

Furthermore, Exhibit 1 shows that the Sharperatio of value stocks (0.24 in 1985-1999 and 0.83 in1999—2007) exceeds the Sharpe ratio of growth stocks(0.14 in 1985-1999 and 0.75 in 1999-2007) indicatingthat value stocks have had better risk-adjusted perfor-mance than growth stocks over our sample subperiods.The^-value of the difference between the Sharpe ratiosof these two portfolios, calculated based on a test of sig-nificance discussed injobson and Korkie [1981], is 0.09for the 1985-1999 subperiod and 0.03 for 1999-2007.

Could it be that the value premium is driven onlyby a few value stocks with very large positive returns?Exhibit 3 reports the percentage of stocks with positiveand the percentage of stocks with negative returns forthe value and growth portfolios for every year over oursample subperiods. In the first subperiod, both value andgrowth stocks experience more positive than negativereturns in 9 out of the 14 years. In the second subperiod,in every year, more stocks in the value portfolio havepositive returns than negative. This is true only in 4 outof the 8 years for the growth portfolio. Consequently,the value premium is pervasive and not the result of afew outliers.

Step 2: Valuation—Is Any Value Added?

Now that we established that there is a value pre-mium over our sample subperiods, which is consistent

SUMMER 2011 THEJOURNAL OP INVESTING 9 1

E X H I B I T 3Percentage of Positive and NegativeReturns by P/E-P/BV-Based Value (Ql)and Growth (Q16) Strategies

Panel A: 1985-1999

Year

19851986198719881989199019911992199319941995199619971998

Q1 (Value)

% of negativereturns

25.0%0.0%

66.7%45.5%70.0%33.3%50.0%14.3%25.0%54.5%35.7%18.2%16.7%69.2%

% of positivereturns

75.0%100.0%33.3%54.5%30.0%66.7%50.0%85.7%

• 75.0%45.5%64.3%81.8%83.3%30.8%

Q16 (Growth)


62.5%11.1%0.0%

72.7%40.0%

0.0%62.5%14.3%37.5%54.5%21.4%72.7%41.7%38.5%


37.5%88.9%

100.0%27.3%60.0%

100.0%37.5%85.7%62.5%45.5%78.6%27.3%58.3%61.5%

Panel

Year

19992000200120022003200420052006

B:1999-2007Q1 (Value)


50.0%50.0%0.0%

37.5%0.0%0.0%

18.2%25.0%


50.0%50.0%

100.0%62.5%

100.0%100.0%81.8%75.0%

Q16 (Growth)


60.0%63.6%33.3%77.8%10.0%30.0%18.2%66.7%


40.0%36.4%66.7%22.2%90.0%70.0%81.8%33.3%

with previous academic research, the question is, can avalue investor with his/her ability to value stocks, usingvalue investing principles, do better than an approachthat naively picks a basket of stocks with the lowestP/E-P/BV combination?

All stocks that were previously sorted in the valuebasket (Ql) are now individually valued in a very timeconsuming and laborious way. First, the intrinsic value ofa stock is estimated as discussed earlier and then theentry price is calculated as intrinsic value less 1/3 of theintrinsic value—the margin of safety. If a stock's currentprice is below its entry price, a decision is made to buythis particular stock. If not, a decision is made not topurchase the stock. We refer to the portfolio with thestocks in which we choose to invest as the "sophisti-cated portfolio" (QIS), whereas the value portfolio Qlis referred to as the "naive portfolio." The annual andoverall mean and median returns of the sophisticated

portfolio and its excess returns from the naive value Qlportfolio are reported in Exhibit 4.""

The sophisticated portfolio (QIS) beats thenaive value Ql portfolio both in mean and medianreturns. The mean (median) outperformance in sub-period 1985-1999 is 1.10% (3.30%), while in subpe-riod 1999-2007 it is 13.20% (3.80%). Exhibit 4 alsoshows that the sophisticated portfolio beats the naiveone in both bear market years and recessionary marketyears. Irrespective of the state of the world, both themean and median returns of the sophisticated portfolioexceed those for the naive portfolio. Moreover, it canbe easily inferred from Exhibit 4 that the sophisticatedportfolio outperforms the naive portfolio by more inadverse states of the world than in favorable states of theworld. Finally, Exhibit 5 reports that, in general, thepercentage of positive returns in the sophisticated port-folio is higher than the percentage of positive returns inthe naive portfolio.

