Hedge Fund Styles and Macroeconomic Uncertainty

Transcription

1 Hedge Fund Styles and Macroeconomic Uncertainty September 2016 Marie Lambert University of Liège, HEC Liège Research Associate, EDHEC-Risk Institute Federico Platania Pôle Universitaire Léonard de Vinci, Paris-La Défense

2 Abstract This paper examines the dynamic trading strategies implemented by hedge fund managers using a Kalman filter of hedge fund betas across styles. We investigate the risk drivers of dynamic trades, examining which conditioning/macroeconomic variables strongly lead time variation in fund trades. We show that hedge fund managers do control the intensity of their exposure to economic uncertainty and that differences between up- and down-market regimes can be observed. Hedge funds tend to dislike high-dividend paying stocks. Moreover, all hedge fund styles display pro-cyclical exposure to directional equity factors, as well as to credit and liquidity risks. Small growth stocks, however, are revealed to be crisis investments whose allocations increase with unemployment, inflation or volatility. As volatility increases, the value of growth options embedded into growth stocks indeed increases. Growth stocks are shown to hedge market reversals and volatility. The outperformance of growth companies in recessions might also relate to their cost flexibility. Investments in small stocks embed strong micro risks and might also constitute a hedge in economic slowdowns. This might explain why funds with such an investment focus appear to be countercyclical. Keywords: Kalman filter, Markov switching, macroeconomic indicators, investment strategies, dynamic betas, commonality. The authors acknowledge financial support from the F.R.S. F.N.R.S. as part of research project T Marie Lambert acknowledges financial support from Deloitte (Belgium and Luxembourg). All remaining errors are ours. EDHEC is one of the top five business schools in France. Its reputation is built on the high quality of its faculty and the privileged relationship with professionals that the school has cultivated since its establishment in EDHEC Business School has decided to draw on its extensive knowledge of the professional environment and has therefore focused its research on themes that satisfy the needs of professionals. 2 EDHEC pursues an active research policy in the field of finance. EDHEC-Risk Institute carries out numerous research programmes in the areas of asset allocation and risk management in both the traditional and alternative investment universes. Copyright 2016 EDHEC

3 1. Introduction Do hedge fund managers shift investment strategies in response to changing market conditions? The dynamic properties of hedge fund trading have been largely documented in the hedge fund literature. In the recent quant crisis, hedge funds managed to unwind part of their exposures to subprime mortgages, contrary to banks or other institutional investors. In the Global Financial Stability Report, the International Monetary Fund (2008) indicates that only 22.8% of hedge funds total losses were related to subprime exposure in 2006, while banks contributed to 53.3% of total losses. The same pattern is found for 2007 (29.2% and 41.3%, respectively). One can capture the dynamic trading component of hedge fund returns through time-varying estimation techniques. Amenc et al. (2003), Brealey and Kaplanis (2001), and Kat and Miffre (2002) propose conditioning hedge fund market exposure on certain financial indicators, such as the default spread, the implied volatility or the term spread of the US market. Hasanhodzic and Lo (2007), Kuenzi and Shi (2007), and McGuire et al. (2005) use rolling-window regression-based analyses to estimate the current market exposures of fund managers. The theory of structural breaks in hedge fund exposures is grounded in the work of Bollen and Whaley (2009) and Patton and Ramadorai (2013). Bollen and Whaley (2009) consider different techniques to model the ease with which hedge funds shift asset classes, investment strategies and leverage. They compare a simple market timing model to a structural change-point regression with one regime switch in the data, as well as to a state-space model in which factor loadings are assumed to follow a mean-reverting process. The structural change-point regression observes two market regimes in the fund return data and estimates factor exposures separately in these two market subperiods. Therefore, structural change-point regression best captures rapid and sharp transitions in fund exposures, while state-space models best model smooth transitions. Criton and Scaillet (2011) further study whether hedge funds display structural breaks in exposure and relate those to turmoil periods. We revisit the state-dependent approach to modelling hedge fund risk exposure using a Kalman filter. We then relate changes in betas to economic state variables. We allow for asymmetric exposure using a Markov switching model. We further consider whether we can identify commonalities in the links between beta exposures and macro factors across strategies. We aim to test whether the strength of the relation between asset allocation and economic conditions varies across hedge fund styles and to distinguish the strategies that are less affected by market cycles from those that might exacerbate business cycles. The paper s objective is not to analyse the market timing skills of hedge fund managers but to report the significance of macroeconomic factors, such as interest and inflation rates, dividend yields, GDP growth, market volatility and the US unemployment rate, when defining their trades. While Chen et al. (1986) show that stock returns are related to innovations in macroeconomic variables, our paper shows that hedge fund trades are sensitive to economic information. We first determine the dynamic trading of hedge fund styles as well as its risk drivers (i.e., which conditioning/macroeconomic variables strongly lead time variation in fund trades). We also examine the market conditions under which hedge funds change their investment positions. Our paper relates to the work of Bali et al. (2014) who recently demonstrated hedge fund macrotiming ability. Macroeconomic conditions affect company fundamentals (e.g., cash flows, cost of capital) and should therefore affect stock prices and trades. Hedge funds with strong exposure to macroeconomic uncertainty indeed outperform funds with weaker exposure. Agarwal et al. (2016) also show that uncertainty about volatility is an important determinant of hedge fund returns. Cao et al. (2013) demonstrate that a hedge fund s state-dependent bets are based on 3

