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9 A summary: the evidence on managed portfolio performance and market efficiency.

The evidence on the performance of professionally managed portfolios relates to the classical question of the informational efficiency of the markets, as summarized by Fama (1970). This section first describes how these ideas are related and then presents some tables that summarize the empirical evidence.

9.1 Market Efficiency and Portfolio Performance

As emphasized by Fama (1970), any analysis of market efficiency involves a "joint hypothesis." There must be an hypothesis about the model for equilibrium expected returns and also an hypothesis about the informational efficiency of the markets. These can be described using the representation for asset pricing models in Equation (4.1). Assume that Equation (4.2) holds when the conditioning information is [[OMEGA].sub.t]:

E{[m.sub.t+1][R.sub.t+1]|[[OMEGA].sub.t]} = 1, (9.1)

where [[OMEGA].sub.t] refers to the information that is conditioned on by agents in the model, and in that sense "reflected in" equilibrium asset prices. (1) The hypothesis about the model of market equilibrium in the joint hypothesis amounts to a specification for the stochastic discount factor, [m.sub.t+1]. For example, the CAPM of Sharpe (1964) implies that [m.sub.t+1] is a linear function of the market portfolio return (e.g., Dybvig and Ingersoll, 1982), while multibeta asset pricing models imply that [m.sub.t+1] is a linear function of the multiple risk factors.

Equation (4.3) defines the SDF alpha, where we use the law of iterated expectations to replace [[OMEGA].sub.t] with the observable instruments, [Z.sub.t]. Note that if the SDF prices a set of "primitive" assets, [R.sub.t+1], then according to Equation (9.1) [[alpha].sub.pt] will be zero when a fund (costlessly) forms a portfolio of the primitive assets, if the portfolio strategy uses only information contained in [OMEGA] at time t. In that case [R.sub.p,t+1] = x([[OMEGA].sub.t])'[R.sub.t+1], where x([[OMEGA].sub.t]) is the portfolio weight vector. Then [[alpha].sub.pt] = E{[E([m.sub.t+1]x([[OMEGA].sub.t])[R.sub.t+1]|[[OMEGA].sub.t])] - 1|[Z.sub.t]} = E{x([[OMEGA].sub.t])'[E([m.sub.t+1][R.sub.t+1]|[[OMEGA].sub.t])] - 1|[Z.sub.t]} = E{x([[OMEGA].sub.t])'1 - 1|[Z.sub.t]} = 0. Informational efficiency of the market says that you cannot get a conditional alpha different from zero using any information that is contained in ?t.

Fama describes increasingly fine information sets in connection with market efficiency. Weak-form efficiency uses the information in past stock prices to form portfolios of the assets. Semi-strong form efficiency uses variables that are obviously publicly available, and strong form uses anything else. The different information sets described by Fama (1970) amount to different assumptions about what information is contained in [[OMEGA].sub.t]. For example, weak-form efficiency says that past stock prices cannot be used to generate alpha while semi-strong form efficiency says that other publicly available variables would not generate alpha.

In summary, informational efficiency says that you cannot get an alpha different from zero using any information [Z.sub.t] that is contained in [[OMEGA].sub.t]. Since alpha depends on the model through [m.sub.t+1], there is always a joint hypothesis at play. Indeed, any evidence in the literature on market efficiency can be described in terms of the joint hypothesis; that is, the choice of [m.sub.t+1] and the choice of the information [Z.sub.t].

How does the evidence on the performance of professionally managed portfolios relate to informational efficiency? All of the fund performance evidence can be described as examples of this simple framework. However, two complications arise with examples of fund performance. One is the issue of costs and the other relates to who is using the relevant information. With respect to costs, we use investment ability versus value added to distinguish performance on a before-cost versus after-cost basis. Studies of market efficiency also consider trading costs, and serious violations of efficiency are usually considered to be those that are observed on an after-cost basis. Thus, our concept of value added is closely related to market efficiency. (2) If we find that a manager has value added in a conditional model that controls for public information, this rejects a version of the joint hypothesis of semi-strong form efficiency. If we do not question the model for [m.sub.t+1] (and the associated OE benchmark) then we may interpret such evidence as a rejection of the informational efficiency part of the joint hypothesis.