Exhibit 4 also shows that the variance of thesophisticated portfolio is somewhat higher than thevariance of the naive one, while Exhibit 6 shows thatthe market cap of these two portfolios is about thesame. The risk-adjusted returns of the sophisticatedportfolio exceed those of the naive portfolio as exem-plified by the higher Sharpe ratio of the sophisticatedportfolio (see Exhibit 4). The Sharpe ratios for thesophisticated and naive portfolios are, respectively,0.30 versus 0.24 for 1985-1999 and 1.07 versus 0.83for 1999-2007." The;j-value of the difference betweenthe Sharpe ratios of these two portfolios, again calcu-lated based on a test of significance discussed in Jobsonand Korkie [1981], is 0.15 for 1985-1999 and 0.01 for1999-2007.'**

Moreover, the valuation exercise described andthe eventual decision to buy a stock in the sophisti-cated portfolio accounts for risk and makes the finalstock selection less risky in the sense of reducing thepossibility of loss of capital.'*' Preserving capital is ofparamount importance in the investment decision pro-cess of value investors. The margin of safety taken offthe intrinsic value to arrive at the entry price ensuresdownside protection that goes beyond diversificationwithout sacrificing the returns of the chosen stocks. Inaddition, Ql and QIS are both from the same basketof stocks and have the same market cap, as shown inExhibit 6. And the fact that the sophisticated portfolio

92 Do VALUE INVESTORS ADD VALUE? SUMMEK 2011

E X H I B I T 4

Mean and Median Annual (%) Returns to P/E-P/BV-Based Naive Value (Ql) and Sophisticated Value (QIS)Strategies by Year

Panel A:1985-1999

Year

19851986198719881989199019911992199319941995199619971998

1985-1999

Variance

Risk-free rate

SHARPE ratio*

Mean

Q1S

20.3%4.2%

-18.8%48.8%

-20.0%10.6%16.7%10.5%55.7%33.9%4.7%

16.1%49.6%

-18.2%

15.3%

6.2%

7.8%

0.3

Return

Q112.4%81.8%-2.2%15.0%

-13.8%1.1%

-10.8%9.4%

36.3%3.8%7.1%

20.6%54.1%

-16.3%

14.2%

7.4%

7.8%

0.24

Value InvestorPremiumQ1S-Q1

7.9%-77.6%-16.6%

33.8%-6.2%

9.5%27.5%

1.1%19.4%30.1%-2.4%-4.5%-4.5%-1.9%

1.1%

MedianQ1S

7.5%5.2%

-18.8%48.8%

-23.7%6.5%

16.7%10.5%65.9%29.2%4.6%

15.8%31.8%

-31.1%

9.0%

Return

Q1

9.3%60.9%-7.3%

1.6%-23.8%

2.1%-3.5%19.1%21.4%-1.5%12.9%15.8%33.6%

-26.9%

5.7%


-1.8%-55.7%-11.5%47.2%

0.1%4.4%

20.2%-8.6%44.5%30.7%-8.3%

0.0%-1.8%-4.2%

3.3%

Panel B:1999-2007

Year

19992000200120022003200420052006

1999-2007

Variance

Risk-free rate

SHARPE ratio**

MeanQ1S

5.7%13.9%71.7%27.5%

100.4%24.7%

112.7%25.0%

47.7%

17.1%

3.6%

1.07

Return

Q1

5.7%1.5%

45.4%-4.6%92.8%32.5%84.8%17.8%

34.5%

14.0%

3.6%

0.83


0.0%12.4%26.4%32.2%

7.6%-7.8%27.9%

7.2%

13.2%

MedianQ1S

1.4%9.6%

46.3%25.6%34.0%24.7%

115.5%25.0%

25.3%

Return

Q1

1.4%0.6%

20.1%1.8%

89.4%28.6%42.1%22.9%

21.5%


0.0%9.1%

26.2%23.8%

-55.4%-3.9%73.4%

2.1%

3.8%

* The p-value of the difference between the Sharpe ratios of the two portfolios is 0.15.