4 volatility levels. Hedge funds are also shown to reduce risk exposure in times of scarce market liquidity. Chen et al. (2016) demonstrate hedge fund timing abilities in stocks that are sensitive to investor sentiment. Finally, Racicot and Théoret (2012) investigate how business cycles affect hedge fund trades and provide evidence of procyclicality in hedge fund risk exposure. They demonstrate that most hedge fund styles are procyclical (e.g., equity long/short (L/S) and equity market neutral). An exception is made for distressed securities, which are shown to increase risk exposure during economic slowdowns. Changes in macroeconomic conditions therefore lead hedge fund managers to dynamically rebalance their asset allocations. The remainder of this paper is organised as follows. Section 2 reviews the literature on hedge fund dynamic trades and develops the hypotheses to be tested. In Section 3, we present a multifactor approach to hedge fund returns and describe our dynamic approach to hedge fund risk exposures. Section 4 estimates time-varying exposures in hedge fund styles and relates those dynamic exposures to macroeconomic uncertainty. Section 5 presents a discussion of the main results and the hypotheses tested. Section 6 concludes. 2. Literature review Fung and Hsieh (1997) were among the first to identify the impact of dynamic trading strategies on the hedge fund return structure. Beyond market factors, their model includes proxies for the strategy component of hedge fund returns. Similarly, asset-based factors that capture optionlike strategies were added to the analyses conducted by Agarwal and Naik (2004) and Fung and Hsieh (2004). On the one hand, Fung and Hsieh (2004) consider the payoffs of lookback straddles to capture trend-following strategies in hedge funds. On the other hand, Agarwal and Naik (2004) consider investment strategies that roll over one-month to maturity call and put options. This research does not capture hedge funds nonlinear payoffs through option-based factors. Rather, we use a dynamic approach to estimate the nonlinear trading of hedge funds for a set of systematic factors. Similarly to Bollen and Whaley (2009), we recognise the importance of modelling time-varying exposures in order to properly and accurately assess hedge fund performance. The authors consider a hedge fund s exposure to risk factors as an unobservable state variable that evolves according to a first-order autoregressive process (AR(1)) and use a Kalman filter to estimate it. Racicot and Théoret (2009, 2010) study how portfolio manager alphas and betas react to certain market and economic variables, and they use a Kalman filter to infer dynamic exposure to risk factors. More recently, Kazemi and Islamaj (2014) study the relationship between hedge fund activeness and its performance using a Kalman filter to estimate the dynamic risk exposure of L/S equity hedge funds. In the mutual fund literature, Swinkels and Van der Sluis (2006) report a return-based style analysis and compare three different approaches to explicitly model the time-varying exposures of mutual funds: rolling-window analysis, the Kalman filter, and the Kalman smoother. Christofferson and Langlois (2013) observe a joint dynamic correlation among equity factors. If this feature is reconciled with market regimes, hedge fund risk exposure could be made conditional on different levels of the mean and volatility of the equity market index. In this framework, Billio et al. (2012) show that hedge fund managers are able to hedge market exposures. They model volatility regime changes in the US market index using a Markov switching model for the period and find that conditional exposure to traditional location factors tends to be reduced in Standard & Poor s (S&P) 500 down states relative to tranquil market states. Similarly 4

