Understanding Hedge Fund Contagion: A Markov-switching Dynamic Factor Approach

Transcription

1 Understanding Hedge Fund Contagion: A Markov-switching Dynamic Factor Approach Ozgur (Ozzy) Akay a Zeynep Senyuz b Emre Yoldas c February 2011 Preliminary and Incomplete Comments Welcome Abstract The article introduces a novel approach to measure the contagion in hedge fund returns. We develop a dynamic factor Markov-switching specification to extract the latent factor that is related to contagion, which allows nonsimultaneous shifts in mean and variance components of hedge fund returns. The new approach is superior to existing models in capturing both subtle and significant crisis periods. While the changes in latent factor is strongly tied to the TED spread, its regime-switching behavior can be explained by margin requirements on S&P 500 futures contracts, a proxy for funding liquidity risk in financial markets. Keywords: Hedge fund contagion, Markov regime-switching models JEL code: G01, C58 a Texas Tech University, Division of Personal Financial Planning, Lubbock, TX, Ozzy.Akay@ttu.edu b University of New Hampshire, Department of Economics, Durham, NH, Zeynep.Senyuz@unh.edu c Contact author. Bentley University, Department of Economics, Waltham, MA, Eyoldas@bentley.edu

2 1. Introduction Hedge funds have become important players in the financial markets recently. Although the financial crisis of 2008 had a negative impact on the performance and therefore asset under management, the industry still manages around $1.77 trillion as of the third quarter of 2010 according to a recent press release by Hedge Fund Research, Inc. 1 One of the reasons behind the growth of the hedge fund industry was that they follow an absolute-return strategy promising a positive return independent of the market conditions. To achieve that, hedge funds can pursue highly complex investment strategies that are not available to the other institutions in the investment management industry due to regulatory constraints. Therefore, one would expect a low correlation between hedge fund returns, since each individual hedge fund or hedge fund style invests in a different set of assets and strategies. However, the financial crisis of 2008 proved that the returns to different hedge fund styles might be more correlated than expected, indicating a systemic risk in the industry. Chan et al. (2007) define systemic risk as the possibility of a series of correlated defaults among financial institutions typically banks that occur over a short period of time, often caused by a single major event. Systemic risk is important because it impedes the benefits of diversification to hedge fund investors, especially in down market conditions. Moreover, as Fed Chairman Bernanke (2006) points outs in his speech 2, it may affect the whole market through asset price changes, liquidity spirals and increased uncertainty in financial markets. Khandani and Lo (2007) illustrate how these forces increased systemic risk in the hedge fund industry during the financial crisis of Report available at 2 The transcript of his speech is available at 1

3 In a related context, some researchers (e.g. Boyson et al., 2010) define hedge fund contagion as the level of correlation that resides after systematic risk factors are accounted for. Extant literature has confirmed the existence of contagion in the hedge fund industry, specifically during crisis periods. The main method in this field has been to study the residuals produced from a factor model to identify correlations that cannot be explained by exposure to economic fundamentals (the latent factor). We aim to introduce a novel method that produces the unobserved (latent) factor in hedge fund index returns and cannot be captured by systematic risk factors. Moreover, this factor is significantly related to liquidity in the market, whereas the type of relation with different proxies of liquidity varies. The contribution of our paper is twofold. First, we estimate the latent factor in hedge fund style returns using a dynamic factor Markov-switching model. Our specification is very flexible in the sense that we allow for non-simultaneous shifts in mean and variance dynamics. Using this flexible specification we are able to identify not only market crashes of October 1998 (Long- Term Capital Management/Russian crises) and September 2008 (Global financial crisis), but also subtle financial crises such as the Mexican peso crisis (December 1994), Asian financial crisis (July 2007) and bursting of dot-com bubble (March 2000). Second, this latent factor is linked to the funding liquidity risk proxy originally developed by Brunnermeier and Pedersen (2009) along with the TED spread. Interestingly, while the movement of the latent factor is related to the TED spread, its regime switching behavior is associated with the funding risk in financial markets. Therefore, we confirm the link between the latent factor in hedge fund style returns and funding and liquidity risks, and clearly identify the source of this link. 2

