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Markov chain models to estimate the premium for extended hedge fund lockups
Abstract
A lockup period for investment in a hedge fund is a time period after making the investment during which the investor cannot freely redeem his investment. It is routine to have a one-year lockup period, but recently the requested lockup periods have grown longer. We estimate the premium for such extended lockup, taking the point of view of a manager of a fund of funds, who has to choose between two investments in similar funds in the same strategy category, the first having a one-year lockup and the second having an n-year lockup. Assuming that the manager will rebalance his portfolio of hedge funds on a yearly basis, if permitted, we define the annual lockup premium as the difference between the rates of return from these investments. We develop a Markov chain model to estimate this lockup premium. By solving systems of equations, we fit the Markov chain transition probabilities to three directly observable hedge fund performance measures: the persistence of return, the variance of return and the hedge-fund death rate. The model quantifies the way the lockup premium depends on these parameters. Data from the TASS database are used to estimate the persistence, which is found to be statistically significant. Copyright © 2009 Wilmott Magazine Ltd
... Browne et al. ([51]) defines liquidity premium as the amount added to an illiquid product to produce the same level of utility as the unrestricted product without the liquidity premium. Derman, Park and Whitt ([14] ) propose Discrete Time Markov Chain (DTMC) and Continuous Time Markov Chain (CTMC) models for Hedge Fund Lockup Premiums as a function of the length of the extended lockup periods. ...
... Recent work by Jagannathan, Malakhov, and Novikov ([50]) finds that more than 25% of the abnormal performance during a three year interval will spill over into the following three year interval. Derman and Park ([14]) find performance persistence in the following strategies: (i) Convertible Arbitrage, (ii) Dedicated Short Bias, (iii) Fixed Income, (iv) Fund of Funds, and (v) Others. ...
Portfolio Selection as introduced by Harry Markowitz laid the foundation for Modern Portfolio Theory. However, the assumption that underlying asset returns follow a normal distribution and that investors are indifferent to skew and kurtosis is not practically suited for the hedge fund environment. Additionally, the lockup and notice provisions built into hedge fund contracts make portfolio rebalancing difficult and justify the need for dynamic allocation strategies. Market conditions are dynamic, therefore, rebalancing constraints in the face of changing market environments can have a severe impact on return generation. There is a need for sophisticated yet tractable solutions to the multi-period problem of hedge fund portfolio construction and rebalancing. In this paper, we generalize the hedge fund asset return distribution to a multivariate K-mean Gaussian mixture distribution; model the multi-period hedge fund allocation problem as a Partially Observable Markov Decision Process (POMDP); and propose practical rebalancing strategies that represent a convergence of literature on hedge fund investing, regime switching, and dynamic portfolio optimization.
... Getmansky, Lo, and Makarov [2004] investigate illiquidity and serial correlation of hedge fund returns. Derman [2007] introduces a three-state model to describe redemption and reinvestment decisions faced by hedge fund investors, and Derman, Park, and Whitt (2009) extend this approach. Ang and Bollen [2009] treat hedge fund redemptions as real options and describe a binomial-tree based pricing methodology. ...
The financial crisis of 2007-2009 highlighted the importance of liquidity to many investors. University endowment funds, for example, were forced to sell publicly traded securities at substantially depressed values in order to meet funding commitments to private investments. Hedge funds engaged in fire sales of publicly traded securities to meet margin calls from lenders and redemption demands from clients. And financial institutions faced with capital calls sold assets at substantial discounts to their government guaranteed values. Investors could guard against these capital calls by maintaining a reserve of highly liquid securities, but this protection would require them to sacrifice the expected return premium of less liquid investments. We propose, as an alternative, that investors consider purchasing liquidity options to meet unscheduled capital calls. We describe how to structure and price liquidity options, and we demonstrate how the price discovery process of liquid securities determines the fair value of illiquid securities.
... Hayes (2006) used discretetime birth-and-death process to calculate the maximum drawdown in hedge-fund returns, and used the autocorrelation condition to calibrate the model. In Derman et al. (2009) we used three-state Markov chain models to estimate the premium from extended hedge-fund lockup. We used the same TASS data to calibrate that model. ...