5 to Billio et al. (2012), we employ a Markov switching model but for time-varying betas estimated using a Kalman filter. The innovative aspect of our paper relies on examining the extent to which hedge funds time their market exposures to economic conditions. We were unable to find a comprehensive review of commonalities in trades among hedge fund styles. However, we have reviewed the extant literature and developed the following 7 hypotheses. Hypothesis 1: All hedge fund strategies, except dedicated short bias, tend to exhibit positive exposure to the size factor (Agarwal and Naik, 2004; Billio et al., 2012; Chen et al., 2016). Hypothesis 2: The credit spread is a proxy for credit risk: the higher the credit spread, the lower the return of the hedge fund strategy (Billio et al., 2012). An increase in the credit spread creates margin calls and forces deleveraging, which results in the sale of illiquid assets at a low price (Khandani and Lo, 2011). Hypothesis 3: Hedge fund exposure to a value-growth factor is positive for short bias and risk arbitrage and negative for other strategies (Billio et al., 2012). Hypothesis 4: Hedge funds showed the greatest sensitivity to the credit spread and the commodity index during the LTCM crisis and to the emerging market factor during the equity bubble. There is an increase in exposure to the credit spread around a crisis event (Criton and Scaillet, 2011) and to emerging markets before the subprime crisis (Bussière et al., 2014). Hypothesis 5: Except for the short selling strategy, equity hedge funds maintain constant exposure to liquidity around a crisis event (Criton and Scaillet, 2011). Hypothesis 6: Hedge funds seek high volatility exposure, as shown in Agarwal et al. (2016) and Brown et al. (2012). Hypothesis 7: Hedge fund exposure is procyclical. An increase in the unemployment rate (a sign of recession) leads to a reduction in leverage, while economic expansion leads to increased exposure (McGuire et al., 2005; Racicot and Théoret, 2012). During an economic slowdown and prior to an economic recovery, the unemployment rate might nevertheless constitute a countercyclical measure as unemployment stays high. Increasing interest rates reduces exposure to market risks (Racicot and Théoret, 2012). (An exception is made for distressed securities, which are shown to increase risk exposure during economic slowdowns.) We will consider these hypotheses when interpreting the results of our empirical analysis. 3. Multi-factor models of hedge fund returns Researchers have proposed numerous macroeconomic and financial risk factors to capture hedge fund risk exposure. We rely on the set of factors chosen by Billio et al. (2012) to explain hedge fund returns by strategy: i) we consider factors that have been used in the hedge fund literature (Agarwal and Naik, 2004; Fung and Hsieh, 2002); ii) the paper demonstrates regime-dependent exposures that reveal a timing effect of these risks; and iii) our objective is not to identify new risk factors but to consider whether hedge fund managers control the intensity of their exposure based on economic uncertainty. Our analysis covers the period from February 1997 to August The following definitions of asset-based risk factors are used in our multi-factor model: 1. SP: the S&P 500 index, characterising the US equity market risk factor; Obtained from Thomson Financial Datastream, Inc. 5

6 2. SMB: the Small minus Big index is computed as the monthly return difference between the MSCI world small minus MSCI world large indexes; 1 3. HML: the High minus Low index is computed as the monthly return difference between the MSCI world value minus MSCI world growth indexes; 1 4. UMD: the Carhart momentum factor or the relative performance of winner over loser stocks; 2 5. EM: the MSCI Emerging Markets index; 1 6. DVIX: the first difference in the implied volatility of the US equity market; 3 7. GSCI: the S&P Goldman Sachs Commodity Index; 1 8. Term: the term spread measured as the difference between yields on 10-year and 3-month Treasury bills computed as the difference between US Citigroup Treasury 7-10Y and US Citigroup 3-month T-bill; and 1 9. DEF: the default spread measured as the difference between yields on BBB-rated and AAA/ AA-rated corporate bonds computed as the difference between the US Citigroup USBIG corporate BBB and US Citigroup USBIG corporate AAA/AA indexes. 1 Using a Kalman filter to estimate unobservable time-varying risk exposure, we perform a dynamic return-based style analysis. We assume that the risk exposure dynamics follow a random walk; hence, the state-space representation of these dynamics is given by the following system of equations: (1) (2) where β i,t represents the time series of risk exposure to factor i,. In the same vein as Lobosco and DiBartolomeo (1997), we do not include an intercept in equation 1, F i,t represents the time series of returns to factor i, and R t is the time series of returns for a given hedge fund strategy. Furthermore, as in Agarwal and Naik (2000), because hedge funds exhibit a great deal of flexibility in terms of asset allocation (e.g., short selling, cash holding), we allow for negative exposure to risk factors and relax the constraint that style weights must sum to one. 3.1 Dynamic exposure and macroeconomic uncertainty We then relate the changes in betas to economic state variables. We consider 6 macroeconomic factors, as in Bali et al. (2014): 1. DIV: the aggregate dividend yield on the S&P 500 Index; 4 2. INF: the US inflation rate; 4 3. GDP: the US monthly growth rate of real GDP per capita; 5 (3) Obtained from K. French s website. 3 - Obtained from CBOE website. 4 - Obtained from Robert Shiller s online data library: Obtained from the Federal Reserve Bank of St. Louis:

7 4. RREL: the relative T-bill rate, defined as the difference between the three-month T-bill rate and its 12-month backward moving average; 6 5. UNEMP: the monthly US unemployment rate defined as the number of unemployed individuals as a percentage of the labour force 7 ; and 6. VIX: the implied volatility on the S&P We include the volatility index that was not revealed to be significant from the previous section. Exposure to Delta VIX should be measured with regard to the relation to economic factors, as noted in Billio et al. (2012). We therefore introduce the level of implied volatility of the market into the potential determinants of trades. We allow for asymmetric exposure using a Markov switching model, and we test for the existence of 1, 2 and 3 different states. The academic literature includes a number of tests to identify the optimal number of states (i.e., the Akaike information criterion and the Bayesian information criterion); these tests tend to penalise higher order states with fewer degrees of freedom. Since our objective is to achieve an economic interpretation of hedge funds trades, we start by testing a 3-state system, and if one or more states is non-significant, we reduce the system to 2 states or 1 state. To estimate Markov regime switching, we use the MATLAB package provided by Perlin (2014). We define the following state representation: for State 1 (4) for State 2 (5) where for State 3, (6) for State 1 (7) for State 2 (8) for State 3. (9) Here, β i,t represents the hedge fund time-varying exposure to factor i, as estimated in the previous section; M j,t is the time series of macro factors j; and, and represent the State 1, 2 and 3 influences, respectively, of macro factors j over β i,t. Note that for some regressions, State 3 will become negligible; in that case, only 2 states will be considered. Using the constant coefficient of each regression as the appropriate indicator, we interpret the states with regard to the hedge fund managers perceptions of market factors. For all strategies, data have been arranged such that State 1 represents an up state; State 2, a down state, if two states are considered. In cases of three-state Markov switching, State 3 represents the intermediate state. 6 - Obtained from the Federal Reserve Board: Obtained from the Bureau of Labor Statistics: Obtained from the CBOE: 7

8 3.2 Hedge fund data Hedge fund returns are drawn from the EDHEC-Risk Institute webpage for the period from February 1997 to August Table 1 reports descriptive statistics for the main hedge fund indexes. Biases (backfill, survivorship, selection) in hedge fund data are well known in the literature. The alternative indexes published by the EDHEC are designed to provide good representation and benchmarking of the hedge fund universe. As we do not aim to measure the performance of hedge funds but rather to understand their investment strategies, we are less concerned by the biases that are intrinsic to the reporting procedures. Table 1: This table reports some descriptive statistics for the main hedge fund indexes. Historical monthly returns from the EDHEC-Risk Institute cover the period from February 1997 to August 2015, representing a total of 223 observations. Among equity-focused funds, L/S equity represents the most liquid strategy. The downside risk (represented by negative skewness) of this strategy is lower than that of other strategies. Expected short selling exhibits positive skewness but performs poorly over the sample period. The marketneutral, merger arbitrage, fixed-income arbitrage and relative value strategies can be considered short volatility strategies. These strategies might suffer in the event of market turmoil and sharp increases in volatility. This is represented by strong negative skewness and positive excess kurtosis. Event-driven, convertible arbitrage and distressed securities suffer under specific downside risk (corporate events), which explains the deeply negative skewness. The global macro strategy is the most diversified hedge fund strategy, which might explain its positive skewness. In our analysis, we do not consider funds of funds, CTAs or emerging markets. First, CTAs require a specific assetbased approach to modelling their returns (which we do not follow here). Second, as our objective is to investigate the impact of US economic indicators on hedge fund specific trades and hedge fund styles, we exclude emerging market oriented strategies and funds-of-funds approaches that aggregate different hedge fund styles. Our sample includes periods of high risk aversion and market correction that might be interesting from a macroeconomic perspective: the Asian financial crisis (1997), the Russian/LTCM crisis (1998), the pre- and post- dot-com bubble (2000), and the subprime market crisis related to high-risk mortgages. 4. Dynamic exposure and macroeconomic uncertainty We examine the time-varying exposures of 10 hedge fund styles. Table 2 reports descriptive statistics for these time-varying exposures. 8

9 Table 2: This table presents some descriptive statistics for each series of asset-based risk factor exposure (time-varying risk exposures estimated through a Kalman filter). Each panel reports a different hedge fund strategy. 9

10 We developed 7 hypotheses in Section 2 based on the extant literature on hedge fund risk exposure. We intend to provide insight on hedge fund trades conditional on the economic context. These hypotheses will therefore allow us to shed more light on the links between macroeconomic information and hedge funds trades. A discussion of these 7 hypotheses can be found in Section Long/short equity An L/S equity strategy is a double alpha strategy that is long (short) in undervalued (overvalued) securities. This strategy was the first and original strategy of hedge funds. It consists of a very liquid and widespread strategy across the hedge fund industry. However, it is by far the least complex strategy with regard to the rebalancing of investment trades, as it can be observed from Figure 1. The ranges of exposures are large for almost all factors. Figure 1: This figure presents the long/short equity strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. Table 3 presents the Markov switching estimates for each risk factor of exposure to those relevant macroeconomic variables. A three-state Markov switching model is applied to the exposure of L/S equity to US equity markets yields under State 1, the exposure to US equity proxy commonly found in the literature (i.e., approximately 65%) (see Table 3, Panel A, State 1). Under State 2, however, hedge funds exhibit short bias towards the US equity market. This regime corresponds to the outset of the major crises (1997, , and 2012) and suggests that L/S managers hedge their market exposure in down states. By contrast, State 3 reveals an exposure that is not different from 0, with no clear market view from the managers. In contrast to the findings of Racicot and Théoret (2012), increases in interest rates have a positive impact on allocation to the US equity market. In the down state, we observe reduced short bias towards the US equity market during times of high dividend yields, making short exposures more costly. US unemployment is also an important factor that reduces exposure (in absolute value terms) to the US equity market in both up market (State 1) and a down or depressed market conditions. 10

