Market Liquidity Risk in Hedge Funds
“Life punishes those who delay.”
-Steve R. Schmidt 10436006
Abstract
This master thesis investigates hedge funds’ exposures towards systematic risks when accounting for innovations in aggregate liquidity. Applying conditional state-dependent asset pricing models and Monte Carlo simulations, it was found that exogenous liquidity fluctuations are broadly not anticipated in the cross-section of funds and most individual styles. Concerning liquidity risk, hedge funds can be viewed as post-shock responders. Delayed transactions turn out to have a delevering effect on market exposures. Liquidity risk simulations have shown that this post-shock delevering is accompanied by an aggregated reduction of outperformance by 4% on average in months of acute liquidity shortage.
University of Amsterdam Supervisor: Dr. Liang Zou
Statement of Originality
This document is written by Student Steve Robert Schmidt, who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents 1 Introduction . . . 1 2 Related literature . . . 2 3 Data . . . 6 4 Methodology . . . 10 5 Results . . . 17
5.1 Is there a hidden exposure to market risk in market neutral funds? . . . 17
5.2 Market exposure and liquidity risk . . . 19
5.3 Do hedge funds respond to liquidity shocks? . . . 22
6 Robustness Analysis . . . 24
6.1 Differences in styles . . . 24
6.2 The impact of a liquidity crisis . . . 27
6.3 Liquidity risk simulations . . . 29
1 Introduction
The common perception that hedge funds are exposed to liquidity risks goes back to the collapse of LTCM in 1998. Henceforth, research has paid more attention to the involved premiums, and costs, that are related to illiquid assets and markets on the performance of hedge funds. As the shockwaves of the financial crisis in 2008 might have taught us, a better understanding of liquidity is much-needed both for investors and the entire economy. Thus, the gauge of these multi-dimensional effects by risk management is more topical than ever.
On behalf of investors and financiers of hedge funds, several questions need to be answered: First, is the market exposure in hedge funds sensitive towards fluctuations in aggregated liquidity? If so, how can these variations be explained, i.e. are they attributed to portfolio transactions in anticipation or in response to shocks and could they be neutralized? And second, is the impact of market liquidity risks associated with a premium or a cost of outperformance?
Many empirical studies have revealed that hedge funds show a weak correlation to traditional asset classes, e.g. stocks and bonds. The attempt to explain their returns in the classical mean-variance context, consequently, leads to low market sensitivities and biased intercepts. The CAPM, being suitable to assess the performance and risk-drivers of low-leverage, buy-side investment pools, such as mutual and pension funds, often delivers questionable predictions regarding the risk-return profile and the portfolio composition of hedge funds. In recent years, significant improvements have been attained in multi-factor models and downside risk models to explain the characteristics of these alternative investments.
Investor sentiment is closely related to demand and supply of securities, price discovery and, not least, liquidity of single assets and markets. Thus it is necessary not only to consider downside risk, but also its interplay with liquidity fluctuations in order to estimate market sensitivities. These altering market con-ditions can be reflected in a model, which allows for multiple scenarios. Conditional on contemporaneous and lagged liquidity innovations, I use a state-dependent multi-factor model to examine systematic risks in hedge funds. In particular, it was found that current shocks to market liquidity are associated with a higher market exposure, especially in downmarkets, while preceding shocks lead on average to a risk reduction suggesting that liquidity risk in markets was broadly not anticipated. The effect was particularly strong in a liquidity crisis, whereby delevering in the last instance involved aggregated costs of about 4% per month. Further, the magnitude of responses varied across styles and was strongest for emerging market funds, long/short portfolios and market neutral strategies. These styles were able to ex post neutralize liquidity fluctuations, or even enhance their risk exposure.
This thesis is organized as follows: Section 2 discusses the literature on market liquidity risk as well as the evidence in hedge funds, Section 3 describes the data, Section 4 explains the methodology, Section 5 presents the results, Section 6 provides further consistency checks addressing heterogeneity in entities and time periods as well as the causal relation between variables, and Section 7 concludes.
2 Related literature
This section aims to provide an overview on the available literature regarding market liquidity risk, both from a theoretical standpoint and with respect to the evidence in hedge funds. Theoretical papers introduce market liquidity as a priced state variable and provide residual measures to shocks in aggregate liquidity; one of which will be summarized in detail below. Following that, empirical findings of several application studies will be presented.
Pastor and Stambaugh (2003) examine an aspect of market liquidity attributed to price changes in-duced by order flows. They design an indicator for aggregate liquidity as a cross-sectional, monthly average of liquidity measures of individual stocks. Thereby, the stock-individual liquidity risk loading, γi,t, in a given
month was estimated by the average effect of the trading volume on the next day’s excess return, whereby the today’s volume was given the sign of the excess return on that day. This signed volume is interpreted as directional order flow. Their model predicts increased liquidity in month t for stock i, if both daily excess returns and the order flow of the preceding day follow on average the same sign, so that γi,t > 0. To the
contrary, a liquidity drop for an individual stock is reflected by a reverse effect of the order flow on the next day’s excess return, so-called return reversal, if volume fluctuations lead on average to lower excess returns, so that γi,t< 0. This can be seen from their regression model
ri,d+1,te = θi,t+ φi,tri,d,t+ γi,tsign(rei,d,t) · vi,d,t+ εi,d,t d= 1, . . . , D ,
where d are trading days in month t, re
i,d,t= ri,d,t− rm,d,t represents the excess return of the stock related to
the CRSP value-weighted market return, vi,d,t is the dollar trading volume, while sign(rei,d,t) · vi,d,trepresents
the order flow; θi,t and φi,t are stock- and month-specific intercept and slope coefficients of the daily excess
returns regressed on plain prior-day returns, respectively.
Using these stock-individual liquidity estimates, ˆγi,t, for N listed stocks on American exchanges in a
given month, the aggregated liquidity factor is calculated as an average liquidity coefficient across the stocks in the market, ˆ γt = mt m1· 1 N N
∑
i=1 ˆ γi,t ,multiplied by the current size of the stock market, mt, in relation to its size in August 1962, m1, such that
the obtained time series is not disturbed by the effect of changing market size, growth and dollar values, and thus comparable in scale over time. In their further analysis, and more relevant to this thesis, Pastor and Stambaugh (2003) extracted an aggregated liquidity risk factor representing the innovations, i.e. shocks to changes in aggregated liquidity, of an AR(2) model with respect to their estimated liquidity factor:
ˆ
γt = a ˆγt−1+ b ˆγt−2+ ut .
Thereby, the normalized residual time series
Lt=
1 100· ut ,
embodies exogenous shocks to aggregated liquidity, which can not be explained by autocorrelation of previous liquidity conditions in markets, where latter are induced by time-varying order flow, and return reversals in particular. By this means, the authors were able to construct a series of random effects equipped with systematic liquidity risk, and coinciding with well-known extreme market events, such as the LTMC collapse, New Market crash, Lehman bankruptcy and the recent financial crisis, among others.
Pastor and Stambaugh (2003) state that expected changes in aggregate liquidity, E[∆ ˆγt], are able to
predict stock market returns one month ahead. Thereby, according to the authors, it is essential to control for liquidity innovations in order to prevent biases in expected stock returns and inherent risks. In their empirical analysis they reveal that stocks with higher sensitivities towards innovations in aggregate liquidity compensate investors on average with higher returns in the long-run. Market liquidity thus can be seen as a priced state variable, or in other words, a risk loading helping to explain returns of stocks and portfolios. The authors observe that stocks of smaller firms tend to be less liquid, and demonstrate that abnormal returns of small-firm decile portfolios can be explained by liquidity risks to a great extent. Furthermore, they show that momentum effects and liquidity risk are interrelated. In particular, the relative size of the momentum coefficient in tangency portfolios reduced by more than half when additionally controlling for liquidity risk spreads, in a mean variance context.