We propose a stochastic difference equation of the form Xn = AnXn-1 + Bn to model the annual returns Xn of a hedge fund relative to other funds in the same strategy group in year n. We fit this model to data from the TASS database over the period 2000 to 2005. We let {An} and {Bn} be independent sequences of independent and identically distributed random variables, allowing general distributions, with An and Bn independent of Xn-1, where E[Bn] = 0. This model is appealing because it can involve relatively few parameters, can be analysed, and can be fitted to the limited and somewhat unreliable data reasonably well. The key model parameters are the year-to-year persistence factor γ ≡ E[An] and the noise variance [image omitted]. The model was chosen primarily to capture the observed persistence, which ranges from 0.11 to 0.49 across eleven different hedge-fund strategies, according to regression analysis. The constant-persistence normal-noise special case with An = γ and Bn (and thus Xn) normal provides a good fit for some strategies, but not for others, largely because in those other cases the observed relative-return distribution has a heavy tail. We show that the heavy-tail case can also be successfully modelled within the same general framework. The model is evaluated by comparing model predictions with observed values of (i) the relative-return distribution, (ii) the lag-1 auto-correlation and (iii) the hitting probabilities of high and low thresholds within the five-year period.
... Our paper is most closely related to Derman (2007), who models hedge fund returns using a three-state model in which hedge funds are good, sick, or dead. Derman, Park, and Whitt (2009) extend this approach to allow for more complex Markov chain models. In both approaches, lockups prevent an investor from withdrawing capital from a sick fund and investing the proceeds in a good fund. ...
Hedge funds often impose lockups and notice periods to limit the ability of investors to withdraw capital. We model the investor’s decision to withdraw capital as a real option and treat lockups and notice periods as exercise restrictions. Our methodology incorporates time-varying probabilities of hedge fund failure and optimal early exercise. We estimate a two-year lockup with a three-month notice period costs approximately 1% of the initial investment for an investor with CRRA utility and risk aversion of three. The cost of illiquidity can easily exceed 10% if the hedge fund manager can arbitrarily suspend withdrawals.
A lockup period for investment in a hedge-fund is a time period after making the investment during which an investor cannot freely redeem his investment. Since longer lockup periods have recently been imposed, it is important to estimate the premium an investor should expect from extended lockups. For this, Derman et al. (2009) proposed a parsimonious three-state discrete - time Markov Chain (DTMC) to model the state of a hedge fund, allowing the state to change randomly among the states 'good,' 'sick' and 'dead' every year. In this paper, we propose an alternative three-state absorbing continuous-time Markov Chain (CTMC) model, which allows state changes continuously in time instead of yearly. The CTMC model is more realistic and flexible, but requires new techniques for parameter fitting. We employ nonlinear programming to solve the new calibration equations. We show that the more realistic CTMC model is a viable alternative to the previous DTMC model for estimating the premium for extended hedge fund lockups.
This paper studies the effect of the bid-ask spread on asset pricing. We analyze a model in which investors with different expected holding periods trade assets with different relative spreads. The resulting testable hypothesis is that market-observed expexted return is an increasing and concave function of the spread. We test this hypothesis, and the empirical results are consistent with the predictions of the model.
Recent literature has found some evidence of performance persistence in hedge funds. This study investigated whether this persistence varies with fund characteristics, such as size and age. Previous research has found that funds face capacity constraints, that investment flows chase past performance, and that as funds age, they become more passively managed, which reduces the likelihood of performance persistence as funds grow older and larger. Consistent with this model, this study found that performance persistence is strongest among small, young funds. A portfolio of these funds with prior good performance outperformed a portfolio of large, mature funds with prior poor performance by 9.6 percent per year.
