Are hedge fund returns predictable?

Are Hedge Fund Returns Predictable? by Robert J. Bianchi1 and Thanula Wijeratne2 Griffith Business School Dept. of Accounting, Finance and Economics Nathan campus, Griffith University 170 Kessels Road, Nathan Brisbane, Queensland, 4111 Australia This article has been published in JASSA The Finsia Journal of Applied Finance, 2009, Issue 4, pp. 17-23. ABSTRACT While earlier empirical research found that stock, bond and hedge fund returns can be predicted with conventional financial and economic variables, recent econometric studies have shown that predictive regressions are spurious when the forecasting instrument is a non-stationary variable. After examining the predictability of hedge fund index returns with stationary forecasting variables, our findings suggest that the forecasting variables discovered in previous studies are statistically insignificant at predicting hedge fund index returns. 1 Dr Robert Bianchi is a Senior Lecturer at the Department of Accounting, Finance and Economics, Griffith Business School, Griffith University, Brisbane, Australia and is a director of H3 Global Advisors Pty Ltd, a boutique fund manager in Sydney, Australia. Email: r.bianchi@griffith.edu.au 2 Thanula Wijeratne is an Analyst in Global Fixed Interest at Queensland Investment Corporation, Brisbane, Australia. Email: t.wijeratne@qic.com 1 INTRODUCTION The ability to forecast financial market returns can be economically significant in the areas of tactical asset allocation and other forms of active asset management. Predicting stock and bond returns has become the holy grail of funds management and legions of researchers have allocated tremendous resources towards this effort. In the past 20 years, empirical researchers such as Keim and Stambaugh (1986), Campbell (1987) and Fama and French (1989) discovered that economy-wide variables (such as the U.S. Treasurybill rate, term spread, term structure of interest rates, default spread and dividend yield) exhibit predictive power in explaining the variability of equity and bond market returns. Subsequent studies by Kandel and Stambaugh (1996), Campbell and Viceira (2001) and Fleming, Kirby and Ostdiek (2001) have found that shifts in asset allocation from these predictive variables are economically significant even when the forecasting variable exhibits low forecasting power or R 2 . The empirical evidence that stock and bond returns can be predicted has led other researchers to examine whether these same forecasting variables can be employed to forecast hedge fund returns. Seminal hedge fund studies by Fung and Hsieh (2004) and Agarwal and Naik (2004) have shown that a large proportion of the variation of hedge fund returns can be explained by market related factors, however, these replication models cannot be employed to forecast hedge fund returns. The emergence of hedge fund forecasting models by Amenc, El Bied and Martellini (2003) and Hamza, Kooli and Roberge (2006) have revealed that hedge fund returns can be predicted with economywide variables including the equity returns, VIX volatility index, oil prices, changes in market volume and U.S. Treasury bill rates. The empirical studies mentioned thus far support the concept that these forecasting variables capture time-varying risk premiums in the market. However, is this evidence as statistically convincing as it appears to be? If stock, bond and hedge fund returns are truly predictable, why haven’t these forecasting models been applied out-of-sample to achieve abnormal profits for active fund managers in the global funds management industry? SPURIOUS REGRESSIONS A new body of research has emerged that criticises the econometric techniques employed in predictive models in finance. Ferson, Sarkissian and Simin (2003) have highlighted the econometric problem of the persistence and nonstationarity of ordinary least squares (OLS) regressors and have cast doubt on the evidence of predictability. When an OLS regression of returns is estimated on the lag of a predictive variable that is persistent (ie. nonstationary), it results in a nonstandard distribution which causes an over-rejection of the null hypothesis. As a consequence, the predictive variable seems to exhibit predictability when in fact the entire exercise