** The p-value of the difference between the Sharpe ratios of the two portfolios is 0.01.

beats the naive one by more in adverse than favorable

states of the world further supports the argument that

the risk of the sophisticated portfolio is not higher than

that of the naive portfolio. Hence, risk does not seem

to drive the outperformance of the stocks that value

investors choose to eventually invest in (i.e., the truly

undervalued stocks), which is the key contribution of

this article.

SUMMER 2011 THEJOURNAL OF INVESTING 9 3

E X H I B I T 5Percentage of Positive and Negative Returns byP/E-P/BV-Based Naive Value (Ql) and SophisticatedValue (QIS) Strategies

Panel

Year

19851986198719881989199019911992199319941995199619971998

A:1985-1999

QIS (Sophisticated)


0.0%0.0%

100.0%0.0%

100.0%0.0%0.0%0.0%0.0%0.0%

50.0%40.0%28.6%75.0%


100.0%100.0%

0.0%100.0%

0.0%100.0%100.0%100.0%100.0%100.0%50.0%60.0%71.4%25.0%

Q1 (Value)


25.0%0.0%

66.7%45.5%70.0%33.3%50.0%14.3%25.0%54.5%35.7%18.2%16.7%69.2%


75.0%100.0%33.3%54.5%30.0%66.7%50.0%85.7%75.0%45.5%64.3%81.8%83.3%30.8%

Panel

Year

19992000200120022003200420052006

B:1999-2007Q1S (Sophisticated)


50.0%33.3%0.0%0.0%0.0%0.0%0.0%

25.0%


50.0%66.7%

100.0%100.0%100.0%100.0%100.0%75.0%

Q1 (Value)


50.0%50.0%

0.0%37.5%0.0%0.0%

18.2%25.0%


50.0%50.0%

100.0%62.5%

100.0%100.0%81.8%75.0%

Finally, not only does the sophisticated portfoliobeat the naive portfolio Ql, but Ql significantly beatsQ16, making the sophisticated portfolio outperformQ16 by a substantial amount, which is too large to beexplained by possible risk differences. As a result, valueinvestors proceeding to the second step in the stockselection process do add value. °

How About 2007-2009?

This study started well before the credit crisis of2008-2009 engulfed the world economies and markets.It ended right at the time the credit crisis hit. As data havenow become available for 2008 and 2009, and as readerswill be interested in knowing how the value investingapproach worked over this period of crisis, we decided toextend this article to also include the credit crisis period.

E X H I B I T 6Mean and Median Market Capitalization(in $ millions) to P/E-P/BV-Based NaiveValue (Ql) and Sophisticated Value (QIS)Strategies by Year

Panel

Year

19851986198719881989199019911992199319941995199619971998

A:1985-1999Q1S (Sophisticated)

Avg Mcap

54.7843.6223.9252.91

687.23544.07

32.136.96

159.99186.3513839.99

100.7588.4

Mdn Mcap

54.5929.0323.9252.91

220.32293.81

32.136.9662.4664.225.6826.5732.1189.97

Q1 (Value)

Avg Mcap

101.7642.97

260.3190.33260.38283.73132.87151.88130.93127.8689.244.499.1

157.84

Mdn Mcap

78.1126.3375.77

115.7979.58

147.7246.56

145.752.8750.0363.826.5752.161.27

Panel

Year

19992000200120022003200420052006

B:1999-2007Q1S (Sophisticated)

Avg Mcap

34.1888.2877.3661.5881.08

425.0951.74

203.29

Mdn Mcap

33.7835.9837.9465.5676.54

425.0955.9

111.12

Ql (Value)

Avg Mcap

44.5591.2997.1495.01

143.94187.83262.97316.75

Mdn Mcap

26.8573.3247.0165.56

147.6944.9171.8987.59

The methodology and process are the same asdescribed earlier. Following the same screenings asbefore, we end up with 223 observations in 2007 and183 observations in 2008. We then form Ql (the valueportfolio) and Q16 (the growth portfolio) for 2007 and2008 with the following ranges for P/E and P/BV:Ql-2007 (min P/E: 3.60, max P/E: 11.92; min P/BV:0.71, max P/BV: 1.23); Ql-2008 (min P/E: 3.80, maxP/E: 11.14; min P/BV: 0.62, max P/BV: 1.10); Q16-2007 (min P/E: 33.46, max P/E: 144.14; min P/BV:5.38, max P/BV: 10.15); Q16-2008 (min P/E: 31.04,max P/E: 112.47; min P/BV: 4.36, max P/BV: 15.93).There were 14 observations in 2007 and 12 observa-tions in 2008 for Ql and Q16. We only found two truly