11 Table 3: This table presents estimates for the long/short equity strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Exposure to emerging markets follows a similar trend, i.e., very high exposure in State 1, nonsignificant exposure (i.e., not significantly different from 0) to this market in State 2 (note that short positions are restricted in some markets) and positive exposure of approximately 22% in State 3 (see Table 3, Panel B). Emerging market trades are not strongly related to any macroeconomic variable. Exposure to emerging markets is determined by managers skills rather than by exogenous macro conditions: we observe a highly asymmetric timing effect between US equity and emerging markets (L/S equity hedge fund exposure to these factors present a correlation of -47%). The unemployment rate and dividend yields appear to be the only economic factors affecting the emerging markets allocation. A rise in the unemployment rate (dividend yields) entails reduced exposure in States 1 and 3 (State 1). As expected, commodity trades are affected by the state of the economy and the business cycle. We consider two regimes: i) State 1 seems to be fully determined by the influence of the unemployment rate, where we observe a significant negative impact on commodity trades; ii) State 2 presents the expected positive impact of inflation on commodity trades. Equity hedge funds allocations of small versus large cap or of growth versus value stocks are highly cyclical. 9 We therefore opt for a two-state Markov switching representation. 9 - Exposure to small versus large capitalisation or value versus growth stocks is highly dynamic, ranging from -64% to 60% and -77% to 52%, respectively. During the recent crisis, the strategies lean towards growth stocks, as shown by the persistent negative exposure. In fact, there is an evident shift in strategy, with a steady downward trend allocation in the HML factor, showing a change in exposure from 35% in June 2007 to -77% in January

12 Exposure to growth versus value stocks is highly conditional on GDP and volatility, i) tilting towards value stocks in State 1 with GDP increases and 2) tilting towards growth stocks during times of increased volatility (higher volatility increases the value of growth options) and towards the US dividend yield. This empirical evidence supports the hedging properties of growth stocks against market discount rates and volatility (Campbell et al., 2016). Small capitalisation stocks are preferred over large cap stocks, as noted by Agarwal and Naik (2004), Billio et al. (2012), and Chan et al. (2006). We observe a long bias in small caps under State 1, with a positive impact of interest rates. We therefore interpret the interest rate level as a proxy for economic expansion, with high growth potential found in small caps. However, in State 2, allocations of small caps decrease with GDP growth but increase with unemployment. Small caps display very specific (idiosyncratic) risks, which may hedge against market risks during economic slowdowns. Large caps are expected to expand more quickly in an up market. As noted by Zhang (2005) for growth stocks, small stocks might also be considered more flexible than large stocks in reducing the level of activity in a down state. Average exposure to credit and term spreads is positive (and significant) under State 1 and negative under State 2. Here, State 1 is an up market period in which hedge fund managers buy the return spread linked to liquidity or default risk. State 2 can be considered a down state in which funds would suffer from margin calls linked to a widening of the spread. This evidence reconciles our results with Hypothesis 2 developed in Section 2. Finally, Table 3, Panel H reports a positive relation between momentum and GDP, indicating that trend-following strategies are preferred during periods of economic expansion. 4.2 Market neutral Market-neutral strategies are double alpha strategies that are neutral with regard to market conditions. Long and short positions are combined to result in zero exposure to directional factors. Figure 2: This figure presents the market-neutral strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. 12

13 As expected, exposure to US and emerging markets is close to 0, on average. A small shift towards US equity occurs when a manager perceives a positive evolution of the market. The credit spread appears to be the most dynamic factor, with several spikes in positive exposure (although negative and heavy spikes are observed in August 1997 and November 2001) during the Asian financial crisis and the dot-com bubble. Table 4 shows the significance of macro variables for explaining trades in US equity, commodities, momentum, credit and term spreads, value versus growth stocks and small versus large cap stocks. Table 4: This table presents estimates for the market-neutral strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Market-neutral funds exhibit differential exposure to the US equity market. They show long bias towards the US equity market under State 1 and negative exposure under State 2 (as shown by the intercept sign in Table 4 Panel A). Their exposure to the US equity market changes significantly according to the economic conditions: i) in an up market (State 1), an increase in inflation or unemployment results in reduced exposure to the US equity market, while exposure tends to increase with GDP growth; ii) in a down or depressed market (State 2), a higher level of implied volatility leads to reduced exposure, while increasing interest and high unemployment rates favour allocations to the US equity market. 13

