Diversification Across Characteristics

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 986 December 2009 Diversification Across Characteristics Erik Hjalmarsson NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.

Diversification Across Characteristics Erik Hjalmarsson* Division of International Finance Federal Reserve Board, Mail Stop 20, Washington, DC 20551, USA December 2009 Abstract I study long-short portfolio strategies formed on seven different stock characteristics representing various measures of past returns, value, and size. Each individual characteristic results in a profitable portfolio strategy, but these single-characteristic strategies are all dominated by a diversified strategy that places equal weight on each of the single-characteristic strategies. The benefits of diversifying across characteristic-based long-short strategies are substantial and can be attributed to the mostly low, and sometimes substantially negative, correlation between the returns on the single-characteristic strategies. JEL classification: G11, G12. Keywords: Diversification; Portfolio choice; Stock characteristics. * Helpful comments have been provided by Lennart Hjalmarsson and Randi Hjalmarsson. Tel.: +1-202-452-2426; fax: +1-202-263-4850; email: erik.hjalmarsson@frb.gov. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.

1 Introduction Portfoliostrategiesbasedonstockcharacteristics,suchasmomentumandvalue,occupyagreatdeal ofthe(cid:133)nanceliterature. Suchportfoliostendtogeneratereturnsthatcannotbereadilyexplainedby standard asset pricing models and therefore represent, to some extent, empirical (cid:145)anomalies(cid:146). Most studies focus on one characteristic at a time and evaluate to what extent a trading strategy based onthatcharacteristicdeliverssigni(cid:133)cantlypositivereturns. Inrecentwork, Asness, Moskowitz, and Pedersen (2009, AMP hereafter) study value and momentum jointly and (cid:133)nd that using a portfolio strategy based on both of these characteristics tends to strongly outperform each of the individual characteristic strategies. In their analysis, AMP start out with typical long-short momentum and value strategies and then combine these two strategies into a joint equal-weighted momentum-value strategy. The generally negative correlation between the returns on the two individual strategies provide substantial diversi(cid:133)cation bene(cid:133)ts and leads to often large increases in the Sharpe ratio, relative to the individual strategies.1 In the current study, I extend the AMP analysis and study the performance of long-short characteristic-based strategies, diversi(cid:133)ed across a relatively large number of characteristics. In particular, I analyze the performance of long-short strategies based on the following characteristics: (i)Short-termreversals,(ii)medium-termmomentum,(iii)long-termreversals,(iv)book-to-market value,(v)cash(cid:135)ow-priceratio,(vi)earnings-priceratio,and(vii)size. Theperformanceofthesinglecharacteristic portfolios are compared to an equal-weighted portfolio of the single-characteristic ones. Theempiricalresultsareclear-cut,withtheequal-weighteddiversi(cid:133)edportfolioalmostalways delivering substantially better Sharpe ratios than any of the single-characteristic portfolios or the two-characteristic momentum-value portfolio considered by AMP. From a portfolio management perspective, there are thus great diversi(cid:133)cation bene(cid:133)ts from combining long-short strategies based on several di⁄erent characteristics. From an asset pricing perspective, the large Sharpe ratios obtained for the diversi(cid:133)ed portfolios illustrates even further the problem of reconciling observed returns on stocks with rational economic models. 1AMPalsostudydiversi(cid:133)cationacrossdi⁄erentassetclassesandcountries,usingjointmomentum-valuestrategies, which leads to even greater Sharpe ratios. In the current paper, I focus only on U.S. stocks. 1