We propose a stochastic difference equation of the form Xn = AnXn-1 + Bn to model the annual returns Xn of a hedge fund relative to other funds in the same strategy group in year n. We fit this model to data from the TASS database over the period 2000 to 2005. We let {An} and {Bn} be independent sequences of independent and identically distributed random variables, allowing general distributions, with An and Bn independent of Xn-1, where E[Bn] = 0. This model is appealing because it can involve relatively few parameters, can be analysed, and can be fitted to the limited and somewhat unreliable data reasonably well. The key model parameters are the year-to-year persistence factor γ ≡ E[An] and the noise variance [image omitted]. The model was chosen primarily to capture the observed persistence, which ranges from 0.11 to 0.49 across eleven different hedge-fund strategies, according to regression analysis. The constant-persistence normal-noise special case with An = γ and Bn (and thus Xn) normal provides a good fit for some strategies, but not for others, largely because in those other cases the observed relative-return distribution has a heavy tail. We show that the heavy-tail case can also be successfully modelled within the same general framework. The model is evaluated by comparing model predictions with observed values of (i) the relative-return distribution, (ii) the lag-1 auto-correlation and (iii) the hitting probabilities of high and low thresholds within the five-year period.
Hedge funds databases are typically subject to high attrition rates because of fund termination and self-selection. Even when all funds are included up to their last available return, one cannot prevent that ex post conditioning biases a.ect standard estimates of performance persistence. In this paper we analyze the persistence in the performance of U.S. hedge funds taking into account look-ahead bias (multi-period sampling bias). To do so, we model attrition of hedge funds and analyze how it depends upon historical performance. Next, we use a weighting procedure that eliminates look-ahead bias in measures for performance persistence. The results show that the impact of look-ahead bias is quite severe, even though positive and negative survival-related biases are sometimes suggested to cancel out. At horizons of one and four quarters, we find clear evidence of positive persistence in hedge fund returns, also after correcting for investment style. At the two-year horizon, past winning funds tend to perform poorly in the future.
The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accurate than the standard tables previously published.
We use a comprehensive data set of funds-of-funds to investigate performance, risk, and capital formation in the hedge fund industry from 1995 to 2004. While the average fund-of-funds delivers alpha only in the period between October 1998 and March 2000, a subset of funds-of-funds consistently delivers alpha. The alpha-producing funds are not as likely to liquidate as those that do not deliver alpha, and experience far greater and steadier capital inflows than their less fortunate counterparts. These capital inflows attenuate the ability of the alpha producers to continue to deliver alpha in the future. Copyright (c) 2008 The American Finance Association.
This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return as well as size, value, and momentum factors. Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the same 34-year period.
Recent evidence suggests that institutional investors wish to commit to hedge funds on a long-term basis, but they are worried that their investments may liquidate prematurely, leading to large capital losses. Providing them with rigorous models to predict liquidation is important, yet current studies of hedge fund lifetimes and mortality have treated all funds that exit the database as liquidated, when many of these funds are not liquidated. This has likely produced imprecise estimates of hedge fund lifetimes, attrition, and survivorship bias. This study aims to reconcile these important issues by applying a competing risks model to account for the different types of exits hedge funds can experience. By treating exit types separately, we avoid blurring the effect of predictor variables on survival because the variables are not attempting to predict a heterogeneous aggregation of exit types. Predictor variables whose value changes over time, such as returns or volatility, are modeled as time dependent variables rather than as fixed variables. This provides better warning signals to investors about possible fund liquidation, since the impact of the predictor variables is measured at every instant of hedge fund lifetimes, rather than during the last months of their life as is done in existing studies. Hedge funds that exit the database for reasons other than liquidation often have very good returns, so the direction of survivorship bias is not always evident. We avoid underestimating survivorship bias because funds that are not liquidated are not counted as dead. We find that separating exit types leads to estimates of annual attrition that are not as high as previously thought. The results of this study will allow investors to better estimate the expected lifetime of a hedge fund before allocating any money to it, and provide better warning signals to investors already committed to a hedge fund about possible fund liquidation, thereby helping all investors avoid the large capital losses that are often associated with liquidation.