9 4 Do VALUE INVESTORS ADD VALUE? SUMMEK 2011

E X H I B I T 7Mean and Median Annual (%) Returns to P/E-P/BV-Based Value (Ql) and Growth (Q16) Strategies by Year,2007-2009

Year

200720082008 (Extended)*

Mean Return

Q1

-30.20%-58.20%-31.20%

Q16

20.20%-33.50%-16.60%

Value Premium

Q1-Q16

-50.40%-24.70%-14.60%

Median Return

Q1

-31.30%-62.30%-34.00%

Q16

9.60%-34.40%-14.60%

Value Premium

Q1-Q16

-40.90%-27.90%-19.30%

Note: "2008 (Extended)" covers May 1, 2008-September 30, 2009.

E X H I B I T 8

Mean and Median Annual (%) Returns to P/E-P/BV-Based Naive Value (Ql) and Sophisticated Value (QIS)Strategies by Year, 2007-2009

Year

200720082008 (Extended)*

Mean Return

Q1S

-45.70%-13.00%

64.70%

Q1

-30.20%-58.20%-31.20%

Value InvestorPremium

Q1S-Q1

-15.50%45.20%95.90%

Median Return

Q1S

-45.70%-13.00%

64.70%

Q1

-31.30%-62.30%-34.00%

Value InvestorPremium

Q1S-Q1

-14.40%49.30%98.70%

Note: "2008 (Extended)" covers May 1, 2008-September 30, 2009.

undervalued stocks in 2007 and only one truly under-valued stock in 2008, and these stocks were included intbe sophisticated portfolio.

Exhibit 7 shows the mean and median annualreturns for Ql and Q16, while Exhibit 8 shows tbemean and median annual returns for QIS (the sophis-ticated/value portfolio) and Ql (the naive/valueportfolio) for the period May 1, 2007, to April 30,2009. In addition, this time, the exhibits also sbowthe returns for Ql, Q16, and QIS for May 1, 2008, toSeptember 30, 2009 (referred to as "2008 extended").These exhibits' extended period returns represent17-month returns for Ql, Q16, and QIS portfolios,as if the stock selections and compositions for value,growth, and sophisticated portfolios had not changedfrom May to September 2009.

We see that over the two years of the "GreatRecession," the mean and median returns for the growthportfolio (Q16) exceed those for the value portfolio(Ql) by a significant amount for both the normal andextended periods. On tbe other band, the sophisticated

portfolio (QIS) underperformed the naive portfolio(Ql) in 2007 but significantly outperformed it in 2008for both the normal and extended 2008 periods. In fact,in 2008, tbe sophisticated portfolio outperformed boththe naive value and the growth portfolio. On average,over the two-year period, the sophisticated portfoliobeat the naive portfolio and the growth portfolio. More-over, the sophisticated portfolio beat the naive duringthe recession and the bear market period of May 1, 2008,to April 30, 2009. These findings are consistent withthose reported earlier for 1985-2007.

CONCLUSIONS

Value investors wish to buy stocks at a discount tointrinsic value. To find the heavily discounted stocks,value investors follow a two-step process. First, theysearch for possibly undervalued stocks, using screeningmetrics, such as P/E or P/BV. Second, they carefullyapply a valuation technology to all possibly under-valued stocks that pass the first step and arrive at their

SUMMER 2011 THEJOURNAL OH INVESTING 9 5

investment decision by applying the concept of marginof safety in order to determine which among thosestocks are truly undervalued.

The purpose of this article was first to examinewhether a value premium existed following a mechan-ical screening process (i.e., the search process) in theCanadian markets between 1985-1999 and 1999-2007and, second, whether value investors added valuein the stock selection process by being able to findtruly undervalued stocks from the universe of thepossibly undervalued stocks identified with the searchprocess.