The second complication relates to whether the portfolio manager or other investors are using the information in question. We have described efficiency in terms of the information in portfolio weights. At the fund level, managers use their information to form the fund's portfolio weights. Evidence about the performance of a fund therefore relates to the information used by the manager. However, much of the evidence in the literature on fund performance is described in terms of portfolio strategies that combine mutual funds. For example, a manager may use private information to deliver alpha, which speaks to strong form efficiency. If these alphas persist over time and investors can use the information in the past returns of the funds to form strategies that deliver value added performance, this speaks to weak form efficiency.

9.2 Mutual Fund Examples

This section presents a summary of the evidence on mutual fund performance. In Table 9.1 we use monthly returns data on individual funds over the 1973-2000 period. The data are the same as in Ferson and Qian (2004). Funds are grouped into five styles: growth, income, sector, small company growth, and timers. The latter category includes balanced funds and asset allocation style funds, those types most likely to be attempting to time the markets. (See Ferson and Qian, 2004 for more detail.) The number of funds with at least 24 monthly returns ranges from 545 sector funds to 2069 growth funds (data for sector and small company growth funds start in 1990). The average annual expense ratios range from 1.01% for the income funds to 1.65% for the sector funds. As discussed by Ferson and Qian (2004), expense ratios have trended up during the sample period.

The first performance measure is the Sharpe ratio. Over this period the monthly Sharpe ratios vary between -0.24 for income funds and 0.15 for market timers. The ratio for the CRSP stock market over this period is 0.12. Many funds turn in lower Sharpe ratios than the stock index. More than one third of the growth funds and timers have lower Sharpe ratios than the index, while more than 85% of the small firm growth funds have lower ratios. Of course, the Sharpe ratio does not reflect portfolio diversification benefits that funds may offer, so we cannot conclude from a low ratio than investors would wish to shun these funds.

The next measure is Jensen's alpha. The averages range between -0.10% per month for timing funds to 0.21% for the sector funds. The results for the sector funds reflect only the 1990-2000 period, during the "dot com" boom. Over longer sample periods alphas tend to be negative on average, and we find negative average alphas for four of the five style groups. To interpret these figures, recall the joint hypothesis related to market efficiency. The model of market equilibrium assumes that the stochastic discount factor, m, is linear in the market index return, as in the CAPM. As a result, the OE portfolio is the market index adjusted with a fixed allocation to cash. These figures say that the mutual funds--with the possible exception of the sector funds--delivered no value added, or after cost return over this period, to an investor holding the market index and cash who ignores taxes and who pays negligible transactions costs for holding the market index and cash. The averages hide the fact that many funds have negative alphas. More than 56% of the growth funds and more than 38% of the sector funds had negative alphas. Thus, an investor selecting even among the sector funds faces a significant risk of choosing a negative alpha fund. While the evidence in the literature on the persistence of funds' alphas is mixed, our reading of the literature suggests that much of the ability of past alpha to predict future alpha, resides in the negative alpha funds. So, it may be difficult for investors to capture the small value added that these figures might suggest, even for the sector funds.

If we add back the funds' average expense ratios to the alphas, the pre-expense ratio performance averages about 1.64% per year. Maintaining the market index as a good benchmark, we can interpret this figure as evidence of investment ability, on average, among the fund managers.