This paper empirically investigates the seasonal behavior of the liquidity premium in asset pricing. The evidence suggests a strong seasonal component. In the 1961–1990 period, the liquidity premium is reliably positive only during the month of January. For the non-January months, one cannot detect a positive liquidity premium. The impact of the relative bid-ask spreads on asset pricing in non-January months cannot be reliably distinguished from zero. In contrast to Amihud and Mendelson (1986), however, our evidence suggests that the size effect is significant, even after controlling for spreads.
Studies of hedge fund survival have treated all funds that exit the database as dead (liquidated), when many such funds are in fact not liquidated. We apply a competing risks model to account for the three types of exits recorded for dead funds. Treating exit types separately avoids blurring the effect of predictor variables on survival. Predictor variables are modeled as time dependent, allowing for the impact to be measured at every instant of life. We avoid underestimating survivorship bias because funds that are not liquidated are not counted as dead. The results of this study provide investors with better warning signals about possible fund liquidation.
Tending to be static and single-database oriented, existing models for correcting performance measurement biases are unable to detect potential data errors arising from (1) hedge funds that migrate from one database vendor to another and (2) merged databases. In general, return measurement biases can be traced to two key events: when a hedge fund elects to enter one or more databases (backfill bias) and when a hedge fund exits a database (survivorship bias). Artificial rules (e.g., ignoring the first x number of months of performance history to minimize backfill bias) and survivorship statistics based on a single database vendor are susceptible to another form of bias as databases evolve and consolidate. The authors posit that one must be mindful of how much of the hedge fund industry one is observing before passing judgment on the performance statistics of the hedge fund industry as a whole.
Investors in hedge funds and commodity trading advisors [CTA s] are naturally concerned with risk as well as return. In this paper, we investigate risk of hedge funds and CTA s in light of managerial career concerns. We find an association between past performance and risk levels consistent with Brown, Harlow and Starks (1996) findings for mutual fund managers. Good performers in the first half of the year reduce the volatility of their portfolios, and poor performersincrease volatility. These variance strategies" depend upon the fund s ranking relative to other funds. The importance of relative rankings as opposed to the absolute ranking suggested by analysis of hedge fund and CTA manager contracts points to the importance of reputation costs.These costsare best thought of in the context of the career concerns of managers and the relative importance of fund termination. We analyze factors contributing to fund disappearance. Survival depends on both absolute and relative performance. Excess volatility can also lead to termination. Finally, other things equal, the younger a fund, the more likely it is to disappear from the sample. Therefore our results strongly confirm an hypothesis of Fung and Hsieh (1997b) that reputation costs have a mitigating effect on the gambling incentives implied by the manager contract. Particularly for young funds, a volatility strategy that increases the value of a performance fee option may lead to the premature death of that option through termination of the fund. The finding that hedge fund and CTA volatility is conditional upon past performance has implications for investors, lenders and regulators. An important result of our finding is that variance strategy depends upon relative rather than absolute
This paper examines the survival analysis of hedge funds using various survival models. Survival analysis has been used in studies of the lifetimes of bonds, labour strikes, marketing preferences and many other areas. By examining several predictor variables, the analysis demonstrates that some variables can be used to predict hedge fund mortality. We use the Product-Limit estimator, Life table method, Accelerated Failure Time Model and the Cox proportional hazards models to investigate the survival times of hedge funds over a 12-year period. The median (half-life) survival time of all hedge funds is exactly 5.50 years. It is found, however, that millions managed, redemption period, performance fee, leverage, monthly returns and minimum purchase have an impact on the mortality of hedge funds. It is also found that certain hedge fund classifications experience higher survival times than others.Journal of Asset Management (2002) 3, 237-252; doi:10.1057/palgrave.jam.2240078
What excess return should a fund of funds expect to earn for investing in a hedge fund with an extended lockup? In this paper, we present a simple model for estimating the premium for long-term lockups. Because there is a demonstrated statistical persistence to the quality of hedge fund returns within a particular hedge fund strategy above average funds tend to continue to do well, and below average funds continue to falter a lockup deprives an investor of the opportunity to redeem an investment in poorly performing funds and reinvest the proceeds in successful ones. The value of that lost future opportunity is the expected premium for committing to the lockup. We estimate the value of the premium for multi-year lockups in a variety of strategies using a discrete-time Markov chain model for the evolution of hedge funds, in which a hedge fund at any time can be in one of three states: Good, Sick or Dead. For convertible bond funds, for example, the return premium for a two-year lockup over a one-year lockup is approximately 48 basis points (b.p.) per year. The premium rises to 76 b.p. per year for a three-year lockup, and approaches a limit of 156 b.p. as the duration of the lockup becomes infinite. The premium is proportional to the standard deviation of the returns themselves, so that strategies with greater standard deviations of returns require greater compensating lockup premiums.