14 As shown in Table 4, Panel B, dividend yields appear to be key indicators, as hedge fund managers tend to reduce their exposure to large caps in the S&P500 when dividend yields increase. Furthermore, Figure 2 shows that exposure to the SMB factor rapidly shifts from a small cap to a large cap bias. We identify only two periods showing a positive tilt towards small caps: and The macroeconomic analysis reveals two regimes, both characterised by deep negative exposure to small stocks. We observe a positive relationship between SMB loading and dividend yields (in both states) and increased allocations to large caps in cases of GDP growth in State 1, whereas allocations to small caps increase during times of volatility (State 2). These results support our contentions that small capitalisation stocks have hedging properties and that large cap stocks experience speedy recoveries during expansion periods. Figure 2 shows that exposure to value and growth stocks ranges from -12% to 9%. Here, Table 4, Panel C reveals that in one state, the investment focus is on value stocks, while in the other state, managers primarily trade in growth stocks (e.g., 2007 onwards), as noted previously. This confirms the cyclicality of trade in those stocks. In both states, higher interest rates result in reduced exposure to both value and growth stocks. Table 4, Panel D reports that the strategy followed by those hedge fund managers switches from a trend-following strategy under State 1 to a reversal strategy under State 2. As expected, in State 1, GDP growth results in greater exposure to trend-following strategies, while in State 2, an increase in volatility and dividend yield favours a trend-following strategy. Table 4, Panel E shows three states of risk exposure to commodities. Indeed, commodity exposure is driven by dynamic interactions among every macroeconomic variable with three well-defined states. State 1, an up state, is characterised by a strong positive exposure of 53%, which is positively affected by GDP. State 2, a down state, presents a negative bias of -5.6%. Under this state, greater exposure to commodities results from an increase in the inflation rate and in GDP. Finally, State 3 is defined by a roughly neutral bias (intercept less than 2%) only determined by the dynamic interaction of macroeconomic variables. These results are consistent with Figure 2, indicating that commodity exposure has three well-defined periods: from late 1997 to mid-2006, we observe a steady decrease in commodity allocation; from mid-2006 onwards, we observe a shift in the trend, with a sharp increase between 2008 and 2009; and from mid-2009 to 2015, exposure to commodities revert to a down trend, reaching short exposure by late A three-state Markov switching regime (Table 4, Panels F and G) provides better insight into the allocation strategy towards credit and liquidity risks. For both trades, we observe an up state in which the allocation is significantly positive (the funds buying the spread). Short exposure to the term spread is observed in the down state (State 2), where hedge funds might suffer under margin calls and liquidity shortages. The significant factors impacting those trades include the implied volatility of the market, GDP growth, and the interest and unemployment rates. 4.3 Event-driven Event-driven strategies involve investing in both security-specific risks and equity risk. Figure 3 shows that event-driven funds were deeply exposed to the credit spread in the pre-financial crisis period (up to 2007). 14

15 Figure 3: This figure presents the event-driven strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. We can observe a sharp decrease at the outset of the financial crisis. Funds seem to catch up with very high levels of exposure in the recent period. The macroeconomic analysis of fund exposures reveals that exposure to the credit spread follows different dynamics in regimes 1 and 2. Table 5: This table presents estimates for the event-driven strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Regime 1 corresponds to an up state given the positive intercept coefficient, while regime 2 defines a down state scenario. Under the up state, dividend yields and inflation positively affect exposure to the credit spread, while unemployment and interest rates significantly reduce this exposure. By contrast, under a down state, unemployment seems to be the only significant variable, exhibiting a positive impact on credit spread exposure. Event-driven or special situation funds are often considered high beta funds: this is confirmed under State 1 by a significant beta of approximately 52% with respect to the S&P 500, a significant 15