The table also reports style-based alphas, where the market index is replaced with a fund style-group specific benchmark. The style indexes are formed as in Ferson and Qian (2004), as portfolios of eight asset class returns that range from short term Treasuries, to corporate bonds, to portfolios of value and growth stocks. The weights used in the portfolio are estimated separately for each fund style group. (See Ferson and Qian for details.) The style alphas are less negative than the market-based alphas on average, and smaller fractions of the funds deliver negative style alphas. Sector funds and small firm growth funds, in particular, look better with a style benchmark. Part of this may reflect the poor relative performance of small stocks during the 1990s, so using a benchmark that puts more weight on small stocks and less weight on large stocks makes these funds look better.

The next measure is the conditional CAPM alpha of Ferson and Schadt (1996). We report the averages of the regression R-squares for the conditional model regression. These may be compared with the R-squares of the Jensen's alpha regression. The difference reflects the explanatory power of the interaction terms between the market index and the lagged conditioning variables, which captures time-variation in the conditional betas. The improvement in the R-squares is on the order of 5%-12%, which is evidence of time-varying fund betas. This is consistent with the findings in the literature, that mutual funds' betas tend to vary over time.

The conditional alphas in Table 9.1 are a little more optimistic about fund performance than the Jensen's alphas in many, but not all, of the cases. For the two fund groups measured over 1990-2000, the average is 26 basis points per month; for the three groups measured over 1973-2000, the average is -7 basis points per month. The fractions of individual funds with negative alphas range between 36% and 70%. Previous studies over different sample periods typically find negative Jensen's alphas and conditional alphas closer to zero, suggesting neutral value added on average. Our figures are broadly consistent with this. The interpretation of the conditional alphas is similar to that of Jensen's alpha, except now the OE portfolio combines the market index and cash with a time-varying weight that reflects a fund's time-varying beta.

The next two measures explore market timing ability. The unconditional measure is the coefficient on the squared market excess return in the Treynor-Mazuy (1966) quadratic timing regression. The average estimates are negative for three of the five style groups. Large fractions of the individual funds have negative timing coefficients: ranging from just over half of the income funds to more than 90% of the small company growth funds. This evidence is broadly consistent with much of the literature, which often interprets this as poor timing performance.

The next measure is a conditional version of the timing coefficient, based on Ferson and Schadt's generalization of the Treynor-Mazuy regression. Consistent with previous studies, the conditional timing coefficients present a slightly less negative impression about timing ability. Smaller fractions of the funds turn in negative conditional timing coefficients in each style group, and about 2/3 of the funds in the timing group record positive coefficients, but the differences are not great. Previous studies over different time periods also find slightly better results with respect to conditional timing coefficients (e.g., Becker et al., 1999), but it still seems puzzling to find so many funds that pursue market timing strategies without clear evidence of success with such strategies.

We do not present results using weight-based measures in Table 9.1. Weight-based measures of performance construct hypothetical returns using the funds reported portfolio holdings and returns data on the underlying securities. Thus, trading costs and expenses are not accounted for. The early measures typically produced returns larger than the returns of the benchmarks, the difference often being on the order of funds' expense ratios. This again suggests the presence of investment ability, but not value added. While the evidence is sparse using conditional weight-based measures, the conditional weight-based performance of pension funds, as measured by Ferson and Khang (2002), is close to zero. This suggests that the investment ability of pension funds can largely be captured through publicly available information. We think that more research is needed using conditional weight-based models to address this question for other kinds of funds.

The literature has found mixed evidence on the question of the persistence of fund performance. Persistence is the crucial issue for investors who wish to find high-return funds: Can a fund that performed relatively well in the past be expected to do so again in the future? It seems that certain characteristics of mutual funds, such as their levels of volatility and style choices, have some persistence over time. But, aside from effects such as momentum that can largely be explained by funds holdings of momentum stocks, the evidence suggests that good performance does not persist to any reliable degree. Perhaps, the best use of past relative performance information in mutual funds is to avoid persistently poor performers.