Hedge funds are often cited as attractive investments because of their diversification benefits and distinctive risk profiles - in contrast to traditional investments such as stocks and bonds, hedge-fund returns have more complex risk exposures that yield complementary sources of risk premia. This raises the possibility of creating passive replicating portfolios or clones using liquid exchange-traded instruments that provide similar risk exposures at lower cost and with greater transparency. Using monthly returns data for 1,610 hedge funds in the TASS database from 1986 to 2005, we estimate linear factor models for individual hedge funds using six common factors, and measure the proportion of the funds' expected returns and volatility that are attributable to such factors. For certain hedge-fund style categories, we find that a significant fraction of both can be captured by common factors corresponding to liquid exchange-traded instruments. While the performance of linear clones is often inferior to their hedge-fund counterparts, they perform well enough to warrant serious consideration as passive, transparent, scalable, and lower-cost alternatives to hedge funds.
This study explores the return persistence properties, styles, and fund characteristics of hedge funds that mainly invest in Asia. We examine, for the first time, a high resolution hedge fund dataset which includes monthly return information as well as detailed fund characteristics data. We find that the returns of Asian hedge funds persist most strongly at monthly horizons to quarterly horizons. This persistence weakens considerably when we lengthen the measurement period beyond a quarter, and does not appear to be due to the imputation of fees or to systematic risk as measured by a simple factor model. Further, we show that Asian funds comove largely with a common Asian equity markets component. Other major components that explain the cross-sectional variation in Asian hedge fund returns include a CTA component, two macro components, and three multi-strategy components. The seven style components in total explain about 64% of the variation in returns. Next, we study the relationship between the cross-section of fund returns and fund characteristics. We document a positive relationship between holding firm size and fund returns which is consistent with an "economies of scale" explanation. Moreover, we find that funds with higher redemption (lockup) periods achieve higher returns on average due to their ability to extricate from their positions in a timely fashion in the face of redemptions. However, there is no evidence to suggest that funds with higher expenses (management and performance fees) achieve higher returns.
Hedge Funds summarizes the academic research on hedge funds and commodity trading advisors. The hedge fund industry has grown tremendously over the recent years. According to some industry estimates, hedge funds have increased from USD 39 million in 1990 to about USD 972 million in 2004 and the total number of hedge funds has gone up from 610 to 7,436 over the same period. At the same time, hedge fund strategies have changed significantly. In 1990 the macro strategy dominated the industry while in 2004 the equity hedge strategy had the largest share of the market. There has also been a shift in the type of investor in hedge funds. In the early 1990s the typical investor was a high net-worth individual investor, today the typical investor is an institutional investor. Thus, the hedge fund market has not only grown tremendously, but the nature of the market has changed. Despite the enormous growth of this industry, there is limited information available on hedge funds. As a result, there is a need for rigorous research from both the investors’ and regulators’ point of view. Investors need research to better understand their investment and their risk exposure. This research also helps investors recognize the extent of diversification benefits hedge funds offer in combination with investments in traditional asset classes, such as stocks and bonds. Regulators can use this research to identify situations where regulation may be needed to protect investors’ interests and to understand the impact hedge funds trading strategies have on the stability of the financial markets. The first part of Hedge Funds summarizes hedge fund performance, including comparisons of risk-return characteristics of hedge funds with those of mutual funds, factors driving hedge fund returns, and persistence in hedge fund performance. The second part reviews research regarding the unique contractual features and characteristics of hedge funds and their influence on the risk-return trade offs. The third part reviews the role of hedge funds in a portfolio including the extent of diversification benefits and limitations of standard mean-variance framework for asset allocation. Finally, the authors summarize the research on the biases in hedge fund databases.