2 Portfolio strategies 2.1 Data and characteristics Monthlydataonreturnsforportfoliossortedondi⁄erentcharacteristicswereobtainedfromKenneth French(cid:146)s web site.2 That is, for each characteristic, all stocks on the NYSE, AMEX, and NASDAQ, are sorted into deciles of the stock characteristic and the equal-weighted return on each decile is recorded. Sevendi⁄erentcharacteristics,orsortingcriteria,areconsidered. The(cid:133)rstthreerepresent serial correlation patterns in stock returns: (i) Short-term reversals (ST-Rev), de(cid:133)ned as the prior month(cid:146)s (t 1) return, (ii) medium-term momentum (Mom), de(cid:133)ned as the returns from month (cid:0) t 12 to t 2, and (iii) long-term reversals (LT-Rev), de(cid:133)ned as the returns from month t 60 (cid:0) (cid:0) (cid:0) to t 13. The next three represent di⁄erent valuation ratios: (iv) Book-to-market value (BM), (cid:0) (v) cash(cid:135)ow-price ratio (CP), and (vi) earnings-price ratio (EP). The (cid:133)nal characteristic is (vii) (cid:133)rm size, measured as market equity (ME). The sample period over which returns on all these characteristic-sorted portfolios are available spans from July 1951 to December 2008, for a total of 690 monthly observations. More exact details on these portfolios are available on Kenneth French(cid:146)s web site.3 From the returns on the decile portfolios for each characteristic, the returns on a long-short high-minus-low portfolio are constructed by calculating the di⁄erence between the returns on the top decile portfolio and the bottom decile portfolio. In the case of short-term reversals, long-term reversals, and size, where the returns are expected to decrease in the characteristic, the returns on the low-minus-high (or equivalently, the negative of the high-minus-low) portfolios are instead constructed. This produces return series for seven long-short characteristic based portfolios. Table 1 shows the correlation structure for the returns on the seven long-short portfolios. Results for the full sample period from 1951 to 2008 are shown, as well as results for three di⁄erent subsamples, spanning the (cid:133)rst and second halves of the sample as well as the last ten years of the sample, respectively. As would be expected, the three valuation ratios, BM, CP, and EP, result in portfolio returns that are fairly highly correlated with each other. Depending a bit on sample 2http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html 3Portfolios sorted on the dividend-price ratio were also available on the website, but we omit this characteristic here since far from all (cid:133)rms pay dividends. In addition, when combined into a joint equal-weighted portfolio, the current set of characteristics provides an attractive equalweight on value and past returns, with three characteristics representing value and three representing past returns. 2

period, the valuation ratios are mostly negatively correlated with Short-term reversals (ST-Rev), only weakly correlated with momentum (Mom), and generally positively correlated with long-term reversals (LT-Rev). Market equity (ME), or size, is most highly positively correlated with longterm reversals and negatively correlated with momentum. Short-term reversals are fairly strongly negatively correlated with momentum, and weakly positively correlated with long-term reversals. Momentum and long-term reversals exhibit a fairly large negative correlation. Overall, and apart from the high correlation between the returns on the valuation ratio portfolios, the correlation matrices shown in Table 1 indicate that there may be substantial diversi(cid:133)cation bene(cid:133)ts across the di⁄erent characteristics. 2.2 Portfolio performance 2.2.1 Single-characteristic portfolios The left hand side of Table 2 shows annualized summary statistics for the returns on the singlecharacteristic portfolios described above. The (annualized) mean, standard deviation, Sharpe ratio, andCAPMalphaandbetaareshown;standarderrorsareshowninparanthesesbelowtheestimates. The excess returns, over the one month T-Bill rate, on the value weighted CRSP portfolio are used as market returns in the CAPM regressions; the annualized mean, standard deviation, and Sharpe ratio for the market excess returns are shown in the right-most column in Table 2. Full sample results, as well as results for the three sub-samples listed above, are shown. From a portfolio performance perspective, the (cid:133)nal sub-sample covering the most recent ten years is of extra interest both because it may be a better indicator of which strategies currently work and also because it spansaverydi¢ cultperiodfortheU.S.stockmarketwithboththedotcomcrashintheearly2000s as well as the recent credit crisis (the average excess return over the period was 2:1 percent). This (cid:0) sampleperiodthusprovidesagoodtestofwhetherthelong-shortstrategiesarecapableofdelivering excess returns in adverse market conditions. Starting with the mean estimates, it is evident that the zero-cost long-short portfolios generally deliver average returns that are statistically di⁄erent from zero. Over the full sample (Panel A), the mean estimates are always more than two standard deviations away from zero. During the (cid:133)rst and second half of the sample period (Panels B and C), it is only for size (ME) in the latter 3