9.3 Hedge Fund Examples

The performance of hedge funds looked promising when academics studies first began to explore it empirically, as hedge funds delivered large alphas in traditional linear beta models. The unique incentive structures and other aspects of the industry suggested that the better managers may be found in this sector. However, as this literature has matured, it may be that the large alphas of hedge funds can be explained through a combination of data biases, such as survivor selection and backfilling, dynamic trading and nonlinear payoffs, asset illiquidity and infrequent trading.

This section presents a summary of the evidence on hedge fund performance. We use monthly returns data on individual funds over the 1994-2005. The data are provided by Lipper/TASS, which is one of the major hedge fund databases used in the literature. We consider both live funds and those funds that have disappeared from the database prior to December 2005. Net returns have already been reduced by the management and performance fees paid by investors to the fund manager, and by the costs of trading. Funds are grouped into one of eleven style categories based upon self-reported primary style categories. These include: Convertible Arbitrage (CA), Dedicated Short Bias (DSB), Emerging Markets (EM), Equity Market Neutral (EMN), Event Driven (ED), Fixed Income Arbitrage (FIA), Fund of Funds (FOF), Global Macro (GM), Long/Short Equity Hedge (LS), Managed Futures (MF), and Multi-Strategy (MS). As discussed in Section 7.1.2, funds typically bring a history of returns data with them upon being added to the databases, thereby creating a potential backfilling bias. We therefore restrict the analysis to nonbackfilled data.

Table 9.2 shows that the number of funds with at least 24 monthly returns ranges from 24 in the DSB group to 1062 for the LS group. The average percentage management and performance fees range from 1.2% to 2.3% and 9.1% to 19.5%, respectively. The proportion of funds that use a high watermark to calculate performance fees ranges from 28% (MF) to 66% (FIA).

The first performance measure is the Sharpe Ratio. Over this period the average monthly Sharpe ratios range from -0.03 for short sellers to 0.42 for Fixed Income Arbitrage funds. The majority of funds deliver Sharpe Ratios exceeding that of the market index for nearly all style categories. The lone exception is the Global Macro category, for which only 46% of funds beat the market Sharpe Ratio. Overall, this suggests that stock market investors could have improved their asset allocation by investing in the hedge fund industry during this period.

The next measure is Jensen's alpha. For all style categories, the nonbackfilled alpha is positive on average and also positive for the majority of funds. For example, the average monthly alpha is 0.11% for Global Macro funds and 0.48% for the Emerging Markets category. These results say that hedge funds appear to have delivered positive value added to an investor holding the market index and cash. This contrasts with the evidence of the previous section that mutual funds deliver no value added to an investor who passively holds the market index and cash. However, our conclusions for hedge funds are subject to the caveat that the Jensen's alpha calculation ignores the differences in tax efficiency and, as we shall soon examine, liquidity provision between a hedge fund and its OE benchmark.

The table also reports style-based alphas, where the market index is replaced with a fund style-group specific benchmark. The style benchmark used for funds within a category is formed as a value-weighted portfolio of a sub-sample funds within that category. Benchmark returns are provided by Lipper/TASS. The style benchmarks explain much more of the variation in hedge fund returns as compared to the market index. The change in the average adjusted-[R.sup.2] ranges from -6% (EMN) to 35% (CA) across style groups. The style alphas are lower on average than the market-based alphas, and a greater fraction of funds deliver negative style alphas for all groups. Event Driven and Fund of Funds, in particular, look worse with a style benchmark. Overall, however, the average alpha is positive for most style groups.

The lagged market model is intended to reduce the potential bias in estimated alpha due to non-synchronous trading of the fund's underlying assets. The higher average adjusted-[R.sup.2] for most style groups indicates the presence of infrequent trading hedge fund assets. Also, the model delivers much lower average alphas for Convertible Arbitrage (0.28%-0.18%), Emerging Markets (0.48%-0.25%), and Fixed Income Arbitrage (0.24%-0.09%) style groups. These groups are those with which illiquid assets are commonly associated (see, e.g., Asness et al., 2001).