First, we apply a cross-sorting process wherebyvalue stocks are defined as the low P/E-low P/BV stocksand growth stocks as the high P/E-high P/BV stocks.Second, we examine whether the previously identifiedvalue stocks beat the growth stocks. Third, we focus onthe low P/E-low P/BV stocks, which we carefully value,and apply the concept of margin of safety to identifythe truly undervalued stocks among them. Finally, wecompare the returns of the truly undervalued stocks tothose of the naively chosen value stocks of the searchprocess.

We find that a strong and pervasive value premiumexists in Canada over our sample period that persists inbull and bear markets and during recessions/recoveries.Value stocks, on average, beat growth stocks even whenusing a very mechanical screening of the search pro-cess. Furthermore, this study demonstrates that valueinvestors do add value, in the sense that their process ofselecting truly undervalued stocks, via in-depth secu-rity valuation of the possibly undervalued stocks andarriving at their investment decision using the conceptof margin of safety, produces positive excess returnsover and above the naive approach of simply selectinglow P/E-P/BV ratio stocks.

The study was extended to the years of the "GreatRecession" (2008-2009) and despite the fact that overthis extended period we had a severe recession and bearmarket, on average, the sophisticated portfolio stillbeat the naive value portfolio, consistent with earlierevidence.

In conclusion, value investors, following the two-step value-investing stock selection process detailedin this study, did add value in Canada over the period1985-2009.

In general, this study's results should be replicablein different markets and time periods as the valuationprocess is robust and theoretically correct (see Greenwaldet al. [2001]). Moreover, the margin of safety appliedin this study is consistent across all value investors asit is one of the key principles that the father of valueinvesting, Benjamin Graham [2003], established as themeans to protect an investment against downside risk,and as such, it is universally used. However, we do rec-ognize some challenges associated with carrying out thisstudy. To make the exercise more manageable, we had toapply a number of screenings to the stock universe thatreduced significantly the number of stocks we had tovalue. While we think that a larger sample may not pro-duce different results, until we apply our methodologyto a larger sample of stocks, we cannot be conclusiveabout it and, therefore, cannot reject an argument thatthe screenings carried out in the study and the resultingsmall sample size may have been conducive to yieldingsupporting results. Moreover, our methodology entailedsome personal judgment regarding the probability of acatalyst or sustainability of competitive advantage, andthis may not be easily replicated, even though somepersonal judgment is normally unavoidable in any valu-ation exercise.

A P P E N D I X ATotal Numher of Companies Examined Each Year forEach Suhperiod

1985-1999 Subperiod

Year

19851986198719881989199019911992199319941995199619971998

Number ofObservations

13314213916814713512698116164222174178197

1999-2007 Subperiod

Year

19992000200120022003200420052006


162175177148144150167178

96 Do VALUE INVESTORS ADD VALUE? SUMMER 2011

A P P E N D I X BValues Each Year for the Low P/E-Low P/BV Basket (Ql) and the High P/E-High P/BV Basket (Q16)for Each Subperiod

1985-1999 Subperiod

Year

19851985'19861986198719871988198819891989199019901991199119921992199319931994199419951995199619961997199719981998

iVIin

MaxiVIin

iVIax

IVIin

MaxMinMaxMinMaxMinMaxMinMaxMinMaxMinMaxMInMaxMinMaxMinMaxMinMaxMinMax

Q1 (Vaiue)

P/E

3.158.923.87

10.251.61

13.931.188.287.308.883.936.842.419.497.49

11.885.68

13.012.28

10.952.76

10.181.419.134.40

12.100.66

15.45

P/BV

0.480.740.400.860.231.230.110.900.431.010.140.790.140.820.421.090.701.120.411.150.260.910.450.780.701.040.561.02

Q16(Growtli)P/E

17.7352.2824.2248.6529.18

101.4822.5249.5018.6855.0918.7141.6026.14

103.1335.94

146.1553.3393.7537.09

130.0025.51

105.0033.27

137.5026.4189.6332.45

129.41

P/BV

2.878.004.46

17.424.23

30.002.87

10.512.33

12.702.296.461.788.472.834.552.99

13.544.01

2.796.913.91

12.153.185.874.04

20.51

1999-2007 Subperiod

Year

1999199920002000200120012002200220032003200420042005200520062006

MinMaxMinMaxMinMaxMinMaxMinMaxMinMaxMinMaxMinMax

Ql (Vaiue)