4 Our paper complements the literature on hedge fund contagion. Boyson et al. (2010) apply quantile regression to the residuals produced from a factor model using raw returns from eight hedge fund styles provided by Hedge Fund Research, Inc. Therefore, they can decompose the effect of systematic risk factors in explaining contagion, thus leaving the effect nonsystematic factors only. They find that the residual is strongly correlated to liquidity shocks captured by the change in the TED spread (the difference between the 3-month LIBOR and the 3-month T-Bill rate). Similarly, Dudley and Nimalendran (2010) use seven hedge fund style indices from the Center for International Securities and Derivatives Markets (CISDM) and estimate conditional correlations to indentify contagion across hedge fund style returns. Then, they employ a copula method to determine the role of funding risk estimated by the margin requirement on S&P 500 futures contracts along with margin requirements on USD/JY currency futures and Eurodollar contracts on hedge fund return contagion. They suggest that margin requirements should be relaxed during financial crises periods to alleviate the effect liquidity spirals in the overall market. Billio et al. (2010) analyze eight hedge fund index strategies and examine the behavior of a latent (idiosyncratic) factor during financial crisis. They find that there is a significant latent factor that spiked during the Long-Term Capital Management crisis in 1998 and the financial crisis of They confirm the findings of Boyson et al. (2010) that traditional systematic risk factors are not sufficient to explain the hedge fund return contagion. While existing research confirms the presence of a latent factor in hedge fund returns, we explicitly identify and quantify this factor and show its source. Therefore, we provide further 3

5 evidence on the hedge fund contagion without exogenously identifying the crisis periods, rather developing a model that captures even subtle crises. The rest of the paper is organized as follows: Section 2 introduces the data and empirical design, section 3 presents the findings and section 4 concludes. 2. Data and Methodology We use hedge fund index returns from the Dow Jones Credit Suisse Hedge Fund Indexes database from January 1994 to March Specifically, we consider Convertible Arbitrage, Dedicated Short Bias, Emerging Markets, Equity Market Neutral, Event-Driven Distressed, Event-Driven Multi Strategy, Event-Driven Risk Arbitrage, and Long/Short Equity to make our findings comparable to existing research. A detailed description of the indices and construction methodology are publicly available at Dow Jones Credit Suisse website. 3 Summary statistics for the returns on monthly hedge-fund style indices and pricing factors are provided in Table 1 Panel-a. We see that all hedge fund indices have positive average returns in the sample with Dedicated Short Bias having the lowest, 0.06% and Long/Short Equity the highest, 0.81%. In terms of volatility, Dedicated Short and Emerging Markets exhibit the most variability. All hedge fund styles have positive first order autocorrelation where Convertible Arbitrage and Distressed Securities display the highest persistence. This is most likely due to these hedge fund styles investments in illiquid securities (Getmansky et al., 2004). In general, hedge fund returns are left skewed with the exception of Dedicated Short, which is slightly right skewed, and Long/Short Equity, which is almost symmetric. For informational purposes we also provide summary statistics of the pricing factors in Table 1 Panel-b

6 To estimate the latent factor, first we run the following model for each of the index return series to get the residuals: 1,,,,, where, is the return of a hedge fund index 1,, 8 in period,,, 1,, 10 are the ten hedge-fund risk factors described in Fung and Hsieh (2001) 4, and, is a possibly heteroskedastic error term such that, 0, and,,, A list of hedge-fund pricing factors and their description can be found in Appendix A. Next, we use the residuals from the above model in dynamic factor framework with Markov regime-switching to identify the latent hedge fund pricing factor and its asymmetric behavior in different states of financial markets. 6 The first equation of the model is the measurement equation, which links the residuals from Equation (1) to the latent pricing factor that represents the co-movement of the underlying hedge-fund residuals: 2,,,, ~ 0,, where, is the residual from Equation (1),,, is the common latent pricing factor, is the factor loading of the residual series that represents its exposure to the common factor, and 4 Definition and historical data of the factors can be found at 5 There may be time variation in factor risk exposures,,, which can be incorporated by creating a dummy variable and adding interaction terms in Equation (1). Billio et al. (2010) consider both an exogenously defined crisis dummy and an endogenously identified one with respect to the estimated regimes of a broadly defined stock market portfolio. We consider both approaches as robustness check for our results and find that our results are robust to inclusion of both types of crisis dummy. The results are available upon request. 6 See Kim (1994), Chauvet (1998), Chauvet (1998/1999), Chauvet and Potter (2000), among others for applications of dynamic factor models with Markov-switching asymmetry in macroeconomics and finance. See Kim and Nelson (1999) for a comprehensive survey and numerous illustrations of this approach using maximum likelihood and Gibbs-sampling. 5