The next measure examines market timing ability. The unconditional timing measure is the coefficient in the Merton and Henriksson (1981) timing model (see Equation (2.6)). The average estimates are negative for seven of the eleven style groups, indicating that hedge funds market beta is actually lower during up-markets as compared to down-markets. However, the fractions of funds with negative timing coefficients are centered more closely around 50% across style groups, as compared to the mutual fund findings reported in the previous section. Taken together, the evidence is broadly consistent with much of the mutual fund literature, which often finds either neutral or poor timing performance.

The previous results ignore the illiquidity of a typical hedge fund share. Yet, many hedge funds impose restrictions on investor redemptions, such as lockups and redemption notice periods, thereby making hedge funds an illiquid investment. Investors may therefore expect higher returns on funds with share restrictions, commensurate with the illiquidity they bear. As discussed in Section 8.7.5, Aragon (2007) finds this to be true for hedge funds during 1994-2001. We follow Aragon (2007) and calculate liquidity-adjusted performance, equal to the raw performance less a liquidity premium given the fund's share restrictions. This involves a two-step procedure in which the performance estimates (e.g., Sharpe Ratio, Jensen's alpha) from the first step are used as dependent variables in the cross-section regression

[a.sub.p] = [[PI].sub.0] + [[PI].sub.1]DLOC[K.sub.p] + [[PI].sub.2]NOTIC[E.sub.p] + [[PI].sub.3][(NOTIC[E.sub.p]).sup.2] + [W.sub.p], (9.2)

where [a.sub.p] is an estimate of fund performance, DLOCK is an indicator that equals one if the fund has a lockup provision and zero otherwise, and NOTICE is the number of days advance notice the fund requires an investor to redeem his shares. A fund's liquidity-adjusted performance is just the sum of the intercept and fund residual in Equation (9.2). The coefficients in Equation (9.2) could be interpreted as in Fama and MacBeth (1973) cross-sectional regressions, as premiums on share illiquidity factors. The presence of a quadratic term in Equation (9.2) is motivated by Amihud and Mendelson (1986). They argue that, if more illiquid assets are held by investors with longer investment horizons, then the relation between expected returns and illiquidity will be positive and concave.

Table 9.3 reports summary information for the liquidity-adjusted performance for each style group. On average, funds within the Managed Futures and Event Driven groups impose the lightest and heaviest liquidity restrictions, respectively. For example lockup usage is only 2% for MF, as compared to 40% for the ED funds. Meanwhile, the average ED fund requires about 48 days for share redemption as compared to only one week's notice for the MF category.

Consistent with Aragon (2007), we find a positive relation between share restrictions and performance. Liquidity-adjusted Sharpe Ratios are lower for every style group. Although the Sharpe Ratio drops from 0.05 to 0.03 for MF funds, the ED category experience a reduction of 0.19 after controlling for share liquidity. The coefficients on the lockup ([[PI].sub.1]) and redemption notice ([[PI].sub.2]) variables are positive and significant. The proportion of liquidity-adjusted Sharpe Ratios falling below that of the market index is now centered at 50% across style groups. Thus, the liquidity adjustments appear to remove the evidence that hedge funds offer large Sharpe ratios.

In Table 9.3 the average liquidity-adjusted alphas are positive for only six of the hedge fund style groups, and they are lower for every category as compared to the unadjusted performance results. This can be explained by a 0.14% monthly lockup premium and a 0.25% average monthly premium per 30-day redemption notice period. The average liquidity-adjusted lagged market model alpha is negative for eight of the eleven style groups, and the average alpha across all funds is -0.12% per month. Overall, the evidence suggests that hedge funds do not deliver positive value-added to stock market investors, over and above the compensation for share restrictions.

Finally, we do not find a significant relation between hedge fund market timing ability and hedge fund share restrictions. This explains why the last rows in Table 9.3 are qualitatively similar to those in Table 9.2.