half of the sample that the null hypothesis of zero average returns cannot be rejected at standard signi(cid:133)cance levels. In the shortest sub-sample spanning the last ten years, the mean estimates are often not precise enough to reject the null. Since the CAPM betas for most of the strategies are small, the signi(cid:133)cant mean estimates also typically translate into signi(cid:133)cantly positive CAPM alphas. The only strategy that exhibits a sizeable positive CAPM beta is the short-term reversal (ST-Rev) strategy. All three valuation ratio strategies (BM, CP, and EP) exhibit fairly large, and signi(cid:133)cant, negative betas. The annualized Sharpe ratios show that over most periods and for most characteristics, the long-short portfolios also deliver sizable risk-adjusted returns. Apart from the size-based portfolios, the other characteristics result in Sharpe ratios that are typically in the region between 0:6 and 1. This is substantially larger than the Sharpe ratios achieved for the market portfolio, which is generally in the 0:4 to 0:5 range as seen in the (cid:133)nal column of Table 2. In the (cid:133)rst half of the sample (Panel B), the short-term reversal strategy performs by far the best, with an annual Sharpe ratio of two. In the second half of the sample (Panel C), the value based strategies all perform well, with Sharpe ratios close to one. Size appears to perform the worst in general, although it did quite well during the last ten years (Panel D). The summary statistics for the long-short portfolios ignore the impact of transaction costs. However, although transaction costs will inevitably lead to lower returns, their impact may not be that great in these types of portfolios, as evidenced by Brandt et al. (2009) who also study characteristic based strategies. They (cid:133)nd that controlling for transaction costs only marginally lowers the performance of their characteristic based portfolios, as long as the transaction costs are taken into account in the portfolio rebalancing decisions. In addition, the qualitative bene(cid:133)ts of diversi(cid:133)cation that are described in the following section are likely to hold also under transaction costs, even if the overall level of the Sharpe ratios may shift downwards. Thus, although a full ananlysis of transaction costs is outside the scope of the current study, there are strong reasons to believe that the conclusions would remain the same also after controlling for transaction costs. 2.2.2 Multi-characteristic portfolios The right hand side of Table 2 shows the summary statistics for the portfolios that are diversi(cid:133)ed across the characteristics. In particular, from the single characteristic portfolios, I create two 4

di⁄erent diversi(cid:133)ed portfolios. The (cid:133)rst one is simply the equal weighted portfolio across all seven characteristics. The second one is the equal weighted portfolio of the momentum strategy and the book-to-market strategy, which are the two characteristics studied by AMP. The empiricalresults presented in the second half of Table 2 are verystrong. In almost all cases, the equal weighted portfolio across all characteristics strongly outperforms the single-characteristic portfolios,measuredbytheSharperatio,andalsoo⁄erssubstantialgainsoverthemomentum-bookto-market portfolio studied by AMP. This is particularly true during the last ten years (Panel D), where the equal weighted portfolio across all characteristics achieves a Sharpe ratio of 1:3, whereas the single characteristic portfolios all have Sharpe ratios below 0:8, and the momentum-book-tomarket portfolio only has a Sharpe ratio of about 0:6. The Sharpe ratio for the market over the last ten years was negative. Only the short-term reversal portfolio, and only during the (cid:133)rst half of the sample (Panel B), ever outperforms the all-characteristics portfolio, in terms of Sharpe ratios. Interestingly, the performance of the all-characteristics portfolio is very similar during the (cid:133)rst (Panel A) and second (Panel B) halves of the sample, whereas the Sharpe ratio for the short-term reversal portfolio is almost twice as large during the (cid:133)rst half of the sample as compared to the second half. Table 2 thus provides strong evidence in favour of the bene(cid:133)ts of diversi(cid:133)cation across characteristics. Importantly, these bene(cid:133)ts appear to have been present also during the last ten years when the market on average performed dismally and most of the single-characteristic portfolios also performed below their longer-run averages. 3 Conclusion From a portfolio management perspective, there appears to be large gains to be had from pursuing diversi(cid:133)ed characteristic-based strategies. The Sharpe ratios obtained for the diversi(cid:133)ed portfolio are consistently large across all sub-samples and almost always greater than the Sharpe ratios for any of the single-characteristic portfolios. Of course, to the extent that these stock characteristics may actually represent priced risk factors, as has been analyzed in many studies (e.g., Fama and French, 1992, 1996), diversifying across the characteristics will not eliminate exposure to these risk factors. However, if the di⁄erent 5