is a spurious regression. The subsequent studies by Lanne (2002), Torous, Valkanov and Yan (2004), Goyal and Welch (2007), Boudoukh, Richardson and Whitelaw (2009) and Ang and Bekaert (2007) have confirmed this weakness in previous empirical finance studies. These findings suggest 2 that many of the models that employ nonstationary forecasting variables to predict stock, bond and hedge fund returns may in fact be erroneous. STATIONARY VS NONSTATIONARY DATA To highlight this problem, it is important to understand the difference between stationary and nonstationary time series data. Stationary time series is data that exhibits a constant mean and variance which does not change through time and is referred to as timeinvariant. This means that a probability distribution for the data is the same regardless at what point in time the data is sampled from. As a consequence, the estimated coefficients from an OLS regression will tend to exhibit stable parameters and reliable statistical inference from their standard errors. In contrast, nonstationary data exhibits a mean and variance that is dependent on the time period in which the data is sampled from. As a result, the estimated coefficients from an OLS regression are spurious. Many economic statistics are nonstationary in nature as they tend to steadily grow over time. Examples of nonstationary data include gross domestic product, consumer price index and hourly wages over time. Hypothesis tests known as unit root tests have been developed to test the stationarity of time series data. Some of these include the Dickey and Fuller (1979) DF test and the augmented DickeyFuller (ADF) test which can control for autocorrelation in the error terms of the hypothesis test. To solve this data problem, it is possible to convert a nonstationary times series data into stationary data through the process of differencing the data and constructing the first difference, ie. xt − xt −1 or by calculating arithmetic or log returns from the data. The difference between stationary and nonstationary data can be easily demonstrated by example with the oil spot market. Figure 1 illustrates oil spot prices that are nonstationary in nature as the estimated mean and variance will be dependent upon the time period you sample from. We calculate the ADF hypothesis test based on the null hypothesis of nonstationarity and we report a test statistic of 1.268 which is greater than the ADF critical value of -3.470, thus we cannot reject the null hypothesis of nonstationarity. Figure 2 illustrates the same data as Figure 1 but the oil spot prices are converted to log or continuous compounded returns. The ADF test statistic for the time series data in Figure 2 is -13.712 which is below the critical value of -3.470 which signifies that we can reject the null hypothesis of nonstationarity and report that oil returns are indeed stationary. This simple transformation of the data alleviates the problem of nonstationarity and allows the researcher to genuinely examine whether financial and economic data can truly forecast hedge fund returns. In light of this, we can re-assess the stationary nature of forecasting variables that have been reported to predict hedge fund returns. 3 Figure 1: West Texas Intermediate Oil Prices – nonstationary time series ADF Test Statistic 1.268, Critical Value=-3.470, p-value 0.998 120 Price in US$ per barrel 100 80 60 40 20 Dec-07 Dec-06 Dec-05 Dec-04 Dec-03 Dec-02 Dec-01 Dec-00 Dec-99 Dec-98 Dec-97 Dec-96 Dec-95 Dec-94 Dec-93 0 Figure 2: West Texas Intermediate Oil Price Continuous Returns – stationary series ADF Test Statistic -13.712, Critical Value -3.470, p-value 0.000 40% 30% 20% 10% 0% -10% -20% 4 Dec-07 Dec-06 Dec-05 Dec-04 Dec-03 Dec-02 Dec-01 Dec-00 Dec-99 Dec-98 Dec-97 Dec-96 Dec-95 Dec-94 Dec-93 -30% Table 1 Summary Statistics of Various Forecasting Variables This table presents the summary statistics of the forecasting variables employed in this study for the January 1994 to December 2007 period. Panel A presents the descriptive statistics and Jarque-Bera test. Panel B reports the autocorrelation of returns from one to six months. Panel C provides the autocorrelation of squared returns from one to six months. Panel D presents the augmented Dickey-Fuller test statistic based on the null hypothesis