# Tilted Portfolios, Hedge Funds, and Portable Alpha

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2 2 Dimensional Fund Advisors Inc. Original Portfolio Market Portfolio Hedge Portfolio Small \$15,000 \$10,000 Long \$5,000 Big 85,000 90,000 Short 5,000 Total Value \$100,000 \$100,000 \$0 This is a general result. We can always decompose a portfolio into its benchmark plus a hedge portfolio of the deviations from the benchmark. Note that the hedge portfolio in our example requires no net investment. The long position in small stocks is financed by shorting big stocks. This is also a general result. Because every extra dollar spent overweighting some stocks in the original portfolio must come from underweighting others, the hedge portfolio that reproduces the original portfolio s deviations from the market (or any other benchmark) always requires no net investment. (In fact, zero net investment is what academics mean when we say something is a hedge portfolio.) Hedge portfolios like this are at the heart of what is called portable alpha. An active manager tries to add value by deviating from the benchmark, underweighting some stocks and overweighting others. The hedge portfolio of his under- and overweights is his contribution to the investor s overall return. Thus, the argument goes, by decomposing his portfolio into the benchmark and a hedge portfolio, an investor can get his market exposure from one manager and his alpha from another. This logic leads to a natural question. Why doesn t Dimensional offer hedge funds that would give clients unadulterated exposure to the size and value premiums? The simple answer, developed in more detail below, is that mutual funds are a more flexible and lower-cost medium for obtaining the tilts than hedge funds, at least as typically constructed. The Three-Factor Model The three-factor model of Fama and French (1993) describes stock returns in terms of the returns on the market portfolio and two hedge portfolios, R jt R ft = a j + b j (R Mt R ft ) + s j SMB t + h j HML t + e jt. In this equation, R jt is the return for period t on portfolio j, R Mt is the market return, and R ft is the risk-free (Treasury bill) return. SMB t is the return on a diversified portfolio of small stocks minus the return on a diversified portfolio of big stocks. HML t is the return on a diversified portfolio of high book-to-market (value) stocks minus the return on a diversified portfolio of low book-to-market (growth) stocks. The coefficients b j, s j, and h j are sensitivities, or loadings, or exposures to the three risk factors. The residual e jt is (by definition) random noise in the return on j for period t; and a j, the alpha of

3 Tilted Portfolios, Hedge Funds, and Portable Alpha 3 the three-factor model, is the average return on j that is not explained by the exposures of the return on j to the three risk factors. If the model captures expected returns, a j should be zero for all securities and portfolios. The size (SMB t ) and value/growth (HML t ) returns in the three-factor model can be viewed as hedge fund returns. Thus, SMB t can be viewed as the return on a hedge fund that is long small stocks and finances this position by shorting big stocks. Similarly, HML t can be viewed as the return on a hedge fund that is long value stocks, financing this position by shorting growth stocks. In terms of average returns, SMB t and HML t hedge funds are attractive. For the seventynine years from 1927 to 2005, the average SMB t return is 3.72% per year and the average HML t return is 5.01% per year. The SMB t and HML t returns also are not highly correlated with the overall stock market return, so they are largely market neutral. On a year-to-year basis, however, the returns have lots of volatility. The standard deviation of the annual SMB t return is 14.47% and the standard deviation of the HML t return is 13.95%. This volatility is to be expected; in an efficient market, high expected returns come at the expense of high risks. The Fama/French story is that the size and value premiums in average returns are rewards for bearing risk. And the fact that the SMB t and HML t returns are quite volatile is a general characteristic of market-neutral hedge fund returns. Hedge Fund Problems What is the most efficient way to trade risk for expected return? We argue that hedge funds are not the answer. The first problem with hedge funds is the high cost of shorting stocks. SMB and HML funds would be short big and growth stocks, respectively, and these short positions would involve substantial trading and holding costs. Moreover, for most and perhaps all of our investors, the costs of shorting would be completely wasted. The short positions would just reverse long positions in the rest of their portfolio. The portfolio we describe above, for example, is long \$90,000 in big stocks (in the market portfolio) and short \$5,000 in the same stocks (in the hedge fund). It is hard to justify the high costs of simultaneously buying and shorting the same big stocks, or of maintaining offsetting long and short positions. It gets worse. If Dimensional were to offer SMB and HML hedge funds, the management fees would have to be at least twice the fees for existing mutual funds in similar size ranges. The reason is that both the long and short positions of hedge funds must be managed, and managing the short side is at least as costly, in terms of Dimensional s time and effort (trading, monitoring, etc.) as managing the long side. Again, if one does not want a net short position in big stocks or growth stocks, it is cheaper to build a portfolio with long positions in Dimensional s existing mutual funds.

5 Tilted Portfolios, Hedge Funds, and Portable Alpha 5 For concrete perspective on this issue, Figure 1 plots annual returns from 1927 to 2005 for a hedge fund that levers HML four times. (The fund return is just HML times four.) The levered fund self-destructs (returns are less than -100%) three times during the period, 1934, 1980, and We suspect that runs on the levered fund would also cause it to bomb in the five additional years when its return is below -50%. In the end, the fund is likely to die in eight of seventy-nine sample years, or about 10% of the time. (According to the academic literature on survival rates among hedge funds, this estimate of the likely death rate is not high.) And if the coffin needs another nail, the returns shown in Figure 1 are before fees and expenses. The 2% annual management fee drops hedge fund returns by this amount every year, and taking 20% of the returns above LIBOR shrinks the expected payoff even more. Figure 1 Levered HML (x4) Returns What attracts investors to high-leverage hedge funds? The answer is clear from Figure 1. Leverage is as powerful on the upside as on the downside. There are many years, and often several years in a row, when the levered hedge fund in Figure 1 has spectacular returns. For example, in eight of seventy-nine years (most recently in 2000), the return on the levered fund exceeds 90%. Over the last six years, the returns of the levered fund are less than 30% just once. Given the way investors chase returns, one can confidently predict massive flows into levered hedge funds after such spectacular performance. In sum, even when the target portfolios of Dimensional clients involve tilts toward small stocks and/or value stocks, we doubt that the targets commonly (if ever) involve

6 6 Dimensional Fund Advisors Inc. short positions in big stocks or growth stocks. Thus, because of their short positions, SMB and HML hedge funds (even hedge funds that are not levered) are an inefficient way to obtain tilts toward small and value stocks. When SMB and HML hedge funds are highly levered (to justify high fund management fees), a strong caveat emptor is appropriate: when bad luck strikes, investments in such funds are likely to be hazardous to your wealth. Finally, if you would like to see a careful study of the historical performance of hedge funds, we recommend Hedge Funds: Risk and Return, by Malkiel and Saha (2005). References Fama, Eugene F. and Kenneth R. French The cross-section of expected stock returns. Journal of Finance 47 (June): Common risk factors in stock and bond returns. Journal of Financial Economics 33 (1): Malkiel, Burton G. and Atanu Saha Hedge funds: Risk and return. Financial Analysts Journal 61 (November/December): Available in

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