Sadka (2006) designed a similar factor for the pricing of market liquidity risk on the basis of price impact costs. Likewise, his measure co-moves with extreme shocks to financial markets. Thereby, Sadka’s factor exhibits a slightly weaker correlation with stock market returns as well as to Fama-French factors, whereas it partly explains news-related return anomalies that can be ascribed to momentum effects and post-earnings announcement drifts. Sadka (2010) studies exogenous liquidity risks in the cross-section of hedge funds, thereby providing empirical evidence to the applicability of his liquidity factor in pricing of alternative investments. He reveals that covariations of hedge fund returns with unanticipated fluctuations
in aggregated liquidity is a vital risk driver and determinant of fund performance. In particular, hedge funds with higher liquidity risk loadings outperformed low-loading funds by 6% p.a. in a sample period from 1994 to 2008. This result suggests that performance tends to be driven by multiple beta factors, i.e systematic components including liquidity risk. Sadka further points out that liquidity risk exposure is priced differently across fund styles. Highest sensitivities were observed for Multi-Strategies, Emerging Markets, Convertible Arbitrage and Equity Long/Short, whereas Global Macro and Fixed Income Arbitrage were less sensitive, when his liquidity factor is included in Fung-Hiesh’s seven factor model (2001 and 2004). In a comparison of crisis and non-crisis periods, he shows that the return spread between high- and low-loading decile portfolios dramatically increases in turbulent times. Essentially, funds with significant liquidity risk exposures bear relatively higher losses.
Brunnermeier and Pederesen (2008 and 2010) detail the economical mechanism in a market-wide liquidity crunch. The authors argue that speculators, such as hedge funds, can face funding constraints in a liquidity crisis. This is triggered by the fact that their financiers (primarily commercial and investment banks), which themselves experience acute refinancing requirements, increase dealer margins. Accompanied by a reduced asset value of their holdings on account of falling prices, hedge funds are forced to delever, i.e. to unwind their positions, and even fire sell part of their portfolio. This puts further pressure on prices, especially of illiquid securities, and thus deteriorates market liquidity even more. Latter, in turn, leads to higher dealer losses, which snowballs higher margins and further sells. These are know as margin and loss spirals, respectively. Based on this theory, Boyson et al (2010) provide evidence that large adverse shocks to asset and funding liquidity lead to a contagion across hedge funds meaning a fund-wide clustering of negative returns in the same months. This positive co-dependence was estimated using quantile regressions. Further, their logit models uncovered its sources, namely, the probability to observe a contagion increases through a widening of the TED spread, and thus limited interbank lending, as well as shocks to credit spreads, banks stocks, prime brokers, hedge fund flows and market liquidity.
In accord with these findings, several related studies demonstrate the existence of liquidity premiums in hedge funds. Teo (2010) reveals in decile portfolio regressions that funds with highest liquidity betas outperformed those with lowest liquidity factor loadings by 5.8% per year. This spread further widens if hedge funds experience higher capital inflows from investors. In contrast, an outflow of capital decreased abnormal returns by 9.13 percentage points compared to high flow portfolios, if market liquidity innovations simultaneously fell into their 20thpercentile. The author ascribes this performance reduction to fire sales of assets. He further shows that excessive liquidity risks are linked to agency problems with respect to manager compensation schemes like reduced performance fees, low option deltas and missing share participation. Aragon (2004) examines share restrictions in hedge funds. In case redemption notice periods are set and/or
lockup provisions are charged to investors, annual excess returns of lockup funds were on average 4% higher compared to non-lockup funds. These sell restrictions imposed to investors justify to claim a premium for holding illiquid shares. Thereby, the effect was captured in so-called liquidity alphas, which turned out to be positive for lookup funds and negative or insignificant for non-lockup funds. Share restrictions were also related to funds’ assets, in a sense that holdings of lockup funds inhered higher liquidity risks loadings and redemption costs. Latter suggests that investors with low-liquidity needs have been the target group of these funds benefiting from high liquidity risk loadings in the long-run.
Gibson and Wang (2010 and 2013) show that the predictable component of explained hedge funds returns reduces significantly when controlling for exogenous liquidity risks. These lower alpha coefficients were observed no matter if investors have (and update) dogmatic, agnostic or sceptical beliefs regarding the managerial abilities of fund managers. Therefore, outperformance in the classical sense, can be seen as a compensation for funds being exposed to liquidity risks. This effect, however, varies across styles, and was strongest for emerging market and event driven hedge funds. In contrast, market neutral funds and long/short portfolios seem to earn a rent on liquidity provision as they act as liquidity providers in times of tight funding, following the authors.
Cao, Chen, Liang and Lo (2013) investigate managers’ abilities to time and exploit liquidity risks in markets. To account for linear and option-like factors in funds, the authors employ Fung and Hiesh’s seven factor model consisting of a coefficient for the market return, here denoted by MKTt, and six other factor
loadings fj, j = {1, . . . , 6}. Additionally, they include a so-called liquidity-timing factor, γp. Latter is the
coefficient of an interaction between the market return and the expected deviation of liquidity innovations, Lt, as introduced by Pastor and Stambaugh (2003), from its long-term mean ¯L. Formally, their model
rp,t = αp+ βpMKTt+ γpMKTt(Lt− ¯L) + J
∑
j=1βjfj,t+ εp,t ,
imposes a state-dependent beta factor being linear in the market return, yet subject to variations in market liquidity, which were stated to be anticipated by fund managers one month ahead. According to the authors, managers would have the ability to foresee liquidity shocks, if the contribution of γp to fund returns rp,t is
negative, such that both below and above average innovations mitigate the impact of market returns on fund performance.
Cao et al (2013) indeed find evidence for liquidity timing in the sense that hedge funds inhered lower market exposures, in case of intensified shocks to market liquidity of the contemporaneous period. Nevertheless, some critical remarks have to be made at this point. If perceived market liquidity gave rise to form reliable expectations causing managers to hedge liquidity risks in advance, then hedge funds would not be affected
by exogenous liquidity shocks, or, if so, only to their benefit. This argumentation, however, stays somewhat in contrast to the literature, especially regarding the effects of “liquidity spirals” as argued by Brunnermeier and Pederesen (2008 and 2010). Further, it appears that their model undermines the liquidity risks in hedge funds, in a sense that below average market liquidity in the preceding month could actually lead to a higher exposure, and thus put pressure on fund returns. Latter occurs if post-shock transactions incurred losses, e.g. via margin calls and fire sales of assets, aggravated by share redemptions and withdrawals of credit. A time lag for the liquidity-timing factor, which was not considered in their model, might help to uncover this effect.
The last instance raises the question whether “timing” has been a result of ex ante “foreseen” fluctu-ations in market liquidty, or rather a mere ex post response to undergone, unanticipated shocks, and thus a (un)lucky accompanying effect to dynamic hedging. In addition to the investigation of exogenous liquidity risks in hedge funds, the answer to this question will be a central aspect of my empirical analysis.