of nonstationarity. * and ** denote statistical significance at the 5% and 1% levels, respectively. Oil Oil T-Bill S&P500 US$ Index MSCI Price Return Yield ΔT-Bill ΔVIX ΔVol. Return Return Return Panel A: Descriptive Statistics Mean 32.753 0.011 0.040 0.0001 0.085 0.025 0.008 -0.001 0.006 Std. Dev. 18.893 0.088 0.016 0.002 3.568 0.145 0.040 0.021 0.042 Skewness 1.231 -0.159 -0.707 -1.097 0.514 0.009 -0.758 -0.031 -0.724 Kurtosis 3.448 3.395 2.082 5.459 11.145 2.544 4.250 3.036 3.991 Median 26.305 0.017 0.047 0.0001 0.035 0.017 0.013 -0.001 0.009 Max. 94.530 0.311 0.064 0.005 16.980 0.347 0.093 0.054 0.098 Min. 11.260 -0.249 0.009 -0.008 -17.840 -0.376 -0.156 -0.055 -0.154 J-Bera Stat. 43.817 1.801 19.886 22.696 471.787 1.451 27.172 0.036 21.541 J-B p-value 0.001** 0.406 0.003* 0.000** 0.000** 0.484 0.001** 0.982 0.002** Panel B: Autocorrelation (First Moment) AC1 0.986** -0.065 0.992** 0.435** -0.115 -0.487 -0.002 0.094 0.074 AC2 0.974** -0.157 0.979* 0.320** -0.144 -0.029 -0.040 -0.027 -0.053 AC3 0.967** 0.109 0.960 0.339** -0.116* 0.244 0.049 0.046 0.037 AC6 0.940** 0.148* 0.880* 0.275** -0.077 0.082 0.038 0.087 Panel C: Autocorrelation (Second Moment) AC1 0.978** 0.066 0.988** 0.298** 0.262** 0.118 0.118 -0.140 -0.009 AC2 0.959** 0.061 0.967** 0.088** -0.007** -0.002 0.228** -0.076 0.196* AC3 0.950** -0.022 0.940 0.180** -0.002** -0.035 0.138 -0.004 -0.051 AC6 0.902** 0.113* 0.824** 0.107** 0.039 0.144 0.004 0.068 Panel D: Stationarity Test ADF Statistic 1.268 -13.712** -2.006 -3.642** -14.417** -15.830** -12.848** -14.787** -12.189** Table 2 Summary Statistics of Hedge Fund Index Returns This table presents the summary statistics of the hedge fund index returns employed in this study. The summary statistics are for the period January 1994 to December 2007. Panel A presents the descriptive statistics of the hedge fund indices. Panel B reports the autocorrelation of returns from one to six months. Panel C presents the autocorrelation of squared returns from one to six months. Panel D reports the augmented Dickey-Fuller test statistic based on the null hypothesis of nonstationarity. * and ** denote statistical significance at the 5% and 1% levels, respectively. Convertible Emerging Equity Market Event Fixed Income Arbitrage Markets Neutral Driven Arbitrage Panel A: Descriptive Statistics Mean 0.0038 0.0047 0.0047 0.0061 0.0018 Std. Dev. 0.0131 0.0459 0.0079 0.0163 0.0107 Skewness -1.4360 -1.2466 0.1571 -3.7032 -3.0918 Kurtosis 6.6365 10.1041 3.5665 30.5896 19.9818 Median 0.0061 0.0122 0.0043 0.0083 0.0038 Max. 0.0306 0.1489 0.0279 0.0337 0.0168 Min. -0.0520 -0.2674 -0.0159 -0.1301 -0.0756 J-Bera Stat. 150.3103 396.7829 2.9376 5712.2881 2286.3410 J-B p-value 0.0010** 0.0010** 0.1733 0.0010** 0.0010** Panel B: Autocorrelation (First Moment) AC1 0.5254** 0.2881** 0.2496** 0.3021** 0.3761** AC2 0.3085** 0.0241 0.1051 0.1116 0.0301 AC3 0.0966 0.0137 0.0375 0.0164 -0.0012 AC6 -0.0040 -0.1135 -0.0249 -0.0412 -0.0621 Panel C: Autocorrelation (Second Moment) AC1 0.3903** 0.0728 0.1569* 0.0421 0.3005** AC2 0.3003** -0.0114 0.2757** -0.0201 0.0583 AC3 -0.0291 0.1128 0.0129 0.0185 0.0225 AC6 -0.0381 -0.0069 0.2207** 0.0007 0.0025 Panel D: Stationarity Test ADF Statistic -6.944** -9.761** -9.604** -9.503** -8.635** 5 DATA AND METHODOLOGY This study re-examines the validity of the forecasting variables discovered in Amenc et al (2003) by re-estimating their models with predictive variables that are stationary. By utilising forecasting variables that are stationary, we can re-assess the genuine power of these variables to forecast hedge fund returns. We employ the same forecasting variables and hedge fund index returns as in Amenc et al (2003), however, we extend the 19942000 analysis by estimating the models out-of-sample from 2001-2007. The forecasting variables include oil spot prices, the U.S. 3 month Treasury bill yield, the change in the VIX Volatility index, the change in the NYSE market volume, S&P500 returns, US Dollar index returns and the MSCI World Equity Index excluding USA returns. Tables 1 and 2 summarise the descriptive statistics of the forecasting variables and the hedge fund index returns, respectively. A closer inspection of Panel D in Table 1 reveals the ADF tests of stationarity. Panel D reports that all time series data