(1) If [X.sub.t+1] is the payoff and [P.sub.t] is the price, then [R.sub.t+1] = [X.sub.t+1]/[P.sub.t] and Equation (*) says that [P.sub.t] = E{[m.sub.t+1][X.sub.t+1]|[[OMEGA].sub.t]}. The equilibrium price is the mathematical conditional expectation of the payoff given [[OMEGA].sub.t], "discounted" using [m.sub.t+1]. In the language of Fama (1970), this says that the price fully reflects [[OMEGA].sub.t].

(2) Grossman and Stiglitz (1980) point out that no one would expend resources to gather information if it did not pay to trade on it. So, it would be hard to imagine an efficient market if no one had investment ability. Investors only see mutual fund returns after the managers have been paid out of the fund's assets. The question of how fund managers are paid for their investment ability has to do with the efficiency of the labor market for fund managers. The value added for investors, on the other hand, is traditionally the central issue for studies of the efficiency of financial markets.
Table 9.1 Summary of mutual fund performance evidence.

Fund style             Growth    Income    Sector   Small-firm   Timers

N                      2069      1137      545      811          799
Avg. expense ratio        1.41      1.01     1.65     1.54         1.27
Sharpe Ratios
Average                   0.14     -0.24     0.13     0.13         0.15
% < Market               33.6      68.9     77.1     85.1         31.3

Jensen's Alphas
Average (%)              -0.04     -0.05     0.21    -0.00        -0.1
Percent < 0              55.9      75.1     38.1     57.0         71.2
Avg. regression          73.8      28.2     36.6     53.3         73.7
 [R.sup.2]

Style Alphas
Average (%)               0.04     -0.06     0.36     0.11         0.04
Percent < 0              45.6      68.0     26.2     47.6         44.3

Conditional CAPM
 [alpha]
Average (%)               0.01     -0.1      0.27     0.25        -0.11
Percent < 0              55.9      66.6     36.3     46.9         70.1
Avg. regression          78.4      41.3     44.8     58.7         78.3
 [R.sup.2]

Unconditional Timing
Avg. coefficient         -0.25      0.24    -1.23    -1.94         0.12
Percent < 0              54.8      54.4     69.0     91.8         38.5

Conditional Timing
Avg. coefficient         -0.11      0.39    -1.24    -1.89         0.18
Percent < 0              50.6      54.4     67.7     89.8         36.5

Note: The sample starts in January of 1973 or later, depending on the
fund group, and ends in December of 2000. The lagged conditioning
variables for the conditional models are a 3-month Treasury yield,
term slope, dividend/price ratio for the CRSP value-weighted stock
market, a credit-related yield spread and a spread of 90-day commercial
paper over treasury yields. N is the number of funds with at least 24
monthly returns. Alphas are reported in percent per month. The average
expense ratios are shown, in annual percent. The average R-squares are
shown for the regressions estimating alphas, in percent. The
conditional CAPM alpha is estimated using the Ferson and Schadt (1996)
model. The unconditional timing model is the Treynor-Mazuy regression,
where the coefficient on the squared market excess return is
summarized. The conditional timing model is the conditional
Treynor-Mazuy model developed by Ferson and Schadt.

Table 9.2 Summary of hedge fund performance evidence.

Fund style         CA       DSB     EM       EMN      ED       FIA

N                  129      24      212      175      267      140
Average Fees
Management fee       1.3     1.2      1.5      1.3      1.3      1.2
Incentive fee       18.4    19.0     16.8     19.3     18.7     19.5
Highwater-mark       0.63    0.58     0.43     0.61     0.63     0.66

Sharpe Ratios
Average              0.37   -0.03     0.23     0.17     0.34     0.42
% < Market           0.36    0.50     0.37     0.40     0.20     0.29

Jensen's Alphas
Average (%)          0.28    0.28     0.48     0.19     0.43     0.24
Percent < 0          0.21    0.33     0.26     0.28     0.15     0.16
Avg. regression      0.04    0.51     0.17     0.08     0.12     0.02
 [R.sup.2]