3 Data
Hedge fund data is often subject to biases. Due to a less restrictive regulatory framework concerning report-ing standards of these investment vehicles, exclusively monthly returns are public available. Hedge funds are predominantly private closed-end investment products. The publication of fund specific information, such as returns and asset holdings, depends on the manager’s decision. Data registration on private fund databases preferably takes place, if funds have been generating positive returns over a longer period of time. Of course, a more subtle intention of making data available to a broader public is indirect advertising, and in this way convincing potential investors of the track record of managers’ portfolios. This example is referred to as backfill bias, or instant history bias, in the literature, i.e. an upward bias owed to the fact that historical performance data is back filled once managers decide to register their funds. A similar upward bias is the so-called survivorship bias, which occurs once bankrupt funds stop reporting and drop out of the sample. Hence, the aggregated statistics of the remaining entities look, as matter of fact, better than they are. To partly alleviate these biases, often the first and last observations are dropped, when examining the data. An alternative, which will be employed later, is the consideration of fund fixed effects, which is particularly useful in panel data regressions without losing information. A multi-period sampling bias might occur, if funds are required to provide sufficient records before they are included in the sample. According to Fung and Hiesh (2000), a performance comparison between portfolios with long and shorter history showed that this bias was actually very small.
data set is unbalanced and involves entities, which have recorded between one and 228 observations. In total, 849 funds were listed on the provider’s North America database over a time period from January 1994 (ear-liest observation) to December 2012 (last date available). The full sample contains various strategies, which predominantly belong to the broad category ”Equity Hedge”. Holdings, which were not accessible, depend on the region individual funds focus on; the vast majority of the funds in the sample operated on a global scale. A subsample of 147 funds exclusively invests in fixed income instruments. Latter represent an isolated category beyond equity-related styles. This is not only attributed to the fact that stocks and bonds behave differently as asset classes, but also due to different investment strategies. Common to both is that perceived fundamental and/or relative misvaluations induced by market conditions and investor sentiment are unveiled and exploited. Usually, the quantitative requirements to screen markets for arbitrage opportunities are higher for fixed income securities. Detailed style definitions of the funds in the sample can be found in the appendix.
Time series of explanatory and control variables were obtained from Wharton Research Data Ser-vices of the University of Pennsylvania. These series encompass monthly data on market returns, i.e. the value-weighted return of all stocks traded on the NYSE, AMEX, and NASDAQ from CRSP, the risk free rate, i.e. the one month Treasury Bill rate, Fama-French portfolio factors (High Minus Low, Small Minus Big), Carhart’s Momentum factor, as well as Pastor-Stambaugh’s liquidity risk factor, i.e. the innovations in aggregated liquidity, Lt, until December 2012. Even though the factor is estimated on the basis of the
North American equity market, presumably, existing leapfrog effects on global exchanges might also allow its applicability on globally oriented funds.
As illustrated in Figure 1, innovations in aggregate liquidity can be interpreted as random shocks that very well capture market extremes, both in time and in size. Negative spikes, i.e. the observations in the first percentile, coincide with events like the collapse of LTCM (Oktober 1998), Dot-com crash (April 2000) or the bankruptcy of Lehman Brothers (September 2008). The risk factor has a slightly left-skewed distribution with a mean of zero, non-constant volatility and infrequent clusters on the left tail. These features should be kept in mind when applying OLS.
Table 1 provides an overview on the descriptive statistics of the individual strategies in the sample. On average, hedge funds generated positive monthly returns with an unconditional mean of 0.66% and a standard deviation of 4.73%, whereas the mean of the market returns was 0.52% with a standard deviation of 4.58%; both moments are quite alike. The highest mean returns were achieved by Emerging Market (0.85%) and Multi Strategy funds (0.91%); the lowest were realized in Balanced (-0.30%) and Tail Risk strategies (-1.29%). The standard deviation of returns was highest in Event Driven (6.63%) and Emerging Market funds (6.32%) and lowest for Equity Market Neutral (1.87%) and Statistical Arbitrage (1.99%). In
total, the distribution of hedge fund returns is skewed to the right, with a skewness of S = 0.71, and heavy tailed, with a kurtosis of K = 36.26, and thus leptokurtic. In comparison to the market, hedge fund returns are relatively more concentrated in the center of the distribution with more frequent, extreme returns on both sides of the tail, whereby the overall range tends to be shifted towards positive values. Clearly, the Jarque-Bera test for normality is rejected in the full sample and in 14 out of 16 styles. However, it is worth mentioning that the test statistic
JB=n 6 S2+(K − 3) 2 4 ∼ χ(2)
reacts quite sensitive towards slight changes in the third and fourth moment, and tends to reject the joint hypothesis for zero-equivalence of skewness and excess kurtosis very easily, especially in large sam-ples. The only categories for which normality could be verfied were Statistical Arbitrage and Tail Risk funds.
Returns of single styles can be widely disperse as illustrated by location measures and the relation of the interquartile range (IQR) to the full range of observations (see again Table 1). For instance, the interior 50% of observed returns of Fixed Income funds range from -0.21% to 1.42%, whereas its full range covers an interval between -76.99% and 108.39% per month. Similar abnormal returns were observed for Emerging Market, Macro and Sector funds. In contrast, strategies, which focus on the reduction of systematic risks, such as Equity Market Neutral and Statistical Arbitrage, had fewer negative and positive outliers as well as a very tight IQR, while earning positive returns in more than 50% of the cases. The highest interior dispersion was observed for Tail Risk with an IQR of 10.31 percentage points. In total, the median and IQR of hedge fund returns were both lower compared to stock market returns in the full sample period.
To give a first indication that returns are affected by fluctuations in market liquidity, Table 1 displays the mean and standard deviation conditional on the sign of the innovations in aggregated liquidity. Positive and negative innovations reflect months for which market liquidity was increased and reduced, respectively. Further, the conditional means and standard deviations with respect to the liquidity state in markets were tested for equality in each category, i.e. the differences in means are equal to zero (µ1− µ2= 0) and the
variance ratios are equal to one (σ1/σ2= 1). The tests indicate that reduced market liquidity is associated
with significantly lower mean returns in 11 out of 16 styles, the full sample and the market. On top of that, the variance of returns was increased when market liquidity was reduced for 15 styles. These results suggest that hedge fund returns are interrelated with shocks in aggregated liquidity, however it can not be interpreted as a causal relation at this point. That is, the existence of a liquidity risk exposure requires more complex models and statistical techniques, which will be introduced in the following sections.
The performance of different strategies can be compared with that of the stock market when forming portfolios of hedge funds. A portfolio with so-called naive diversification is composed of all active hedge
funds i of a given style j with equal weights wit = wt in month t. Thereby, the value of a style portfolio, Ptj=
∑
i wtpitj , with∑
i wt= 1 ,is normalized by the average portfolio value at December 1999, such that P12/99j = 1. This date was chosen for two reasons: first, the majority of funds was launched after 2000, and second, the end of the 90s represent the hight of the New Market; the subsequent months thus allow a performance comparison in falling markets. The resulting charts for selected styles are illustrated in Figure 2. As can be seen, all portfolios outperformed the returns of American stock markets between December 1999 and December 2012, especially Emerging Market funds. Overall higher pro-cyclical sensitivities towards market movements were observed in Equity Long Only and Sector funds. Judging from the graphs, hedge funds more or less behaved acyclically in the New Market crash in 2000, which can not be stated for the financial crisis in 2008. Style portfolios such as Macro, Fixed Income and Equity Long/Short seem to have outperformed in both downmarkets, however they did not relatively gain in subsequent upmarkets. It has to be emphasized that this is not necessarily the case on the level of individual funds, as diversification benefits in portfolios of funds mitigate the impact of individual return fluctuations, especially for Fixed Income strategies in this particular instance. That is, individual fund positions can inhere substantial systematic and idiosyncratic risks.