is stationary with the exception of oil spot prices and U.S. Treasury Bill yields that were discovered as significant forecasting variables in previous hedge fund studies. In this analysis, we rectify this nonstationarity problem by transforming the data into spot oil returns and the change in the T-bill yield. The ADF tests in Panel D of Table 1 show that spot oil returns and the change in the T-bill yield are indeed stationary variables that can be readily employed in a predictive regression. This study employs the predictive multifactor models as in Amenc et al (2003), however, we augment them to ensure that all forecasting variables are stationary. The augmented models employed in this study are mathematically expressed as: RConvertible,t = α + RConvertible,t-1 + MA(S&P 500t-1) +Oil Returnt-1 + ∆ T-billt-1 + εt (1) REmerging, t = α + REmerging , t-1 + Oil Returnt-1 +MA(MSCIt-1) + εt (2) REquity Market Neutral,t = α + MA(S&P 500t-1) + Oil Returnt-1 + ∆T-billt-1 + εt (3) REvent Driven, t = α + REvent Driven, t-1 + Oil Returnt-1 + εt (4) RFixed Income Arbitrage, t = α + MA(S&P 500t-1) + Oil Returnt-1 + ∆VIXt-1 + Volt-1 + εt (5) RGlobal Macro, t = α + RGlobal Macro, t-1 + MA(s&p 500t-1) + Oil Returnt-1 + Volt-1 + εt (6) where Ri,t represents the return on a hedge fund style at time t, MA(S&P 500t-1) is the historical three-month moving average of the return on the S&P 500, Oil Returnt-1 is the previous month oil price return, ∆T-billt-1 is the change in the three-month treasury bill rate at time t-1, MA(MSCIt-1) is the historical three-month moving average of the return on the Morgan Stanley Composite World Equity Index ex U.S, ∆VIXt-1 is the change in the intramonth average of the VIX volatility index, Volt-1 is the dollar value of shares traded on the New York Stock Exchange, and εt is the error term. 6 Table 3 OLS Predictive Regressions with Stationary Forecasting Variables This table presents the ordinary least squares (OLS) predictive regressions results of Thomson/Tremont hedge fund indices. The regression coefficients are estimated with Newey-West (1987) corrected standard errors for heteroscedasticity and autocorrelation. These regression estimates employ stationary forecasting variables only. The time period is from January 1994-December 2007. The table reports the regression coefficients and the standard errors are displayed in the parentheses. * and ** denotes statistical significance at the 5% and 1% levels, respectively. Regression Variable Convertible Arbitrage Emerging Markets α 0.0010 (0.0018) 0.0007 (0.0061) Ri,t-1 0.5241** (0.1282) 0.2983* (0.0926) MA(S&P) 0.1303* (0.0639) Oil returns 0.0078 (0.0135) Δ T-bill -1.1228 (1.0692) Equity Market Neutral Panel A: 1994-2000 0.0053** (0.0013) Event Driven Fixed Income Arbitrage Global Macro 0.0037 (0.0022) -0.0009 (0.0019) 0.0042 (0.0059) 0.3331* (0.0532) 0.0347 (0.0344) 0.0362 (0.0598) 0.0086 (0.0116) -0.0016 (0.0137) -0.0106 (0.1218) 0.2323** (0.0787) 0.3728 (0.3031) -0.0047 (0.0119) -0.0082 (0.0439) -1.3073 (0.4960) Δ VIX -0.0012 (0.0007) Δ Volume -0.0044 (0.0066) -0.0434 (0.0270) 0.0886 0.2424 0.0013 0.0057** (0.0018) 0.0025 (0.0009) 0.0085** (0.0015) MA(MSCI) Adj R² -0.0240 (0.2632) 0.3886 0.0548 α 0.0019 (0.0012) 0.0087* (0.0026) Ri,t-1 0.3892** (0.1065) 0.2031 (0.1182) MA(S&P) -0.0264 (0.0422) Oil returns -0.0114 (0.0143) Δ T-bill -0.7717 (0.4631) 0.0322 Panel B: 2001-2007 0.0040** (0.0007) 0.2340 (0.1315) -0.0104 (0.0245) -0.0391 (0.0286) 0.0032 (0.0077) -0.0235 (0.0125) 0.0591 (0.1001) 0.0307 (0.0570) 0.0325 (0.0413) -0.0053 (0.0109) -0.0136 (0.0156) -0.2859 (0.2475) Δ VIX 0.0000 (0.0002) Δ Volume 0.0061 (0.0067) -0.0053 (0.0083) 0.0000 0.0000 MA(MSCI) Adj R² 0.1648 -0.0173 (0.0820) 0.0131 0.0000 7 0.0471 To address the problem of heteroscedasticity and autocorrelation, Amenc et al (2003) employ the Generalized Least Squares (GLS) estimation method. Fox (1997) informs us that GLS is an inappropriate estimation method (in the presence of autocorrelated errors) when the dependent variable appears as a lagged effect on the right-hand side of a model. This raises two issues. First, the statistically significant autocorrelation of returns (for one month) of hedge fund index returns in Panel B of Table 2 clearly provide us with the knowledge that the residuals in these