16 average exposure of 39% for SMB and an exposure of up to 170% for HML. Exposure to US equity is reduced during periods of increasing interest rates, unemployment and dividend yields, but this exposure increases during periods of high volatility under State 1. Under State 2, the strategy maintains significant negative exposure to US equity, which is even more negative in the case of an increase in dividend yields. Exposures to small versus large cap as well as to value and growth stocks might change by regime. Under State 1, these funds present a significant tilt towards small caps, which increase during times of high interest rates, and a tilt towards value stocks, although they are negatively affected by dividend yields, unemployment, volatility and inflation. This explains why those funds maintained short exposure to the HML factor during the period , as shown in Figure 3. Only GDP growth has a positive impact on the allocation of value stocks. Figure 3 shows a reversal strategy after the crisis period. This finding is confirmed by the negative loading on the momentum factor under State Merger arbitrage Merger arbitrage strategies (i.e., risk arbitrage) take an equity stake in companies involved in merger transactions. The investment strategy involves capturing part of the acquisition premium, i.e., the spread between the market price of the target and its offered price. The probability of merger failure is embedded in the spread, with higher price spreads indicating higher risk. This investment strategy thus involves strong exposure to the specific risk of a deal during normal conditions. In down markets, however, the risk of a failed or postponed merger is very high, resulting in systematic risk exposure and downside potential (Fung and Hsieh, 2004). Figure 4: This figure presents the merger arbitrage strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. This strategy resembles a short put on the underlying market index: while the upside is limited, the downside is not (Mitchell and Pulvino, 2001). Such a strategy might be strongly negatively affected if volatility increased in a down market; this could explain why we observe reduced (even negative) exposure to the implied volatility from May 2007 onwards in Figure 4. This finding confirms the results regarding the short volatility strategy noted by Mitchell and Pulvino (2012). M&A activity is positively influenced by market cycles. Merger arbitrage funds show stable exposure to the S&P 500 throughout the period, with mean and median values of 11.48% 16

17 and 12.34%, respectively, and a small standard deviation of 1.77%. However, we observe that those hedge funds reduce their exposure in the early stage of a financial crisis to maintain a maximum of 10% exposure. Exposure to emerging markets was significantly reduced during the Asian crisis. In the prelude to the subprime crisis, growth was observed in emerging markets rather than in developing markets, which might explain the loading on this factor. Consistent with Figure 4, our analysis reveals one main regime (State 1) with a significant average exposure close to 17%, as presented in Table 6 Panel A. Table 6: This table presents estimates for the merger arbitrage strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Merger arbitrage funds take long positions in the target and short positions in the acquirer. An increase in the dividend yield results in a decrease in exposure to the S&P 500, since the short leg of the trade might become expensive. Funds tend to be slightly more exposed to the US equity market during times of high expected volatility. Fund exposure to a momentum strategy varies between 40% and -10%. The Markov switching model confirms the existence of two regimes with regard to the UMD factor. Under State 1, the funds exhibit trend-following strategies (as shown by the positive and significant intercept coefficient), with a positive impact of GDP growth and volatility and a negative effect of dividend yields and unemployment rate. By contrast, under State 2, we observe a reversal strategy modulated by the positive effect of dividend yields and the negative impact of higher interest rates. This finding is supported by Figure 4, which shows the use of momentum strategies over the periods and identified by Alexandridis et al. (2012) as merger waves. Macroeconomic factors have different impacts on exposure to those strategies. In a bullish market, volatility has a positive impact on the success of a merger. In a down market, the strategy returns suffer with increased interest rates. Figure 4 shows a sharp transition between positive and negative exposure to the value factor. The strategy has a focus on value stocks that decrease with the level of dividend yields, as already noted. However, during the recent financial crisis (2010 onwards), we observe a tilt towards growth stocks. The macroeconomic analysis reveals that exposure to growth stocks rises with reduced GDP growth, which supports our hypothesis that such investments are crisis investments. 17

18 Finally, merger arbitrage funds are small cap oriented under State 1 and seem to be indifferent between large or small cap firms under State 2 (the intercept is not significantly different from zero). However, allocation to mergers involving small caps is reduced when the unemployment rate and volatility increase under State 1 (as shown in Figure 4 over the period ). Under State 2, dividend yields positively affect the allocation weight for small stocks (consistent with preferences for low-dividend-paying stocks). 4.5 Distressed securities A distressed securities hedge fund strategy involves maintaining a stake in undervalued securities prone to restructuring. This is essentially a bet on a specific (micro) risk, as the success of the strategy relies primarily on the ability of the company to renegotiate its borrowing. Figure 5: This figure presents the distressed securities strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. The credit spread appears to be the most important dynamic factor. An analysis of credit risk exposure reveals two regimes: i) under State 1, managers maintain positive exposure to credit risk (which we qualify as an up state), and ii) under State 2, managers have a significant negative stake in this risk given the margin calls. Under both regimes, GDP growth has a positive impact. Funds are more likely to capture the credit spread related to company recovery. In addition, under up market conditions, managers tend to decrease their exposure to the credit spread when interest rates increase. Under down or depressed market conditions, we observe greater exposure to credit risk (roughly 15%) for a unit increase in the interest rate. Interest rate increases also appear to be signs of market recovery. 18 Figure 5 shows that this strategy tends to yield a very dynamic trade in value versus growth stocks (with exposure ranging from -66% to +45%). Indeed, our analysis shows no particular tilt towards value or growth stocks (the intercept is not significantly different from zero), indicating fully cyclical allocation based on the levels of key macro indicators, such as the unemployment rate, volatility and GDP, consistent over time. The higher the volatility, the higher the investment in growth stocks, a pattern we relate to the growth options embedded in growth firms whose values vary positively with volatility (see Campbell et al., 2016; Grullon et al., 2012). Furthermore, the higher the GDP, the higher the exposure to value stocks. Finally, the higher the dividend yield, the higher the exposure to growth stocks; hence, hedge fund managers following this strategy focus more on the potential returns of investments.