7 , is the white noise idiosyncratic term for the residual series. The second equation is the transition equation that describes dynamics of the latent factor: 3, ~ 0,, where is the unobservable state variable that drives dynamics of the latent hedge-fund pricing factor. The drift term and volatility are both subject to regime shifts determined by 0,1. This specification captures both time variation in expected returns and heteroskedasticity, well known stylized facts of financial returns. In particular, we have 4 1, 5 1. The model is completed by specifying dynamics of the unobservable state variable,. This state variable evolves according to a first order two-state Markov process, with transition probabilities given by Pr where, 0, 1}. For this two-state specification transition probabilities are collected in a 2 2 matrix, say, given by The latent factor is assumed to be uncorrelated with the idiosyncratic terms at all leads and lags. Since the extracted factor summarizes information common to all residual series and it is not observable, we need to define a scale for identification and interpretation. Therefore, we normalize the first factor loading to unity, i.e. 1. Note that, this has no effect on the dynamic properties of the extracted factor as well as the regime classification. For model estimation we combine a nonlinear discrete version of the Kalman filter with Hamilton s (1989) filter using Kim s (1994) approximate maximum likelihood method. The filter estimates the latent factor and the probabilities associated with the Markov-state variable 6

8 using available data. Based on information available at time, the algorithm produces the prediction of the latent factor and probabilities of the Markov states. After estimating the model parameters, we make inference about the unobserved state using filtered and smoothed probabilities. Filtered probabilities use information available up to time, Ω, whereas smoothed probabilities are based on the entire sample, Ω where Ω denotes information set available as of time Empirical Results 3.1 Two-State Markov Regime Switching Model We run the regression model specified in Equation (1) for each of the eight hedge fund indices and provide the estimation results in Table 2. We note that Fung and Hsieh rick factors are explaining between 31 and 72 percent of the variation (R 2 ) in hedge fund index returns, and thus are appropriate to for our empirical design. The R2 measures in our regression are comparable to presented in other research (e.g. Billio et al., 2010; Boyson et al., 2010). The autoregressive component is significant for all of the hedge fund indices, pointing to the serial correlation imposed by illiquid assets Getmansky et al., 2004). The significance ans sign of factors varies for hedge fund indices, which suggests different investment strategies across the styles. While equity market (EM) and emerging market (EMG) factors are significant for most of the indices, the bond market factor (TERM) is not significant in explaining any of the index returns. Next, we use the residuals from the regression in a Markov regime-switching model specified in Equation 3 and 4. Table 3 provides the maximum likelihood estimates of the twostate specification. The drift of State 0 is around -0.6, whereas the one for State 1 is slightly 7 For a detailed discussion of the filter and smoother algorithms, see Hamilton (1994) and Kim and Nelson (1999). 7

9 positive, around Given the autocorrelation coefficient of the dynamic factor (0.12), this corresponds to an annualized mean return of in State 0 and 0.63 in State 1. These two regimes are also characterized by different variances. The state with negative drift also has the high variance. In this state, the standard deviation of the latent factor is estimated to be In the low volatility state, the standard deviation estimate is given by State 0 has a shorter duration than State 1 as implied by the estimated transition probabilities. The expected duration in State 0 is 7 months, which is much shorter than that of State 1 with an expected duration of 67 months. Estimated factor loadings suggest that all series are positively correlated with the latent factor with the exception of Dedicated Short Bias. Equity Market Neutral index has very little exposure to the latent factor with an estimated factor loading of 0.09, which is insignificant. All other hedge fund investment styles are significantly related to the latent factor. After accounting for each style s exposure to the latent factor, we see that Dedicated Short Bias and Emerging Markets have the most volatile idiosyncratic components. The extracted latent factor is plotted in Figure 1. The factor displays a smoother behavior than the individual hedge fund returns as it reflects the common behavior across them. The factor takes large negative values in August 1998 and September 2008 due to the failure of LTCM and Lehman Brothers, respectively. Figures 2 and 3 provide the filtered and smoothed probabilities of the high volatility low return state (State 0). In both figures, we observe two short lived spikes in State 0 probabilities. The first one takes place in August 1998 following the LTCM failure associated with the Russian default. The second is associated with the recent subprime led financial crisis which peaked in September 2008 with the Lehman bankruptcy. The smoothed probabilities identify this period from July 2008 to January On the other hand, the filtered 8