The return distributions for the full sample and a crisis subsample is illustrated in Figure 3. Thereby, the latter data set consists of 7742 observations conditional on market returns or liquidity innovations falling into the 5th percentile of their respective distributions, whereby the subsequent month has been included to account for after-shock effects. Further, returns were winsorized at a level of 0.5% on both sides of the distribution. Looking at the tails one might ask whether the “hedge” in hedge funds indeed refers to risk management measures. While the unconditional distribution exhibits a longer right tail, the prevalence and co-dependence of negative extremes is more pronounced in the crisis sample with a longer left tail. This is supported by the findings of Boyson et al (2010), and again suggests that fund returns are affected by both market and liquidity risk. Likewise, outliers are a result of taking on excessive leverage, i.e. in parts credit financed positions in financial derivatives, which is motivated by Brooks and Kat (2002).
The positive interrelation between fund returns and systematic risk components is also underlined by the cross-correlations of variables presented in Table 2. The difference between individual fund returns and the market return of the previous month, xit = rit− rm,t−1, is highly correlated with the return difference
in markets between these two subsequent months, xm,t = rm,t− rm,t−1, both with about 0.62 in the full and
crisis sample. The correlation between plain fund and market returns, rit and rm,t, was positive as well,
however with a value of 0.34 rather low (not displayed here). Latter, might be attributed to the fact that a great deal of the long and short positions in the cross-section of funds annul each other, which often leads
to the questionable conclusion that market exposure in hedge funds is generally low. Fama-French factors and Carhart’s factor seem to be practicable control variables, whereby the value and momentum factor were negatively correlated with the return differences between hedge funds and markets. Strikingly, the correla-tion of xit with innovations in aggregated liquidity increased from 0.10 to 0.32 in crisis periods. Similarly,
the respective correlation to preceding liquidity shocks turned from negative to positive significant. This indicates that Pastor and Stambaugh’s factor uncovers a vital source of risk supplementary to funds’ general market exposures, especially in times of financial distress.
On the whole, the descriptive statistics and the cross-correlations support the applicability of market liquidity innovations as a factor in an asset pricing model on hedge funds. Its interplay with price-related risk loadings appears to be useful to mitigate omitted variable biases, while not simultaneously imposing threats of multicollinearity, as the magnitudes of the Pearson correlation coefficients are overall moderate. This notion will be revisited in the next sections.
4 Methodology
Equity hedge is a board category of hedge funds that are designed to screen stock markets for promising price opportunities. Subcategories, such as market neutral funds and long/short portfolios, employ statistical techniques to predict price developments, and to detect and exploit potential mispricing by maintaining both long and short positions in equities and related financial derivatives. If their quantitative and/or fundamental investment approach is able to generate positive returns in different environments, or even independent of the market, a model is required that distinguishes between rising and falling markets on the one side. In this respect, asset pricing with downside risk appears to be appropriate, as suggested by Zou (2005) and Ang et al (2005). The decomposition of returns in positive and negative observations incorporates the possibility to reflect option-like payoffs in hedge funds and also might mitigate the eroding effect of equalizing long and short positions on regressions coefficients in comparison to single factor models.
Market liquidity, in a broader sense, is a sentiment indicator measuring the ease of trading an asset. It gained in importance for monetary policy, and also has become a focus of attention in the academic literature concerning financial economics, especially after the financial crisis in 2008. Assessing whether hedge funds bear risks arising from fluctuations in market liquidity demands for a model extension that allows to isolate the effect of an increase or decrease in market liquidity from their general market exposure. The magnitude and direction of this additional liquidity risk effect most likely differ in rising and falling markets. In a nutshell, I propose to estimate an incremental liquidity-based risk surcharge that comes on top
of both up- and down market exposures once market liquidity is reduced. These needs can be served in a state-dependent multi-factor model:
xit = αi + αLDt + β1x¯m,t + β2xm,t + δ1x¯m,t× Dt + δ2xm,t× Dt
+ γ1r2m,t + γ2HMLt + γ3SMBt + γ4MOMt + γ5Lt + γ6Lt−1 + uit , (1)
where xit = ri,t− r denotes the excess return of an individual fund i, ¯xm,t= rm,t− r if rm,t≥ r, zero otherwise,
and xm,t= rm,t− r if rm,t < r, zero otherwise, represent mutually exclusive excess market returns subject to a
reference point r in up and down markets, respectively. To reduce variation in residuals, thus to improve the estimation of idiosyncratic risk in hedge funds measured by σu=pVar[uit], control variables are included
in the regression: r2m,t as a proxy for the market volatility, HMLt, SMBt, and MOMt as value, size and
momentum factors introduced by Fama-French and Carhart, as well as Lt and Lt−1as contemporaneous and
lagged innovations in aggregated liquidity introduced by Pastor and Stambaugh. To reduce the impact of outliers, which are a likely result of leveraged bets, the regressions will base on winsorized fund returns with p = 0.5%.
On top of excess market returns in up and down markets, the model in (1) includes interaction vari-ables ¯xm,t× Dt and xm,t× Dt, where Dt is an indicator variable equal to one, if innovations in aggregated
liquidity are negative, i.e. Lt < 0, and zero otherwise. In case market liquidity is scarce (Dt = 1), the
coefficients of the interaction terms, δ1 and δ2, measure incremental risk surcharges that simply can be
added to the plain up and down market sensitivities, represented by β1and β2, respectively. In this way, the
model estimates market sensitivities in four mutually exclusive scenarios: liquid up markets by β1, liquid
down markets by β2, illiquid up markets by β1+ δ1and illiquid down markets by β2+ δ2. By this means,
not merely up and down markets are represented, but rather whether these states of rising or falling prices where simultaneously accompanied by abundant or scarce market liquidity.
Certainly, this four-fold representation is a simplification of the real interplay between price discov-ery and liquidity fluctuations in markets. However, it has to be emphasized that the correlation between the liquidity state dummy, Dt, and the real innovations in aggregated liquidity, Lt, computes to 0.76, which is
still very strong. Thus, the binary definition of liquidity states, using Dt, will preserve a great deal of the
outlined cross-correlations to other covariates, and may help to calculate average market sensitivities in the four modelled states of the world.
Apart from that, some comments have to made with regard to the alphas in the regression model. First, the inclusion of intercepts, αi, which represent fund fixed effects in the panel, prevents from an
the origin of ordinates. In other words, the slope estimates can be biased in a model without intercept, when applying OLS. Second, the inclusion of a liquidity alpha, αL, is of technical nature, as the consideration of a
direct effect of reduced market liquidity on performance is necessary for the model to distinguish between a liquid and an illiquid scenario. Last, the constant in asset pricing models has a predictive component, as it represents the manager’s ability to constantly outperform markets, and alpha has come to be known as a common decision criterion for many investors. In summary, this linear factor model combines Carhart’s four-factor model (1997), which is an extension of Fama-French’s three-factor model with an additional momentum factor, and twofold market sensitivities on account of downside risk. Latter aspect relates to proposed downside risk models by Zou (2005) and Ang et al (2005). Regression coefficients, however, are obtained by minimizing least squares, not by the general method of moments.