Style Alphas
Average (%)          0.06    0.15     0.13     0.13    -0.07     0.16
Percent < 0          0.33    0.42     0.36     0.30     0.44     0.20
Avg. regression      0.39    0.54     0.38     0.02     0.29     0.14
 [R.sup.2]

Lagged Market Model Alphas:
Average (%)          0.18    0.43     0.25     0.16     0.33     0.09
Percent < 0          0.26    0.29     0.30     0.31     0.16     0.21
Avg. regression      0.06    0.53     0.19     0.09     0.19     0.07
 [R.sup.2]

Unconditional Timing
Avg. coefficient     0.09    0.21    -0.69     0.03    -0.18    -0.05
Percent < 0          0.27    0.38     0.66     0.45     0.68     0.44
Avg. regression      0.07    0.51     0.18     0.09     0.14     0.04
 [R.sup.2]

Fund style         FOF      GM       LS        MF       MS

N                  790      168      1062      369      115
Average Fees
Management fee       1.5      1.5       1.2      2.3      1.4
Incentive fee        9.1     18.0      18.9     17.9     18.1
Highwater-mark       0.44     0.46      0.61     0.28     0.61

Sharpe Ratios
Average              0.26     0.08      0.18     0.05     0.31
% < Market           0.30     0.54      0.32     0.47     0.23

Jensen's Alphas
Average (%)          0.18     0.11      0.43     0.21     0.47
Percent < 0          0.20     0.30      0.22     0.30     0.12
Avg. regression      0.16     0.06      0.21     0.06     0.13
 [R.sup.2]

Style Alphas
Average (%)         -0.19    -0.41     -0.02     0.03     0.13
Percent < 0          0.56     0.53      0.40     0.33     0.25
Avg. regression      0.45     0.11      0.25     0.33     0.16
 [R.sup.2]

Lagged Market Model Alphas:
Average (%)          0.05    -0.08      0.30     0.18     0.38
Percent < 0          0.27     0.36      0.28     0.29     0.18
Avg. regression      0.23     0.07      0.24     0.06     0.17
 [R.sup.2]

Unconditional Timing
Avg. coefficient    -0.19    -0.10     -0.25     0.34    -0.17
Percent < 0          0.64     0.42      0.60     0.18     0.49
Avg. regression      0.17     0.06      0.22     0.08     0.14
 [R.sup.2]

Note: The sample starts in January 1994 or later, depending on the
fund, and ends in December 2005. The estimation excludes all return
observations that precede the data the fund was added to the database.
Fund styles are Convertible Arbitrage (CA), Dedicated Short Bias (DSB),
Emerging Markets (EM), Equity Market Neutral (EMN), Event Driven (ED),
Fixed Income Arbitrage (FIA), Fund of Funds (FOF), Global Macro (GM),
Long/Short Equity (LS), Managed Futures (MF), and Multi-Strategy (MS).
N is the number of funds with at least 24 monthly returns. Alphas are
reported in percent per month. The average management and incentive
fees are shown, in annual percent. High watermark equals one if the
fund uses a high watermark to calculate incentive fees. The average
R-squares are shown for the regressions estimating alphas, in percent.
The lagged market model is the Jensen's alpha regression including
three lags of the market excess return. The timing model is the
Henriksson-Merton regression, where the coefficient on the positive
part of the market excess return is summarized.

Table 9.3 Summary of liquidity-adjusted hedge fund performance evidence.