Since hedge funds specify significant lock-up periods, we investigate persistence in the performance of hedge funds using a multi-period framework in which the likelihood of observing persistence by chance is lower than in the traditional two-period framework. Under the null hypothesis of no manager skill (no persistence), the theoretical distribution of observing wins or losses follows a binormial distribution. We test this hypothesis using the traditional two-period framework and compare the findings with the results obtained using our multi-period framework. We examine whether persistence is sensitive to the length of return measurement intervals by using quarterly, half-yearly and yearly returns. We find maximum persistence at the quarterly horizon indicating that presistence among hedge fund managers is short term in nature.
This paper examines holding period returns to constant duration portfolios of U.S. Government notes and bonds, and measures the return premium generated by liquidity differences in bonds. The approach compares constant duration portfolios constructed in two distinct ways: one using only bonds issued in the most recent Treasury auction, one using all other bonds. Comparisons of the resulting series are made meaningful by choosing narrow duration ranges in the portfolio formation procedure. This, in turn, induces a missing data problem in the created time series. Parameters of return distributions are therefore estimated employing a maximum likelihood framework that explicitly accounts for the missing data. It is estimated that recently issued bonds are priced to return a premium of around 55 basis points per annum over otherwise equivalent instruments.
Using a robust bootstrap procedure, we find that top hedge fund performance cannot be explained by luck, and hedge fund performance persists at annual horizons. Moreover, we show that Bayesian measures, which help overcome the short-sample problem inherent in hedge fund returns, lead to superior performance predictability. Sorting on Bayesian alphas, relative to OLS alphas, yields a 5.5% per year increase in the alpha of the spread between the top and bottom hedge fund deciles. Our results are robust and relevant to investors as they are neither confined to small funds, nor driven by incubation bias, backfill bias, or serial correlation.
I document the profits on a trade that is long the old 30-year Treasury bond and short the new 30-year Treasury bond, and is rolled over every auction cycle from June 1995 to November 1999. Despite the systematic convergence of the spread over the auction cycle, the average profits are close to zero. The difference in repo-market financing rates between the two bonds is a significant cost of carry in this trade. I show that variation in the bond/old-bond spread is driven by the Treasury supply of 30-year bonds as well as aggregate factors affecting investors’ preference for liquid assets.
Performance persistence studies typically suffer from ex-post conditioning biases. As stressed by Carhart [Carhart, M.M., 1997. Mutual Fund Survivorship, Working Paper, Marshall School of Business, U.S.C.] and Carpenter and Lynch [J. Financ. Econ. 54 (1999) 337.], standard methods of analysis on a survivorship free sample are subject to look-ahead biases. In this paper, we show how one can easily correct for look-ahead bias using weights based on probit regressions.First, we model how survival probabilities depend upon historical returns, fund age and aggregate economy-wide shocks, using two samples of US based ‘income’ and ‘growth’ funds. Subsequently, we employ a Monte Carlo study to analyze the size and shape of the look-ahead bias in performance persistence that arise when a survivorship free sample is used with standard techniques. In particular, we show that look-ahead bias induces a spurious U-shaped pattern in performance persistence. Finally, we demonstrate how a weighting procedure based upon probit regressions can be used to correct for this bias. In this way, we obtain look-ahead bias-corrected estimates of abnormal performance relative to a one-factor and the Carhart [J. Finan. 52 (1997) 57.] four-factor model, as well as its persistence. The results suggest that in this sample, look-ahead bias is of minor importance and does not seriously affect estimates of persistence. Our bias-corrected results closely correspond to the findings of Carhart [J. Finan. 52 (1997) 57.], implying that there is no evidence on a risk-adjusted basis for persistence in performance.