The advantage of the formal structure in (1), specifically the binary implementation of liquidity states, can be seen in testing for varying systematic risks under different market conditions. Thereby, the coefficients of interest, δ1 and δ2, indicate incremental systematic risk loadings induced by a drop in market liquidity.
The existence of such incremental effects is verified by the t-statistics of δ1 and δ2. These coefficients
are presumed to have different signs in the first place. Concisely, I expect δ1 to be negative and δ2 to be
positive arguing that reduced market liquidity increases price impact costs in the form of a widening of bid-ask-spreads due to changes in demand and/or supply for securities. If assets had to be sold in an illiquid market environment, profits should be lower in both rising and falling markets. Hence, hedge fund returns are expected to be lower on account of a reduction in market liquidity, as their gross market exposures (including liquidity risk surcharges), β1+ δ1and β2+ δ2, are presumably lower in rising markets and higher
in falling markets.
Subsequently, the hypothesis that hedge funds inhere on average the same market exposure in liquid up and down markets (i.e. if Dt= 0) can be tested by H0: β1= β2; the illiquid equivalent (Dt= 1) is verified
by H0: β1+ δ1= β2+ δ2. Beneficial for hedge funds in terms of an efficient risk management would be if
both tests are rejected against the positive alternatives, i.e. H1: β1> β2and H1: β1+ δ1> β2+ δ2, because
upside risks on average would outweigh downside risks of the same magnitude, irrespective of the liquidity state in markets. The last hypothesis pursues to test manager’s ability to a priori neutralize liquidity risks; put differently, it states that exogenous liquidity fluctuations do not lead to a change of the overall systematic risk in hedge funds. Thereby, fund returns in a liquid state are compared with those in an illiquid state: H0: αi+ β1+ β2= αi+ αL+ β1+ β2+ δ1+ δ2, whereby the left-hand side represents the gross effects in
case of abundant market liquidity (Dt = 0) and the right-hand side reflects the exposure in case of scarce
market liquidity (Dt = 1). Since the coefficients for control variables cancel out by construction, this comes
rejected towards H1 : αL+ δ1+ δ2 > 0 would correspond to higher systematic risks in hedge funds once
market liquidity is reduced. If this is true liquidity shocks neither were anticipated nor a priori timed.
Investors’ decisions concerning the deposition of assets as well as their perception of gains and losses are closely related to prospect theory introduced by Kahneman and Tversky (1979 and 1991). According to the authors, investors utility can be expressed by an S-shaped value function being concave over gains, and convex, yet steeper, over losses. If decision problems are formulated over final assets, the purchase price can serve as a natural reference point, implying a reference investment return of zero. By construction, gains are viewed as less advantageous than losses of the same size are viewed as disadvantageous. The authors point out that the reference point and investors preferences are subject to changes. Shifts of reference can be caused by tax withdrawals, recent (not yet adopted) changes of wealth or even fees charged by investment managers. Evidence supporting non-zero reference points and alternatives to prospect theory have been proposed by several studies in the financial literature. Baker, Pan and Wurgler (2010) examine reference points in mergers and acquisitions. They argue that past peak-prices, rather than current market prices, form more reliable anchors for valuing targets, positively affect the deal success and help to explain merger waves. Degeorge, Patel and Zeckhauser (1999) assess behavorial thresholds for earnings management. According to their analysis, managers keep track of multiple reference points. In particalur, executives aim to report positive profits, sustain recent performance and try to meet analyst forecasts. The choice of reference points matters in asset pricing, and it opens the door for modelling complex portfolios. For instance, Zou (2005) adopts the risk-free rate as a reference level for downside risk, and Ang et al (2006) define excess returns subject to the average market return to account for reference dependence in a mean-variance framework.
Obviously, the choice of a reference point has implications for the modelled portfolio structure, and the resulting (joint) model statistics. Bearing in mind the theoretical debates regarding reference dependence as well as for the reason of comparison, I calculate the above introduced model for in total four different reference points: the risk free rate (r1= rf,t), a moving average market return over the preceding 12 months
(r2= 121 ∑12k=1rm,t−k), an option-like market rate (r3= rm,t−1 if rm,t−1 > rf,t−1 , rf,t−1 else), and last, the
previous market return (r4= rm,t−1). Thereby, the consideration of time-lags allows for a continuous update
of reference levels and may illustrate the effect of preceding shocks on current prices and corresponding portfolio transactions. As will be demonstrated explicitly in the empirical analysis, market-linked reference points can be empirically applied when analysing risk-return preferences of hedge fund investors, and are in statistical terms preferable to the risk-free rate.
In order to show that the extended model in (1) and the associated quantitative input in fact result in a better explanation of the hedge fund returns and their variability, it is necessary to draw comparisons to
the classical approaches in asset pricing, such as the CAPM:
xit = αi + β xm,t + uit , (2)
a multi-factor model with liquidity risk loadings:
xit= αi + β xm,t + γj0wj + uit , (3)
and a model with plain downside risk:
xit= αi + β1x¯m,t + β2xm,t + γj0wj + uit , (4)
where γj0wjrepresent controls. The theoretical implications in (1), however, differ from these models, when
changing the reference point. Therefore, I derive the conditional, state-dependent expected value as well as the variance of the returns implied by (1). For reasons of simplification, controls were neglected and the previous market return, rm,t−1, is chosen as a reference point:
xit := rit− rm,t−1= αi+ αLDt+ β1x¯m,t+ β2xm,t+ δ1x¯m,t× Dt+ δ2xm,t× Dt+ uit ⇔ rit = αi+ αLDt+ β1[rm,t− rm,t−1]++ β2[rm,t− rm,t−1]− + δ1[rm,t− rm,t−1]+× Dt+ δ2[rm,t− rm,t−1]−× Dt+ rm,t−1+ uit ⇔ rit = αi,1+ β1(rm,t− rm,t−1) + rm,t−1+ uit i f rm,t ≥ rm,t−1, Dt = 0 αi,2+ β2(rm,t− rm,t−1) + rm,t−1+ uit i f rm,t < rm,t−1, Dt = 0 αi,3+ β3(rm,t− rm,t−1) + rm,t−1+ uit i f rm,t ≥ rm,t−1, Dt = 1 αi,4+ β4(rm,t− rm,t−1) + rm,t−1+ uit i f rm,t < rm,t−1, Dt = 1 , where
αi,1= αi,2= αi, αi,3= αi,4= αi+ αL,
β3= β1+ δ1, β4= β2+ δ2
⇔ rit = αi,k+ βkrm,t+ (1 − βk)rm,t−1+ uit , uit iid
∼ (0, σu) , ∀ k ∈ {1, 2, 3, 4}
⇒ µi := E[rit] = αi,k+ βkE[rm,t] + (1 − βk)E[rm,t−1] , ∀ k ∈ {1, 2, 3, 4}
=: αi,k+ µm, iff E[rm,t−1] = E[rm,t] =: µm
Assume rm,t and ui,t to be independent covariance stationary processes formalized as
E[rm,t] = 0, Var[rm,t] = σm2, Cov[rm,t, rm,t−l] = 0,
E[ui,t] = 0, Var[ui,t] = σu2, Cov[ui,t, ui,t−l] = 0, and Cov[ui,t, rm,t−l] = 0 ∀ l ∈ [1;t]
As demonstrated, the expected fund return is beta-weighted average of the contemporaneous and previous expected return of the market in each state k. The restriction that beta-coefficients add up to one allows to model hedge funds as if they smooth market returns over time and thereby exploiting mean-reversion in stock returns. Under the assumption that the expected market return over time is constant, i.e. E[rm,t−1] = E[rm,t],
the model implies that the expected fund return is the sum of the expected market return and a fund-specific, state-dependent alpha, i.e. E[rit] = αi,k+ E[rm,t], which is independent of state-dependent betas βk. This
implication appears to be not unrealistic in the light of the presented statistics, namely that the mean return of all funds in the panel over the sample period is approximately equal to the observed mean of the market re-turn, assuming that αi,kare in sum (or jointly) equal to zero. If instead the expected market return is assumed
to be zero, the model simplifies and predicts an expected fund return that is equal to state-dependent alphas, αi,k, i.e. the sum of fund fixed effects or manager’s skill to outperform markets, αi, and a constant exogenous
effect, αL, being related to reduced market liquidity in this setting. It has to be stressed that the coefficients
αLand βk are common to all funds, which can lead to a biased view on the level of individual funds.