regressions will exhibit autocorrelation. Second, equations 1-6 show us that this GLS problem exists here as the dependent variable is indeed a lagged variable on the right hand side of these models. To address the weakness of GLS and the problems of heteroscedasticity and autocorrelation, this study employs an ordinary least squares (OLS) regression with Newey and West (1987) corrected standard errors. EMPIRICAL RESULTS Table 3 presents the regression estimates for the 1994-2000 period and the out-of-sample results from 2001-2007. The first observation from Table 3 is that the size of the S&P500 factor loading declines in the out-of-sample period and becomes statistically insignificant. Second, spot oil returns are statistically insignificant in both in-sample and out-of-sample test periods. This finding differs from previous studies that employed the nonstationary oil prices as the forecasting variable. It is clear that stationary oil returns cannot forecast hedge fund index returns and nonstationary oil prices are an erroneous forecasting variable. The third observation from Table 3 is the statistical insignificance of the change in T-bill yields (which is stationary) in both sample periods. Once again, previous studies show that nonstationary T-bill yields are a significant forecasting variable of hedge fund index returns when in fact it is not. Again, the results in this study differ to the findings in previous studies because we are employing changes in T-bill yields which are a stationary variable. Table 3 also reveals that changes in the VIX, market volume and the moving average of the global equity returns are all statistically insignificant in both sample periods. These findings are new as previous studies have concluded that these variables can also forecast hedge fund index returns. The differences in these findings can be explained by the fact that the OLS method employed in this study provides robust estimates in comparison to the weaknesses in the GLS method employed in previous studies. Table 3 reports that the single variable that seems to predict hedge fund index returns is the lagged dependent variable. One must treat this finding with caution as studies by Asness, Krail and Liew (2001) and Getmansky, Lo and Makarov (2004) inform us that many hedge fund returns exhibit significant autocorrelation which can be explained by stale pricing, illiquidity and nonsynchronous effects. Second, from a practical point of view, the publication of the monthly rates of return from hedge fund index providers generally occurs in the last 7-14 days of the following month which tends to be too late for this information to be exploited by an investor. 8 Finally, we can observe in Table 3 that the forecasting power or adjusted R 2 for all regressions declined from the 1994-200 to 2001-2007 period which demonstrates that these forecasting models have performed poorly out-of-sample. Overall, we can conclude that these stationary forecasting variables have not withstood the test of time as variables that can predict hedge fund index returns. CONCLUDING COMMENTS The major shortcomings of previous hedge fund forecasting studies were their use of nonstationary forecasting variables in a GLS framework. This study employed forecasting variables that were stationary in a more robust OLS framework. It was found that these stationary forecasting variables were indeed insignificant in both sample periods. Overall, this study provides no evidence to suggest that external forecasting variables can predict hedge fund index returns. Recent studies have shown that stock and bond returns are not as predictable as originally thought. This study provides new evidence to suggest that hedge fund index returns are also difficult to forecast. This finding provides a warning to active asset allocators who attempt to opportunistically market-time their investments in and out of asset classes and markets. The lessons from this study suggest that forecasting models in traditional and alternative asset classes must be carefully developed in order to ensure their methodological validity. REFERENCES Agarwal, V. & Naik, N., 2004, Risks and portfolio decisions involving hedge funds, Review of Financial Studies 17, 63-98. 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