This paper presents evidence on the relation between hedge fund returns and restrictions imposed by funds that limit the liquidity of fund investors. The excess returns of funds with lockup restrictions are approximately 4–7% per year higher than those of nonlockup funds. The average alpha of all funds is negative or insignificant after controlling for lockups and other share restrictions. Also, a negative relation is found between share restrictions and the liquidity of the fund's portfolio. This suggests that share restrictions allow funds to efficiently manage illiquid assets, and these benefits are captured by investors as a share illiquidity premium.
This paper investigates the returns on British collectible postage stamps over the very long run, based on stamp catalogue prices. Between 1900 and 2008, we find an annualized return on stamps of 6.7% in nominal terms, which is equivalent to an average real return of 2.7% per annum. Prices have increased much faster in the second half of the 1960s, the late 1970s, and the current decade. However, we also record prolonged periods of real depreciation, for example in the 1980s. As a financial investment, stamps have outperformed bonds, but underperformed stocks. After unsmoothing the returns on stamps, we find that the volatility of stamp prices approaches that of equities. There is mixed evidence that stamps are a good hedge against inflation. Once the problem of non-synchronous trading is taken into account, stamp returns seem impacted by movements in the equity market.
Using data on the monthly returns of hedge funds during the period January 1990 to August 1998, we estimate six-factor Jensen alphas for individual hedge funds, employing eight different investment styles. We find that about 25% of the hedge funds earn positive excess returns and that the frequency and magnitude of funds’ excess returns differ markedly with investment style. Using six-factor alphas as a measure of performance, we also analyze performance persistence over 1-year and 2-year horizons and find evidence of significant persistence among both winners and losers. These findings, together with our finding that hedge funds that pay managers higher incentive fees also have higher excess returns, are consistent with the view that fund manager skill may be a partial explanation for the positive excess returns earned by hedge funds.
This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return as well as size, value, and momentum factors. Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the same 34-year period.
This article examines whether there is a flight-to-liquidity premium in Treasury bond prices by comparing them with prices of bonds issued by Refcorp, a U.S. government agency, which are guaranteed by the Treasury. It finds a large liquidity premium in Treasury bonds, which can be more than 15% of the value of some Treasury bonds. This liquidity premium is related to changes in consumer confidence, the amount of Treasury debt available to investors, and flows into equity and money market mutual funds. This suggests that the popularity of Treasury bonds directly affects their value.
The authors examine the performance of the off-shore hedge fund industry over the period 1989 through 1995 using a database that includes both defunct and currently operating funds. The industry is characterized by high attrition rates of funds, low covariance with the U.S. stock market, evidence consistent with positive risk-adjusted returns over the time, and little evidence of differential manager skill. Copyright 1999 by University of Chicago Press.
If information is costly to collect and implement, then it is efficient for trades by informed investors to occur at prices
sufficiently different from full-information prices to compensate them for the cost of becoming informed. This notion is tested
by evaluating investment performance in the mutual fund industry over a 20-year period. The study finds evidence that is consistent
with optimal trading in efficient markets. Risk-adjusted returns in the mutual fund industry, net of fees and expenses, are
comparable to returns available in index funds; and portfolio turnover and management fees are unrelated to fund performance.
We examine the performance of the off-shore hedge fund industry over the period 1989 through 1995 using a database that includes both defunct and currently operating funds. The industry is characterized by high attrition rates of funds, low covariance with the U.S. stock market, evidence consistent with positive risk-adjusted returns over the time, and little evidence of differential manager skill.