How-ever, since this thesis aims to provide an indication of the aggregated effects of market liquidity fluctuations on the hedge fund industry as well as their anticipation, this framework can be estimated in the context of a panel data regression. For a more detailed view on fund-individual risk loadings measured by βi,k, the
esti-mation of seemingly unrelated regression equations might be more appropriate, which is not considered here.
Abstracting from the expected fund return µi, the model explains hedge fund returns as state-dependent
market returns. Thereby, market sensitivities and managers’ actions (in anticipation or response) to price relevant information, in this case market liquidity, are reflected in state-dependent betas. With a reference point r4= rm,t−1, hedge fund returns are modelled by a portfolio strategy that smoothes market returns
over two subsequent periods, whereby βk’s represent the weights that are put on the current market return,
rm,t, in state k. In the simplest case, i.e. if betas are identical in each scenario (βk= β ), investors receive a
two-period moving average of market returns. Especially, if β ∈ (0, 1) such a strategy would outperform a plain market investment in consequence of a lower portfolio variance and kurtosis. The proof of this statement can be found in the appendix. However, in this case both upside and downside potentials are limited. Different up- and downside betas (βk6= β ∀ k) reweigh market returns and can generate a skewed
return distribution. Provided that upside betas exceed downside betas (β1 > β2), the model puts more
weight, i.e. higher than 100%, on positive market returns, when passing through rising and falling markets in two subsequent months, and vice versa if β1 < β2. This, in turn, can be aggravated or mitigated by
liquidity risk surcharges in up or downmarkets depending on the signs of the incremental effects δ1 and
δ2. In a nutshell, this framework expresses the optionality of hedge fund returns under different market
The choice of the previous market return as a reference level can be justified for several reasons. First, it allows modelling hedge fund returns to be more dependent on market returns with a simultaneously lower variance and under further extensions a skewness being different from zero. This flexibility appears to be desirable regarding the data, especially for styles making use of both long and short positions. Second, risk awareness (or appetite) of hedge fund investors, as high net-worth individuals or institutions, suggest a more daring reference point being linked to market prices. Form the perspective of a well-diversified investor, who already earns the market return through various investments, rm,t−1 might be an objective
return target, beyond the risk-free rate, to be attained in order not to suffer overproportionally from losses over time. Last, active management often involves risks that trace back to positions entered in the previous period, which can lead to forced closings of future contracts and, in severe cases, fire sales of assets as discussed in Brunnermeier and Pedersen (2009).
Obviously, these arguments can not be put forward in the framework of the CAPM. The crucial point is that the CAPM leads to an entirely different perception of risk and expected return, and consequently different implications for the underlying portfolio structure. Given investors have mean variance preferences, the best advice would be to form portfolios by combining a risk-free asset with a (at times leveraged) long-only market investment representing a relative weight of β in the portfolio. These efficient portfolios, which are located on the capital market line, exhibit an expected return of
E[rp] = (1 − β )rf+ β E[rm] = rf+ β E[rm− rf] ,
and a variance of
Var[rp] = β2σm2 ,
which only involves systematic risk being minized for β = 0. For any other portfolio shall hold that
E[ri] = α + rf+ β E[rm− rf] and Var[ri] = β2σm2+ σu2.
Especially, a zero-beta portfolio would have an expected return of E[ri] = α + rf and a constant variance
of Var[ri] = σu2, thus only involving idiosyncratic risk. Eventually, for a zero-beta portfolio to be
CAPM-efficient, 100% of the funds’ assets would have to be invested at the risk-free rate, thereby generating an outperformance of α = 0. This being said, such a portfolio structure can not be considered as the typical result of the investment process of hedge funds. In contrast to the CAPM, the simplified dynamic model, as introduced above, implies
E[ri] = αk+ βkE[rm,t] + (1 − βk)E[rm,t−1] and Var[ri] = (2βk2− 2βk+ 1)σm2+ σu2,
which vary in different market states. Abstracting from the idiosyncratic risk, hedge funds inhere reduced systematic risk exposures in this framework, if state-dependent betas range between zero and one with a
global minimum at βk = 0.5. On the other hand and counter-intuitively, a theoretical zero-beta portfolio
would in this context involve systematic risks that are to 100% attributable to the impact of rm,t−1 on ri,t.
These implications will be investigated in that what follows.
5 Results
This part is organized as follows: in subsection 5.1 Equity Market Neutral funds are investigated in single and multi-factor models with different reference points, in subsection 5.2 results of models with downside risks and contemporaneous liquidity effects are presented, and in subsection 5.3 hedging activity in response to liquidity risks in markets is examined.
5.1 Is there a hidden exposure to market risk in market neutral funds?
Market neutral funds aim to generate positive returns independent of their underlying markets. The literature classifies funds as neutral in case of zero net long positions (dollar neutrality) and/or zero market exposure (beta neutrality). Since their commercial launch, several studies attempted to disprove this concept. Capocci (2005) finds an increased market exposure of funds in top and bottom decile portfolios. He further reveals that about one third of individual funds are not beta neutral, and market sensitivities tend vary in rising and falling markets. Dunis and Ho (2005) formed portfolios, where weights for both long or short constituents were determined from two separate cointegration equations of the stock market. While each cointegrated portfolio was highly correlated with the benchmark (EuroStoxx50), their difference, i.e. long minus short, was not. In different balancing settings, index tracking (long-only) and market neutral portfolios (long/short) outperformed the benchmark, but inhered a higher volatility. An in-depth analysis on market neutrality has been provided by Patton (2009). In this study, the author defines five neutrality concepts: subject to mean, variance, market correlations, value at risk, and tail characteristics of hedge fund returns. A joint test for the overall effect demonstrated that one quarter of market neutral funds in the sample were in fact not neutral, and thus positively dependent on market returns. Their market exposure, however, was significantly reduced compared to other styles.
Looking for supportive evidence, I propose to show that market neutral funds do inhere systematic risks. Based on the reference dependence discussed above, evidence is provided that the previous market return can serve a reference point when analysing hedge fund returns. For this reason, a comparison between the projections of risk and return in the CAPM and the proposed model with alternative excess market
returns, xt = rm,t− rm,t−1, is made. In each case, sensitivities in up and down markets as well as liquidity
interactions are disregarded for the time being. I intentionally narrow the analysis down to market neutral funds, as this style is considered to reduce systematic risks. If this is the case, the expectations with regard to the slope coefficients would be a beta close to zero in the CAPM, and a beta close to 0.5 the proposed model. The estimates of the corresponding single factor and multi-factor models are presented in Table 3.