Fund style         CA      DSB     EM      EMN     ED      FIA

Liquidity Variables
Lockup?             0.25    0.25    0.17    0.22    0.40    0.23
Notice (days)      39.0    26.3    27.2    27.4    48.4    37.1

Sharpe Ratios
Average             0.21   -0.14    0.12    0.06    0.15    0.28
% < Market          0.48    0.75    0.52    0.59    0.40    0.41

Jensen's Alphas
Average (%)        -0.04    0.04    0.27   -0.04    0.10   -0.04
Percent < 0         0.54    0.54    0.32    0.47    0.37    0.36

Style Alphas
Average (%)        -0.11    0.04    0.01    0.01   -0.26    0.00
Percent < 0         0.57    0.42    0.39    0.47    0.65    0.34

Lagged Market Model Alphas
Average (%)        -0.21   -0.13   -0.02    0.12   -0.08   -0.27
Percent < 0         0.64    0.58    0.38    0.58    0.48    0.47

Unconditional Timing
Avg. coefficient   -0.11   -0.22   -0.67    0.05   -0.16   -0.03
Percent < 0         0.26    0.38    0.64    0.40    0.63    0.39

Fund style         FOF     GM      LS      MF     MS

Liquidity Variables
Lockup?             0.18    0.10    0.33   0.02    0.29
Notice (days)      37.4    17.8    30.0    6.4    32.1

Sharpe Ratios
Average             0.11    0.01    0.05   0.03    0.17
% < Market          0.54    0.67    0.54   0.51    0.33

Jensen's Alphas
Average (%)        -0.10   -0.06    0.15   0.15    0.19
Percent < 0         0.51    0.42    0.37   0.30    0.33

Style Alphas
Average (%)        -0.35   -0.49   -0.15   0.00   -0.02
Percent < 0         0.71    0.58    0.47   0.36    0.42

Lagged Market Model Alphas
Average (%)        -0.31   -0.29   -0.04   0.10    0.04
Percent < 0         0.66    0.51    0.45   0.32    0.46

Unconditional Timing
Avg. coefficient   -0.17   -0.09   -0.24   0.34   -0.15
Percent < 0         0.60    0.42    0.58   0.18    0.46

Note: The sample starts in January 1994 or later, depending on the
fund, and ends in December 2005. The estimation excludes all return
observations that precede the data the fund was added to the database.
Fund styles are Convertible Arbitrage (CA), Dedicated Short Bias (DSB),
Emerging Markets (EM), Equity Market Neutral (EMN), Event Driven (ED),
Fixed Income Arbitrage (FIA), Fund of Funds (FOF), Global Macro (GM),
Long/Short Equity (LS), Managed Futures (MF), and Multi-Strategy (MS).
N is the number of funds with at least 24 monthly returns. Alphas are
reported in percent per month. The lagged market model is the Jensen's
alpha regression including three lags of the market excess return. The
timing model is the Henriksson-Merton regression, where the coefficient
on the positive part of the market excess return is summarized. The
table summarizes liquidity-adjusted coefficients. The
liquidity-adjusted coefficient equals [adj.sub.p] =
[[alpha].sub.p]-[[[PI].sub.1][DLOCK.sub.p] + [[PI].sub.2][NOTICE.sub.p]
+ [[PI].sub.3] [([NOTICE.sub.p]).sup.2]], where [[PI].sub.1],
[[PI].sub.2], and [[PI].sub.3] are the estimated coefficients of the
following cross-sectional regression:

[[alpha].sub.p] = [[PI].sub.0] + [[PI].sub.1][DLOCK.sub.p] +
[[PI].sub.1][NOTICE.sub.p] + [[PI].sub.3][([NOTICE.sub.p]).sup.2] +
[w.sub.p],

where [[alpha].sub.p] is an estimate of fund p's performance, DLOCK is
an indicator variable that equals one if the fund has a lockup, and
NOTICE is the redemption notice period.
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Title Annotation:Portfolio Performance Evaluation
Author:Aragon, George O.; Ferson, Wayne E.
Publication:Foundations and Trends in Finance
Geographic Code:1USA
Date:Apr 1, 2006
Words:5691
Previous Article:8 Recent empirical evidence.
Next Article:10 Conclusions.
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