19 Table 7: This table presents estimates for the distressed securities strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. As shown in Table 7, Panel D, allocation to small versus large caps follows two regimes. In State 1, exposure to small caps decreases with volatility, GDP growth, and dividend yield. Indeed, the negative relation with GDP growth confirms the evidence of Racicot and Théoret (2012) that distressed securities strategies benefit from economic slowdowns. By contrast, in State 2, volatility seems to be the only variable with a positive significant impact on the allocation to small firms Finally, exposure to emerging markets also differs by market regime. In State 1, exposure to emerging markets is positive, on average, and increases with US GDP growth, and it seems to be the only variable determining this state. By contrast, exposure in State 2 exhibits negative bias (negative intercept) and seems to be determined by a number of variables, particularly GDP growth and inflation. Such negative relationships mean that recovery might be found in other than emerging markets, which are always affected by a flight-to-quality phenomenon. Exposure to the term spread is positive in State 1 (positive intercept) and negative in State 2 (negative intercept). Under State 1, managers tend to capture the liquidity return spread from investing in distressed securities. Under the down state, the strategy is short in liquidity risk, but this negative exposure is reduced as interest rates and GDP rise (i.e., as the market shows signs of recovery). 4.6 Bond-like strategies This category includes fixed-income and convertible bond arbitrage funds. On the one hand, fixed-income arbitrage involve trades in the bond market. On the other hand, convertible arbitrage funds take long undervalued convertible bonds, hedging their trades with short positions in the underlying stocks. By doing so, they protect themselves against fluctuations in equity risk. Figures 6 and 7 provide insight into the dynamic trading in this specific strategy. 19

20 Figure 6: This figure presents the fixed-income arbitrage strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. Figure 7: This figure presents the convertible bond arbitrage strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. For both strategies, exposure to credit and term spreads follows two regimes. Fixed-income strategies aim to capture the credit premium in the market, as shown by its positive intercept coefficient under State 1. Exposure to liquidity risk in the up state is small. In the down state, however, fixed-income hedge funds, surprisingly, exhibit short positions in the liquidity spread, and the magnitude of the short bias increases with the level of GDP and market volatility but decreases with the unemployment rate. Conversely, funds have short positions in the credit spread under the down state, but their short positions weaken in cases of economic recovery (i.e., increases in GDP, decreases in unemployment rate). 20

21 Table 8: This table presents estimates for the convertible arbitrage strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Table 9: This table presents estimates for the fixed-income arbitrage strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. With regard to convertible bonds, exposure to credit risk tends to increase with GDP growth in both states. Such evidence explains why exposure to credit spread increased during the recent up period. In the second regime (State 2), we observe an average significant negative exposure to the credit spread that is strengthened by an increase in volatility and diminished with GDP, the unemployment rate, and dividend yields. Exposure to SMB and HML for fixed-income funds depends on macroeconomic factors. As commonly shown for other strategies, exposure to small and/or growth stocks increases with market volatility and the unemployment rate. A negative intercept in Table 8, Panel D indicates that convertible arbitrage funds show a preference for allocating funds to growth rather than to value stocks. As shown in Agarwal et al. (2016), hedge funds favour market uncertainty during good market conditions and increase their exposure to the SMB spread during times of high volatility to take advantage of potential micro risk that is intrinsic to small caps. 21

22 4.7 Relative value Relative value strategies combine long and short positions to capture the price spread that might arise from mispricing between two securities. Figure 8: This figure presents the relative value strategy s time-varying exposure obtained by the Kalman filter from February 1997 to August Upper graph: exposure to SP, EM, and DVIX. Middle graph: exposure to UMD, SMB, and HML. Lower graph: exposure to GSCI, Term, and DEF. The credit spread appears to be the most dynamic factor: exposure to credit risk follows two regimes. Table 10: This table presents estimates for the relative value strategy s time-varying exposure to six different macroeconomic variables (namely, DIV, INF, GDP, RREL, UNEMP, and VIX). Each panel reports a different time-varying exposure (dependent variable) and the corresponding estimated coefficients, with p-values in parentheses. We test for three different regimes (State 1, State 2, and State 3) using a Markov switching model. Under the up state (State 1), exposure to credit is impressively positive and significant, independent of any macroeconomic variable. Under the down state, exposure is timed according to the level of unemployment (positive exposure), volatility (negative exposure), and GDP (negative exposure). GDP growth tightens the spread, while high unemployment widens the spread. The strategy maintains positive exposure to small stocks and short exposure to large caps, but this changes according to the macroeconomic indicators in each state. Among the important factors, 22