Apparently, hedge funds of this style were indeed able to provide a reduced market exposure, which is consistent with the projections of both theoretical frameworks. In the CAPM in column (1), the coefficient β = 0.108, however, is significantly greater than zero, yet presumably low enough to declare these funds as “neutral” towards price movements in markets. In column (2), the estimated coefficient, β , yields 0.555, but rejects the hypothesis H0: β = 0.5 at a level of 5%, and unsurprisingly the zero-equivalent. Controlling
for market volatility using the proxi r2m,t lead to no significant improvement in the CAPM-type factor model
in column (3), whereby the sensitivity with respect to market volatility turned out to be insignificant. In economic terms, the CAPM as well as the related two factor model in (3) would lead to the conclusion that market neutral funds are so-called “zero-beta portfolios” being neutral to both prices and volatilities, which is consistent with Patton’s results (2009).
Conclusions about fund’ investment processes and hedging activities, however, hardly can be drawn from regression coefficients being close to zero. As a matter of fact, the CAPM-type model does not give a real insight to the explanation of returns of market neutral strategies. This is not necessarily the case in the proposed two factor model in column (4). Here the aggregated market price factor, β , now was estimated at a value of 0.507, and does not reject the hypothesis β = 0.5 with a p-value of 0.7312. With an overall (dynamic) market sensitivity being close to β = 0.5, market neutral funds appear to smooth market returns in such a way that portfolio variance and kurtosis are reduced (see again appended proof). This is also in line with the presented descriptive statistics of this style. Literally speaking, systematic risks in market neutral funds are not just neutralized, but dynamically minimized. The positive significance of the market volatility coefficient, with γ1= 3.004, further suggests that market risks have been actively hedged, whereby
intensified price fluctuations had a positive impact on fund returns. In the light option theory, these portfolios most likely employ rebalancing strategies that are Delta-neutral and keep a positive Gamma. Judging from the explained variance, the proposed model in (4) is in statistical terms preferable to the CAPM in (1) as highlighted by the adjusted R2and the F-statistic for joint significance, which both increased from 7.84% to 53.23% and from 45.38 to 538.83, respectively.
Adding control variables to the regressions, slope coefficients followed the same direction, but slightly change in magnitude. The covariates were insignificant in a CAPM-type multi-factor model with liquidity
risk loadings in column (5), yet were significantly different from zero in the dynamic model in column (6). According to the negative size and value factors in (6), strategies in which stocks with a small market capitalization (small caps) and/or a low book-to-market ratio (growth stocks) are sold would have been beneficial to this style. The positive momentum factor indicates that rising stocks were bought, while falling stocks were simultaneously sold, which is in line with the overall mean-reverting model characteristics. Interestingly, this style inhered a negative liquidity risk premium with respect to both contemporaneous and previous shocks to aggregated liquidity. Hence, reduced market liquidity appears to have been anticipated and exploited by some means. Similar results, which are not presented here, were attained for Statistical Arbitrage strategies as a subclass of market neutral funds.
In summary, the proposed model revealed that market neutral funds are dependent on market returns. While a static model framework supports neutrality with respect to mean and variance of market prices, this does not apply in the proposed dynamic model. Sensitivities towards price movements in markets tend to be dynamically minimized in a mean-variance context, whereby market volatility risk is actively hedged. The choice of the previous market return as a reference point thus appears to be applicable for this style. Eventually, further empirical support is required to be confident about reference dependence regarding hedge fund returns in general.
5.2 Market exposure and liquidity risk
The purpose of the following analysis is to demonstrate that hedge funds’ overall sensitivity towards markets varies once liquidity is reduced. I will start by the CAPM and subsequently conduct model extensions to show that this is the case. Thereby, this subsection focuses on contemporaneous liquidity effects. Keeping in mind that the mean returns were lower accompanied by a higher variance in times of reduced market liquidity, it will be of interest whether liquidity shocks were anticipated and timed.
The regression results of a single and a multi-factor model dependent on the risk-free rate as well as models with downside risk and different reference points are presented in Table 4. The CAPM in column (1) resulted in a common slope coefficient of β = 0.322, suggesting a weak correlation of hedge fund returns with the market returns of North American exchanges as one of the leading, international stock markets they are operating in, and thus conveys a moderate market exposure. This instance does not necessarily imply that variables are per se not related with each other. The Pearson correlation coefficient measures the linear relation between variables, however it often fails to uncover more complex interrelations, such as piecewise linear or even non-linear dependence structures. Empirically, this finding is very well documented by similar
studies on hedge funds, in which the CAPM had been applied. The low correlation of hedge funds returns with those of financial markets and related products, and thus the difficulty to linearly predict returns, has been stressed in Fung and Hiesh (1999), Agarwal and Nail (1999), Liang (1999) and Capocci et al (2004), among others.
Judging from the goodness of fit, the CAPM hardly explains the characteristics of the dependent variable. Several reasons can be mentioned in this respect. First, the estimated coefficient is most likely biased due to the omission of variables that are correlated with the independent variable, i.e. excess market returns. Second, the model does not allow for variations of returns in different states of the market. Hence, it provides an oversimplified view on the systematic component of risk and the optionality of payoffs regarding hedge funds. Last, it is somewhat awkward to assume that hedge funds have a portfolio structure similar to CAPM-efficient portfolios. As hedge funds make use of leveraged investments in both directions, long and short, modelling returns using the CAPM would lead to a distorted reality. Therefore, the expectations for the CAPM to lead to economically and statistically meaningful results for hedge funds are a priori low.
Adding controls slightly improved the model fit of a CAPM-type multi-factor model in column (2). It appears that innovations in aggregated liquidity had a positive impact on fund returns, whereas its first lag, Lt−1, had a negative effect; a more detailed view will be provided below. The significance of these
factors therefore indicates the existence of supplementary liquidity risks in hedge funds, which are not yet captured in the coefficient of the market risk, here β1. Fama-French’s value and Carhart’s momentum factor,
were negative and significant at a level of 1%. As the sign of the factors suggests, hedge funds would have relatively gained from selling growth stocks, while buying value stocks, as well as anticyclical investments, i.e. stocks that decreased in price were bought, while those which increased were sold. The positive size factor might suggest that performance was partly generated by intensified investments in stocks of small capitalized firms. As the magnitude of these coefficients, however, is rather low, these conclusions ought to be treated with reserve.
Decomposing beta in up and down markets leads to some remarkable changes of the coefficient estimates as well as to a significant reduction of the residual deviance, particularly for reference points, which are related to the market return of the previous month. Almost consist throughout all models, as displayed in Table 4 columns (3) to (6), was that contemporaneous liquidity innovations, again, were significantly positive, while its lag was negative. If the risk-free rate or a moving average of market returns are considered as reference points, hedge fund returns turn out to have a higher upside and a lower downside exposure. The somewhat understated downmarket sensitivity in (3), however, is counteracted by a higher market volatility, which had a negative impact on returns here. The classical approach based on the risk-free rate would thus lead to an
overall optimistic view regarding price directions, whereas market risks, as seen in intensified volatilities, appeared not to have been hedged. With respect to the statistics of the model fit, i.e. adjusted R2 and F-statistic for joint significance, this view only has a weak support. The opposite can be said for an option-like reference point (r3= rm,t−1 if rm,t−1 > rf,t−1 , rf,t−1 else) and the previous market return (r4 = rm,t−1).