P/E

2.389.720.427.232.658.193.458.723.269.825.05

10.774.05

11.302.55

12.82

P/BV

0.350.720.390.670.270.780.330.780.470.720.541.090.731.030.581.27

Q16 (Growth)

P/E

25.0083.7229.12

144.0021.46

140.0027.17

133.3323.9185.0028.64

135.0030.95

135.0029.8086.11

P/BV

2.4117.643.87

11.483.288.523.766.412.855.233.317.194.94

13.344.57

18.61

A P P E N D I X CNumber of Observations for Each Basket Each Year for Each Subperiod

1985-1999 Subperiod

Year

19851986198719881989199019911992199319941995199619971998Totai

Q1 (Vaiue)


899

11109878

1114111213

140

Q16 (Growth)


899

11109878

1114111213

140

1999-2007 Subperiod

Year

19992000200120022003200420052006Totai

Q1 (Vaiue)


10101189

10111281

Q16 (Growth)


1011129

1010111285

SUMMER 2011 THEJOUKNAI. OF INVESTING 9 7

A P P E N D I X DFinal Number of Stocks per Year in the Invested"Sophisticated" Portfolio

ösi/Stecätete

33223311334574

ENDNOTES

This article represents an extension of a pilot studycarried out at the Richard Ivey School of Business in 2008by George Athanassakos, Reyer Barel, and Saj Karsan, enti-tled "Searching for and Finding Value: Canadian Evidence1999-2006." The pilot project and its extension have beenfunded by an Ivey Research Grant and would not have beenpossible without the hard work and commitment of a group ofstudents who worked diligently on company valuations. Thestudents and the time periods they covered are Reyer Bareland Saj Karsan (1999-2006); Dalton Baretto, Scott Gryba,Ali Sabur, and Carter Yu (1985-1998); and Scott Gryba, AliSabur, and Carter Yu (2007-2009). Many thanks also go toCarly Vanderheyden for excellent assistance.

'These periods were chosen and kept separate for thefollowing reasons. The first subperiod (1985—1999) wascharacterized by a classic bull market with steadily risingstock prices, while the second subperiod (1999-2007) wasa challenging period for the stock market. With the excep-tion of the materials and oil sectors, the stock market overallremained mostly fiat over this subperiod, which also includedthe bursting of the stock market bubble. The study was sub-sequently extended to cover the years of the "Great Reces-sion," 2008-2009.

^Previous academic evidence supports this hypothesis(see Basu [1977], Chan, Hamao, and Lakonishok [1991],Fama and French [1992, 1993, 1996], Lakonishok, Shleifer,

and Vishny [1994], Chan and Lakonishok [2004], andAthanassakos [2009, 2011]).

•'The performance of legendary value investors, such asWarren Buffett and Walter Schloss, over long time periodssupports this hypothesis. Under Buffett, Berkshire Hathawayhas averaged a 25% + annual return to its shareholders forthe last 25 years, while employing large amounts of capitaland minimal debt. Walter Schloss and his son Edwin, overthe period 1956 to 2000, provided investors a compoundedreturn of 15.3% compared with the S&P 5OO's annual returnof 11.5% (see http://www.bengrahaminvesting.ca/Teaching_Applications/Guest_Speakers/2008_speakers.htni).

''We exclude financial services companies, such asbanks and insurance companies, because the high leveragenormally employed by these companies does not have thesame meaning as for non-financial companies for which highleverage indicates financial distress.

'See La Porta, Lakonishok, Shleifer, and Vishny [1997],Griffin and Lemmon [2002] and Cohen, Polk, and Vuolteenaho[2003].

'Because our sample only includes firms with fiscalyear-end December of year (t - 1), all firms have releasedtheir annual reports needed for the valuations and informa-tion for earnings per share and book value per share by Aprilof year t.

'For subperiod 1985-1999, the no-income-trust screeneliminated 182 observations; price over $1, 39 observations;the P/E restrictions, 722 observations; and the P/BV restric-tions, 108 observations. In addition, 407 and a further 846observations were eliminated as there were either no price orno EPS data, respectively, available in Compustat. For subpe-riod 1999-2007, the no-income-trust screen eliminated 971observations; price over $1, 622; the P/E restrictions, 563;and the P/BV restrictions, 15 observations. In addition, 811and a further 220 observations were eliminated for a lack ofprice and EPS data, respectively.