characteristics represent, or load on, somewhat di⁄erent risk factors, the diversi(cid:133)cation should reduce the sensitivity to any given risk factor. References Asness, C.S., T.J. Moskowitz, and L. Pedersen. (cid:147)Value and Momentum Everywhere.(cid:148)Working Paper, Stern School of Business, New York University (2009). Brandt, M.W, P. Santa-Clara, and R. Valkanov. (cid:147)Parametric Portfolio Policies: Exploiting Characteristics in the Cross-Section of Equity Returns.(cid:148)Review of Financial Studies, 22 (2009), 3411-3447. Fama, E.F., and K.R. French. (cid:147)The Cross-Section of Expected Stock Returns.(cid:148)Journal of Finance, 47 (1992), 427-465. Fama, E.F., and K.R. French. (cid:147)Multifactor Explanations of Asset Pricing Anomalies.(cid:148)Journal of Finance, 51 (1996), 55-84. 6

Table 1: Correlations for the single-characteristic portfolios. The table reports the correlations of the monthly returns on the single-characteristic portfolios for the following seven characteristics: (i) Short-term reversals (ST-Rev), (ii) medium-term momentum (Mom), (iii) long-term reversals (LT-Rev), (iv) Book-to-market value (BM), (v) cash(cid:135)ow-price ratio (CP), (vi) earnings-price ratio (EP), and (vii) (cid:133)rm size (ME). Panel A reports the results for the full 1951-2008 sample, Panels B and C report the results for the (cid:133)rst and second halves of the sample and Panel D reports the results for the (cid:133)nal 10 years of the sample. ST-Rev Mom LT-Rev BM CP EP ME Panel A. Jul. 1951 - Dec. 2008 ST-Rev 1:000 Mom 0:565 1:000 (cid:0) LT-Rev 0:290 0:368 1:000 (cid:0) BM 0:083 0:064 0:504 1:000 (cid:0) (cid:0) CP 0:105 0:012 0:349 0:818 1:000 (cid:0) EP 0:108 0:028 0:267 0:768 0:893 1:000 (cid:0) ME 0:346 0:418 0:689 0:205 0:059 0:027 1:000 (cid:0) (cid:0) Panel B. Jul. 1951 - Dec. 1979 ST-Rev 1:000 Mom 0:538 1:000 (cid:0) LT-Rev 0:390 0:384 1:000 (cid:0) BM 0:243 0:355 0:771 1:000 (cid:0) CP 0:075 0:209 0:576 0:786 1:000 (cid:0) EP 0:011 0:141 0:523 0:715 0:868 1:000 (cid:0) ME 0:444 0:479 0:610 0:508 0:267 0:175 1:000 (cid:0) Panel C. Jan. 1980 - Dec. 2008 ST-Rev 1:000 Mom 0:580 1:000 (cid:0) LT-Rev 0:231 0:363 1:000 (cid:0) BM 0:261 0:108 0:301 1:000 (cid:0) CP 0:215 0:155 0:157 0:844 1:000 (cid:0) EP 0:176 0:129 0:067 0:805 0:912 1:000 (cid:0) ME 0:286 0:382 0:760 0:017 0:111 0:180 1:000 (cid:0) (cid:0) (cid:0) (cid:0) Panel D. Jan. 1999 - Dec. 2008 ST-Rev 1:000 Mom 0:608 1:000 (cid:0) LT-Rev 0:159 0:222 1:000 (cid:0) BM 0:346 0:283 0:138 1:000 (cid:0) CP 0:256 0:294 0:070 0:860 1:000 (cid:0) EP 0:206 0:243 0:060 0:871 0:927 1:000 (cid:0) ME 0:269 0:308 0:828 0:070 0:089 0:129 1:000 (cid:0) (cid:0) (cid:0) (cid:0) 7

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