10 probabilities signal an abrupt switch back to State 1 as they drop below 0.5 during November and December and then rise again in January. 3.2 Markov Regime Switching Model with a Dynamic Specification In section 3.1, we assumed that both the mean and variance asymmetries are driven by the same unobservable state variable. In other words, we restricted the mean and variance to switch across regimes at the same time. This analysis provided a regime classification that identifies only periods of extreme turmoil in financial markets, the LTCM failure and the subprime crisis followed by the Lehman bankruptcy. In order to gain further insight into the regime switching dynamics of hedge fund returns, we consider a less restrictive version of this standard formulation which incorporates two Markov state variables as in Hamilton (2008). By considering not just one but two Markov state variables, we obtain a flexible specification that allows mean and variance asymmetry to have different dynamics. This is especially relevant given the fact that hedge funds follow highly nonlinear investment strategies which require measures of risk beyond volatility. For example, Convertible Arbitrage and Equity Neutral investment styles have relatively small standard deviations but they have the most left skewed distributions with fattest tails among the eight styles we consider (see Table 1). This behavior may also suggest that the mean and variance switching dynamics are not necessarily synchronized. The new specification is obtained by replacing Equations (4) and (5) with the following 7 1, 8 1, where 0,1 and 0,1 are the independent Markov state variables such that,,, 0,1. The transition probabilities are given by 9

11 Pr and Pr. The regime probabilities are now collected in a 4 4 matrix elements of which are simply products of transition probabilities pertaining to each state variable. The estimation results from the second specification are presented in Table 4. The drift and autocorrelation estimates suggest a different form of mean asymmetry across the two states compared to the first model. Specifically, the low mean regime is now characterized by -3.66% annualized return for the latent factor as opposed to -8.3% implied by the first model. Moreover, the high mean regime now corresponds to an annualized return of 5.01% as opposed to 0.63%. The low mean regime is relatively more persistent than the high mean regime according to the transition probability estimates of and On the other hand, volatility estimates of the two regimes are very similar to that of the first specification. This observation also applies to the transition probabilities associated with the state variable driving volatility with the high variance regime being much less persistent than the low variance regime. Finally, note that the estimated factor loadings are almost identical between the two models, so our results regarding the exposure to the latent factor do not change. The extracted latent factor is plotted in Figure 4. The dynamics of this factor are very similar to that of the one estimated with the first specification. We see that the factor now takes even a larger negative value during both the LTCM failure and the Lehman bankruptcy. Figures 5 and 6 show the filtered and the smoothed probabilities of low mean regime identified by the first state variable,. The regime classification with respect to the mean is very different from the previous model which imposes synchronized regime switching of mean and variance. Filtered probabilities label the beginning of a high mean state in May 1995 that prevailed until the end of There are very short-lived increases in probabilities in April 1997 and October 10

12 1998 associated with the Asian and Russian crisis, but these periods are not identified as low mean regimes by the smoothed probabilities which take into account all information available in the sample. This period is clearly labeled as the period during which the latent common hedge fund factor contributed to above average returns, according to the smoothed probabilities. When we calculate the averages for hedge fund residuals in the two regimes we find that the average across the styles is -2.95% on an annualized basis in the low mean regime while it is 3.59% in the high mean regime. Moreover, the low mean regime prevails approximately 55% of the time. These figures lead us to conclude that there is substantial mean asymmetry in hedge fund returns after accounting for standard pricing factors due to exposure to the common latent risk factor. Figures 7 and 8 plot the filtered and smoothed probabilities of high volatility regime identified by the second state variable,. This regime classification is very similar to the one obtained by the first model with a longer duration of the high volatility regime. When we multiply the probabilities of low mean and high volatility regimes to obtain the joint probability of low mean high variance regime, we observe that the probabilities are above 0.5 only during the recent subprime meltdown. Therefore, we conclude that this period is the only one in the entire sample during which the first two moments of hedge fund residuals switch simultaneously. 3.3 Liquidity and the Latent Factor It has been suggested that a major channel through which hedge fund returns exhibit comovement beyond that implied by the hedge fund pricing factors is funding and market liquidity, see Bilio et al. (2010), Boyson et al. (2010), and Dudley and Nimalendran (2010). The theoretical framework for using the liquidity variables in explaining hedge fund contagion is provided by Brunnermeier and Pedersen (2009). In their model, funding liquidity constraints in the form of margin requirements might trigger a market wide selloff, which might impede asset 11