Here downward sensitivities outweighed upside risks, whereby the coefficient of market volatility has been positive in both models. With an adjusted R2 of 50% and F of 2794.6, there is evidence that the dynamic asset pricing model might be more appropriate compared to a static multi-factor model. Also, Carhart and Fama-French factors experience some interesting changes. The momentum factor turned from negative in (3) to positive in (6), which is supported by the empirical findings on momentum effects and downside risk by Ang et all (2001) as well as its covariation with liquidity risk, following Pastor and Stambaugh (2003) and Sadka (2006). The reverse sign change was observed for the size factor, whereas the value premium was consistently negative, which suggests that hedge funds act as net sellers of small caps and growth stocks.
The estimation of equation (1), i.e. incorporating interactions of market liquidity risk with up- and downmarket exposures, is presented in Table 5. Consistent throughout all regressions was the direction of the risk surcharges on account of reduced market liquidity. Opposed to my initial expectation, the coefficient for a liquidity surcharge in rising markets, δ1, was significantly positive in model (2) and (4), which might
be explained by short-run momentum effects. In so far, hedge funds would benefit from liquidity-induced return reversals, at least in up markets. The risk surcharge associated with falling markets, δ2, was positive,
as I expected, and ranged between 0.03 and 0.18 percentage points. Hence, contemporaneously reduced market liquidity amplifies the effect of falling prices on hedge fund returns. Taken together, both incremental effects result in a generally higher market exposure once liquidity is reduced, which is underlined by the rejection of the hypothesis H0 : αL+ β1+ β2= 0 against the alternative H0 : αL+ β1+ β2 > 0, for all
reference points. Reconfirming the previous estimates, the model based on the risk-free rate in (1) resulted in higher upside risks and a lower downside exposure, both for liquid and illiquid markets. The opposite was revealed in the proposed dynamic model in (4), as downmarket sensitivities outweighed upside risks indicated by the hypotheses tests, β1< β2and β1+ δ1< β2+ δ2. With respect to the increased gross market
exposures on account of reduced market liquidity, especially on the downside, it remains questionable whether liquidity risks in markets indeed were anticipated.
Reviewing the results that have been the presented so far, the proposed model leads to a significant improvement of the explained deviance as well as the economical and statistical relevance of the considered factor loadings. Thereby, the best fit was achieved in a dynamic model, in which excess returns depend on the market return of the previous month. By this means, hedge funds returns can be modelled as the result of rebalancing portfolio strategies, which tend to smooth market returns on average, whereby latter
itself are subject to mean-reversion. Further, the consideration of state-dependent betas provided evidence for the existence of a liquidity-based risk surcharge in hedge funds’ overall market exposure. Irrespective of the reference point, both up and down market sensitivities tend to increase once market liquidity is simultaneously low suggesting that liquidity risks were generally not anticipated by hedge fund managers. This might be different for individual styles, and will be examined later.
5.3 Do hedge funds respond to liquidity shocks?
In Pastor and Stambaugh’s model (2003), stocks’ daily excess returns were explained to be the result of daily volume-based return reversals over a time horizon of one month. The scaled, market-wide average of these stock-individual volume sensitivities indicates the level of aggregate liquidity in a given month. Innovations in aggregated liquidity represent a residual shock to this level, which can not be explained by the levels of the past two months. Current stock prices are thus subject to both stock-individual reversal effects based on past prices and exogenous liquidity fluctuations. This implies that shocks to market liquidity can trigger prices in the subsequent month. For this reason, it is of interest whether hedge funds respond to liquidity innovations in the aftermath. This will be examined in the following.
To analysize this question, equation (1) is estimated with modified interaction terms which are now subject to reduced market liquidity in the previous month, i.e. Dt−1 = 1, if Lt−1< 0, zero otherwise. By
this means, the economical interpretation of the coefficients changes. The estimates β1 and β2 now reflect
hedge funds’ up- and downmarket sensitivities conditional on increased liquidity in the previous month (Dt−1 = 0), but being unrestrictedly exposed to current (positive or negative) liquidity shocks. Hence,
these coefficients embody both current price and liquidity risks. Furthermore, the response coefficients, δ1 and δ2, measure the net effect to up- and downmarket betas of actions that have been taken in order
to alter hedge funds’ market exposures based on the information that market liquidity was reduced in the previous month (Dt−1 = 1), whereby the constant, αL, measures the average direct return costs of these
actions. As a result, the totals β1+ δ1and β2+ δ2represent ex post gross exposures in up and downmarkets.
Differences between state-dependent betas then allow to draw conclusions about the managers’ response to liquidity shocks. Following Zou (2005), the hypotheses for identical market sensitivities H0: β1= β2
and H0: β1+ δ1= β2+ δ2are tested, where in either case, it would be beneficial, if downside risk is offset
by upside potential in ex ante liquid and illiquid markets, respectively. The hypothesis whether funds’ risk profiles vary systematically in response to liquidity shocks is verified by a Granger causality test on H0: αL+ δ1+ δ2= 0. If this hypothesis is rejected against H1: αL+ δ1+ δ2< 0 hedge funds are predicted
reference points can be found in Table 6.
Again, the model with excess returns based on market returns of the previous month explains hedge fund returns best, see column (4). Judging from the explained deviance there is no significant improvement or deterioration detectable compared to the framework in 5.2. The dynamic model in (4), again, supports the view that hedge funds benefit from increased market volatility, as the coefficient of rm,t2 was positive. Further, negative size and value premiums as well as a positive momentum factor could be reconfirmed here; all factors are significant at a level of 0.1%. Residual risk loadings regarding contemporaneous shocks to aggregate liquidity generally weakened and were not verifiable in model (4) anymore; also the coefficient of Lt−1has been to be closer to zero compared to the earlier findings. As expected and argued above, liquidity
risk is now partly captured in up- and downmarket exposures.
Conditioning on market liquidity states of the previous month resulted in higher market sensitivities, if market liquidity was ex ante abundant (Dt−1= 0), while being simultaneously exposed to current liquidity
shocks. This is consistent with the findings of subsection 5.2, both in up and downmarkets. Except for model (1), hedge funds tend to be more sensitive on the downside by shocks they did not anticipate, as β1< β2could
be verified. If market liquidity was previously scarce (Dt−1= 1), the response coefficients in downmarkets,
δ2, were significantly negative, ranging between -0.19 and -0.41 percentage points, and outnumbered
the equivalent effects in subsequent upmarkets, as δ1 ranged between 0.04 and 0.20 percentage points.
Apparently, reduced liquidity induced actions to lower funds’ market exposures, which is supported by the rejection of the third hypothesis towards to alternative H1: αL+ δ1+ δ2< 0 throughout all models. This risk
shift is a post-shock response. Further, the direction of the response coefficients resulted ex post in a higher upmarket exposure, as the relation β1+ δ1> β2+ δ2was consistently verified. Hence, hedge funds were able
to exploit liquidity-based return reversals in markets and thereby providing an ex post optimized risk-return profile over the entire sample period. Thus, information-based rebalancing delivered benefits in the long-run.
In summary, it can be said that hedge funds bear liquidity risks varying under different market con-ditions. This result is in line with the related literature, e.g. Sadka (2010), Teo (2010), and Gibson and Wang (2013). Market exposure was higher in months, in which liquidity was simultaneously low, especially on the downside. Opposed to the findings of Cao et al (2013), the liquidity-adjusted exposures suggest that liquidity risk in markets was generally not anticipated and timed in advance, but rather managed in response to shocks: market exposure is lower, if market liquidity was ex ante low. These projections require further consistency checks.