'See Note 1 for the reasons these periods •were keptseparate.

'The reason for this discrepancy in the latter subperiodis the following. Unlike Q16, we actually carry out valuationson Ql stocks, and while a few stocks in the low P/E-lowP/BV basket did not possess the ticker suffix used for filteringincome trusts (namely, ".U"), upon closer inspection duringvaluation of Ql stocks, we found that some stocks were actu-ally income trusts and thus were subsequently eliminated.For this reason, in some years, •we have fe wer stocks in Qlthan Q16.

'"See Fama and French [1992], Lakonishok, Shleifer,and Vishny [1994] and La Porta, Lakonishok, Shleifer, andVishny [1997].

98 Do VALUE INVESTORS ADD VALUE? •SUMMER 2011

"The P/E and P/BV sorting requirement was madein order to reduce the number of stocks we had to actuallyevaluate due to the labor intensity of the project.

'^For Ql, there were 1 stock in 1986, 1993, 1996, 1997,and 2002, and 2 stocks in 2000 that stopped trading withina given year. For Q16, there was 1 stock in 1986, 1987, 1997,2000, 2001, and 2002 that stopped trading within a givenyear. Combined in Ql and Q16, we had overall seven compa-nies in 1985-1999 and six companies in 1999-2007 for whichwe had to use the six-month T-bill assumption. The stockscontained in Ql and Q16, as well as the stocks that stoppedtrading within a year and for which a T-bill assumption hadto be made, are available from the author upon request.

'Mn the first subperiod, the valuation team found anLunber of companies that were outside their "circle of compe-tence" to value reliably. These companies were (26) resourcecompanies (eliminated due to uncertain real options), (6)private equity firms or holding companies (eliminated due touncertain vakie of investments or holdings), and (12) compa-nies of high business and financial risk (due to extreme finan-cial distress situations). In addition, five companies had nodata available and two companies were recent IPOs for whichno historical data were available, and they were thus elimi-nated at the valuation step. The exclusion of such companiesalso helped reduce the number of companies that had to bevalued and made the project more manageable. As a result,89 companies were actually valued and not 140 as originallyindicated for subperiod 1985-1999. In the second subperiod,where there were fewer companies to be. valued, at the valu-ation step, the valuation team eliminated six companies thathad high business and financial risk and two companies forwhich annual reports were not available. No other compa-nies were eliminated in this subperiod as the valuation teamfelt that the remaining companies were within their "circleof competence" and could be reasonably valued. As a result,73 companies were actually valued and not 81 as originallyindicated for subperiod 1999-2007.

'•'See http://www.thedowtheory.com/bear&reces-sions.htm.

"The risk issue will also be addressed in the followingsection, where risk is incorporated in the valuation exercise,intrinsic value, entry price and final investment decisionmaking.

""The kind of reports we produced for each stock inportfolio Ql, as well as the actual stocks we chose to pur-chase and include in the sophisticated portfolio (QIS) persubperiod after painstaking valuations are available from theauthor upon request.

"It is possible that the exclusion of the companies indi-cated in Note 13 from the second step of the value investingprocess may have impacted the strength of the findings in

the first subperiod as there may have been many truly imder-valued stocks among the excluded companies.

'"It should be noted that this test has low power in thesense that is it is difficult to find statistical significance evenif the true difference in Sharpe ratios is not zero.

'' The issue of whether risk or behavioral factors drivethe value premium has arisen because academics deal onlywith the first step of the value investing process. Not knowingwhat stocks value investors tend to buy, academics resort toarguments about risk to justify the value premium (see Famaand French [1992, 1993, 1996]). However, if one knows theintrinsic value of a stock and its entry price (which accoLmtsfor the margin of safety) and, hence, what stocks value inves-tors would buy, as per the second step of the value investingprocess, then one should know the risk of the portfolio/stocks. In the valuation process, risk is adjusted through therisk premium in the discount factor, and in the final selectionprocess, risk is controlled for via the margin of safety.

^"Our sophisticated portfolio is quite concentrated.However, the margin of safety acts as a way to protect capitalthat is distinct from, and in many respects consistent with,diversification. Moreover, the superior performance of thesophisticated portfolio is consistent with Kacperczyk et al.[2007], who find that all concentrated funds in their studydid well, but the more concentrated did better.

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