13 liquidity and cause liquidity spirals that adversely affect the prices of all financial assets. Since hedge funds, in general, use leverage extensively, it is of interest to analyze the relationship between our extracted latent hedge-fund factors and various liquidity measures including a proxy for funding liquidity risk. We consider two funding and three market liquidity measures. The funding liquidity measures are the margin requirement on S&P500 futures relative to the level of the index (MRGN), and the TED spread (TED). 8 Our market liquidity proxies are the level of aggregate liquidity (AL), innovations to aggregate liquidity (IAL), and the traded liquidity factor (TL) introduced by Pastor and Stambaugh (2003). Table 5 presents the results of regressions of the extracted latent hedge fund factor from our second specification on these liquidity measures. 9 The first row provides the results when all liquidity measures are included in the regression. TED stands out as the only measure that is significant at 5% level while MRGN is significant at 10% level. All these measures help explain 14% of the variation in the latent hedge fund pricing factor. Regressions that include each one of these liquidity measures individually yield significant estimates except for TL. These regressions also indicate that most of the explanatory power is coming from TED in the joint regression. Next, we consider probit regressions in which the dependent variable is a dummy variable that reflects the regime classification due to mean asymmetry. This dummy variable equals one when the smoothed probability of the low mean state is greater than 0.5 and zero otherwise. The results are presented in Table 6. As opposed to the level of the factor, the regime changes are mostly related with MRGN, which is significant at any conventional significance level in the joint probit regression. The MacFadden from the joint regression is 14% while individual probit models indicate that the entire explanatory power is due to MRGN. Therefore, we conclude that the 8 We thank Markus K. Brunnermeier for providing the margin requirements data on S&P 500 futures contracts. 9 When we use the latent factor from the first specification we obtain very similar results. 12

14 movements in the latent pricing factor is tied to the TED spread, which reflects the degree of distress in funding markets, while its regime switching behavior is associated with the margin requirement on S&P500 futures. Thus, we provide support for the premise of Brunnermeier and Pedersen (2009) that adverse shocks to funding liquidity might impact overall liquidity in the market and might cause liquidity spirals that would eventually increase correlations across asset returns. We also confirm the findings of Boyson et al. (2010) that TED spread is related to hedge fund contagion. 4. Concluding Remarks Our results confirm the contagion among hedge fund styles and develop a dynamic factor Markov regime switching model to identify the source of the contagion. The dynamic model is more sensitive to subtle shifts in the first and second moments of returns and thus able to capture even the short-lived crises along with the material crises of August 1998 and September This is the first paper, to our knowledge, that explicitly produces and pictures the latent factor behind hedge fund style returns without exogenously imposing crisis periods on the model. We also show that the latent factor is related to well-documented liquidity factors in financial markets, whereas the form of the relation varies across variables. While traditional microstructure liquidity variables explained in Pastor and Stambaugh (2003) are inconclusive about the source of the contagion, funding liquidity variables TERM and margin requirements on S&P 500 futures contracts collaboratively explain the movements and shifts in hedge fund contagion. 13

15 References Billio, M., M. Getmansky Sherman, and Loriana Pellizon, 2010, Crises and Hedge Fund Risk, Working Paper, University of Massachusetts. Boyson, N.M., C.W. Stahel, and R.M. Stulz, 2010, Hedge Fund Contagion and Liquidity Shocks, Journal of Finance, 65(5), Brunnermeier, M. and L. Pedersen, 2009, Market Liquidity and Funding Liquidity, Review of Financial Studies, 22, Chauvet, M. 1998, An Econometric Characterization of Business Cycle Dynamics with Factor Structure and Regime Switching, International Economic Review 39, Chauvet, M., 1998/1999, Stock Market Fluctuations and the Business Cycle, Journal of Economic and Social Measurement, 25, Dudley, E. and M. Nimalendran, 2010, Margins and Hedge Fund Contagion, Journal of Financial and Quantitative Analysis, forthcoming. Fung, W. and D.A. Hsieh, 2001, The Risk in Hedge Fund Strategies: Theory and Evidence from Trend Followers, Review of Financial Studies, 14, Getmansky Sherman, Mila, A.W. Lo and Igor Makarov, 2004, "An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns", Journal of Financial Economics, 74 (3), Hamilton, J.D., 1989, A New Approach to the Economic Analysis of Nonstationary Time Series and Business Cycles, Econometrica, 57, Hamilton, J.D., 1994, Time Series Analysis, Princeton University Press, Princeton. Kim, C.-J., 1994, Dynamic Linear Models with Markov-Switching, Journal of Econometrics, 60, Kim, C.-J., Nelson C.R., 1999, State-Space Models with Regime Switching: Classical and Gibbs Sampling Approaches with Applications, MIT Press, Cambridge. Pastor, L. and R. Stambaugh, 2003, Liquidity Risk and Expected Stock Returns, Journal of Political Economy, 111,