Academics and practitioners alike have developed numerous techniques for benchmarking investment returns to properly adjust seemingly high numbers for excessive levels of risk. The same, however, cannot be said for liquidity, or the lack thereof. This article develops a model for analyzing the "ex ante" liquidity premium demanded by the holder of an illiquid annuity. The annuity is an insurance product that is akin to a pension savings account with both an accumulation and decumulation phase. We compute the yield (spread) needed to compensate for the utility welfare loss, which is induced by the inability to rebalance and maintain an optimal portfolio when holding an annuity. Our analysis goes beyond the current literature, by focusing on the interaction between time horizon (both deterministic and stochastic), risk aversion, and preexisting portfolio holdings. More specifically, we derive a negative relationship between a greater level of individual risk aversion and the demanded liquidity premium. We also confirm that, "ceteris paribus", the required liquidity premium is an increasing function of the holding period restriction, the subjective return from the market, and is quite sensitive to the individual's endowed (preexisting) portfolio. Copyright The Journal of Risk and Insurance.
Traditional models of portfolio choice assume that investors can continuously trade unlimited amounts of securities. In reality, investors face liquidity constraints. I analyze a model where investors are restricted to trading strategies that are of bounded variation. An investor facing this type of illiquidity behaves very differently from an unconstrained investor. A liquidity-constrained investor endogenously acts as if facing borrowing and short-selling constraints, and one may take riskier positions than in liquid markets. I solve for the shadow cost of illiquidity and show that large price discounts can be sustained in a rational model. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
We use a comprehensive dataset of Funds-of-Hedge-Funds (FoFs) to investigate performance, risk and capital formation in the hedge fund industry over the past ten years. We confirm the finding of high systematic risk exposures in FoF returns. We divide up the past ten years into three distinct subperiods and demonstrate that the average FoF has only delivered alpha in the short second period from October 1998 to March 2000. In the cross section of FoFs, however, we are able to identify FoFs capable of delivering persistent alpha. We find that these more successful hedge funds experience far greater (and steadier) capital inflows than their less fortunate counterparts. Berk and Green's (2004) rational model of active portfolio management implies that diminishing returns to scale combined with the inflow of new capital leads to the erosion of superior performance over time. In keeping with this implication, we provide evidence that even successful hedge funds have experienced a recent, dramatic decline in risk-adjusted performance.
Previous studies of liquidity span short time periods and focus on the individual security. In contrast, we study aggregate market spreads, depths, and trading activity for U.S. equities over an extended time sample. Daily changes in market averages of liquidity and trading activity are highly volatile and negatively serially dependent. Liquidity plummets significantly in down markets. Recent market volatility induces a decrease in trading activity and spreads. There are strong day-of-the-week effects; Fridays accompany a significant decrease in trading activity and liquidity, while Tuesdays display the opposite pattern. Long- and short-term interest rates influence liquidity. Depth and trading activity increase just prior to major macroeconomic announcements. Copyright The American Finance Association 2001.
How marketability affects security prices is one of the most important issues in finance. The authors derive a simple analytical upper bound on the value of marketability using option-pricing theory. They show that discounts for lack of marketability can potentially be large even when the illiquidity period is very short. This analysis also provides a benchmark for assessing the potential costs of exchange rules and regulatory requirements restricting the ability of investors to trade when desired. Furthermore, these results provide new insights into the relation between discounts for lack of marketability and the length of the marketability restriction. Copyright 1995 by American Finance Association.
The effects of asset liquidity on expected returns for assets with infinite maturities (stocks) are examined for bonds (Treasury notes and bills with matched maturities of less than six months). The yield to maturity is higher on notes, which have lower liquidity. The yield differential between notes and bills is a decreasing and convex function of the time to maturity. The results provide a robust confirmation of the liquidity effect in asset pricing. Copyright 1991 by American Finance Association.
Spreads, depths, and trading activity for U.S. equities are studied over an extended time sample. Daily changes in market averages of liquidity and trading activity are highly volatile, negatively serially dependent, and influenced by a variety of factors. Liquidity plummets significantly in down markets but increases weakly in up markets. Trading activity increases in either up or down markets. Recent market volatility induces less trading activity and reduces spreads. There are strong day-of-the-week effects; Fridays are relatively sluggish and illiquid while Tuesdays are the opposite. Long- and shortterm interest rates influence liquidity and trading activity. Depth and trading activity increase just prior to major macroeconomic announcements.
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