16 Table 1: Descriptive Statistics Panel-a: Hedge Fund Returns CA DS EM EN DSTR EDMS RA L/S Mean Std. Dev Min Max Autocorrelation Skewness Kurtosis Panel-b: Pricing Factors SBD SFX SCOM SIR SSTK EM SIZE TERM CRT EMG Mean Std. Dev Min Max Skewness Kurtosis

17 Table 2: First Stage Regression Results CA DS EM EN DSTR EDMS RA L/S Cons (2.95) (1.88) (1.72) (3.94) (3.14) (3.69) (3.93) (3.97) AR (4.40) (1.71) (4.05) (2.37) (5.47) (4.63) (3.46) (1.94) SBD (-0.82) (0.20) (-1.96) (-0.11) (-1.61) (-2.03) (-1.68) (-1.48) SFX (-0.63) (0.07) (-0.94) (1.83) (0.44) (0.91) (0.68) (0.05) SCOM (-0.40) (-0.88) (1.59) (1.32) (1.59) (0.70) (0.04) (1.77) SIR (-1.26) (-1.66) (0.14) (-1.75) (-0.59) (-1.57) (-1.78) (-1.46) SSTK (0.78) (-0.80) (1.27) (1.65) (-0.01) (0.77) (-0.69) (1.91) EM (0.59) (-9.22) (-0.84) (2.60) (5.32) (2.67) (2.70) (5.53) SIZE (0.10) (-6.40) (0.30) (0.32) (2.94) (2.13) (3.94) (4.66) TERM (-1.03) (-0.70) (-1.38) (0.78) (-0.05) (-0.08) (-1.38) (-1.07) CRT (-2.80) (-0.88) (-0.44) (1.08) (-0.70) (-1.56) (0.12) (0.39) EMG (1.67) (-2.05) (10.19) (0.82) (2.41) (4.23) (2.72) (2.82)

18 Table 3: Maximum Likelihood Estimates of the Markov-Switching Dynamic Factor Model Parameter Estimate Parameter Estimate (-0.95) (6.02) (0.85) (6.75) (3.84) (4.11) (6.88) (5.37) (6.86) (16.11) (86.92) (18.88) (1.17) (18.12) (19.04) (-2.18) (16.06) (4.26) (11.65) (0.85) (18.35) (17.04) 17

19 Table 4: Maximum Likelihood Estimates of the Markov-Switching Dynamic Factor Model Parameter Estimate Parameter Estimate (-1.35) (0.93) (4.17) (6.21) (4.08) (6.84) (3.91) (4.11) (15.70) (5.62) (17.91) (15.97) (8.34) (18.92) (79.4) (18.12) (-1.35) (19.04) (15.63) (-1.98) (12.54) (4.43) (18.16) (17.46) 18

20 Table 5: Regressions of the Latent Hedge Fund Pricing Factor on Liquidity Proxies Cons MRGN TED AL IAL TL (2.26) (-1.89) (-2.68) (0.09) (1.51) (-1.12) (2.13) (-2.14) (-0.03) (-2.23) (0.96) (2.27) (-0.09) (1.85) (-0.08) (-0.14) 19

21 Table 6: Probit Regressions of the Mean Regime Dummy on Liquidity Proxies Cons MRGN TED AL IAL TL MacFadden (-5.71) (5.89) (1.17) (-0.50) (0.15) (0.53) (-5.67) (6.12) (1.11) (0.84) (0.47) (-1.46) (1.11) (-0.84) (0.99) (0.53) 20

22 Figure 1: The Latent Hedge Fund Pricing Factor from Model I Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 21

23 Figure 2: Filtered Probabilities of the Low Mean - High Volatility State from Model I Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 Figure 3: Smoothed Probabilities of the Low Mean - High Volatility State from Model I Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 22

24 Figure 4: The Latent Hedge Fund Pricing Factor from Model II Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 23

25 Figure 5: Filtered Probabilities of the Low Mean State from Model II Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 Figure 6: Smoothed Probabilities of the Low Mean State from Model II Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 24

26 Figure 7: Filtered Probabilities of the High Volatility State from Model II Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 Figure 8: Smoothed Probabilities of the High Volatility State from Model II Feb-94 Nov-94 Aug-95 May-96 Feb-97 Nov-97 Aug-98 May-99 Feb-00 Nov-00 Aug-01 May-02 Feb-03 Nov-03 Aug-04 May-05 Feb-06 Nov-06 Aug-07 May-08 Feb-09 25