Asset Prices and Trading Volume Under Fixed Transactions Costs2004
We propose a dynamic equilibrium model of asset prices and trading volume with heterogeneous agents facing fixed transactions costs. We show that even small fixed costs can give rise to large "no-trade" regions for each agent's optimal trading policy and a significant illiquidity discount in asset prices. We perform a calibration exercise to illustrate the empirical relevance of our model for aggregate data. Our model also has implications for the dynamics of order flow, bid/ask spreads, market depth, the allocation of trading costs between buyers and sellers, and other aspects of market microstructure, including a square-root power law between trading volume and fixed costs which we confirm using historical US stock market data from 1993 to 1997.
An Econometric Model of Serial Correlation and Illiquidity in Hedge-Fund Returns2004
The returns to hedge funds and other alternative investments are often highly serially correlated in sharp contrast to the returns of more traditional investment vehicles such as long-only equity portfolios and mutual funds. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure, i.e., investments in securities that are not actively traded and for which market prices are not always readily available. For portfolios of illiquid securities, reported returns will tend to be smoother than true economic returns, which will understate volatility and increase risk-adjusted performance measures such as the Sharpe ratio. We propose an econometric model of illiquidity exposure and develop estimators for the smoothing profile as well as a smoothing-adjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedge-fund style categories and may be a useful proxy for quantifying illiquidity exposure.
Sifting Through the Wreckage: Lessons from Recent Hedge Fund Liquidations2004
We document the empirical properties of a sample of 1,765 funds in the TASS Hedge Fund database from 1994 to 2004 that are no longer active. The TASS sample shows that attrition rates differ significantly across investment styles, from a low of 5.2% per year on average for convertible arbitrage funds to a high of 14.4% per year on average for managed futures funds. We relate a number of factors to these attrition rates, including past performance, volatility, and investment style, and also document differences in illiquidity risk between active and liquidated funds. We conclude with a proposal for the U.S. Securities and Exchange Commission to play a new role in promoting greater transparency and stability in the hedge-fund industry.
It’s 11pm—Do You Know Where Your Liquidity Is? The Mean-Variance-Liquidity Frontier2003
We introduce liquidity into the standard mean-variance portfolio optimization framework by defining several measures of liquidity and then constructing three-dimensional mean-variance-liquidity frontiers in three ways—liquidity filtering, liquidity constraints, and a mean-variance-liquidity objective function. We show that portfolios close to each other on the traditional mean-variance efficient frontier can differ substantially in their liquidity characteristics. In a simple empirical example, the liquidity exposure of mean-variance efficient portfolios change dramatically from month to month, and even simple forms of liquidity optimization can yield significant benefits in reducing a portfolio's liquidity-risk exposure without sacrificing a great deal of expected return per unit risk.
The Statistics of Sharpe Ratios2002
The building blocks of the Sharpe ratio—expected returns and volatilities— are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, I derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic theory under several sets of assumptions for the return-generating process—independently and identically distributed returns, stationary returns, and with time aggregation. I show that monthly Sharpe ratios cannot be annualized by multiplying by except under very special circumstances, and I derive the correct method of conversion in the general case of stationary returns. In an illustrative empirical example of mutual funds and hedge funds, I find that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent because of the presence of serial correlation in monthly returns, and once this serial correlation is properly taken into account, the rankings of hedge funds based on Sharpe ratios can change dramatically.
Econometric Models of Limit-Order Executions2002
Limit orders incur no price impact, however, their execution time is uncertain. We develop an econometric model of limit-order execution times using survival analysis, and estimate it with actual limit-order data. We estimate versions for time-to-first-fill and time-to-completion, and for limit-sells and limit-buys, and incorporate the effects of explanatory variables such as the limit price, the limit size, the bid/offer spread, and market volatility. We find that execution times are very sensitive to limit price and several other explanatory variables, but not sensitive to limit size. We also show that hypothetical limit-order executions, constructed either theoretically from first-passage times or empirically from transactions data, are very poor proxies for actual limit-order executions.
We develop a dynamic equilibrium model of an asset market with multiple securities in which investors trade to share risks and smooth consumption over time, and investigate the empirical implications for the cross-sectional characteristics of trading volume and the dynamic volume-return relation. We extend the model to include fixed transactions costs, and when calibrated to aggregate data, the model implies realistic levels of trading volume. We also evaluate the efficacy of technical analysis in capturing the relation between prices and volume heuristically.
Risk Management for Hedge Funds: Introduction and Overview2001
Although risk management has been a well-plowed field in financial modeling for over two decades, traditional risk management tools such as mean-variance analysis, beta, and Value-at-Risk do not capture many of the risk exposures of hedge-fund investments. In this article, I review several aspects of risk management that are unique to hedge funds - survivorship bias, dynamic risk analytics, liquidity, and nonlinearities - and provide examples that illustrate their potential importance to hedge-fund managers and investors. I propose a research agenda for developing a new set of risk analytics specifically designed for hedge-fund investments, with the ultimate goal of creating risk transparency while, at the same time, protecting the proprietary nature of hedge-fund investment strategies.
The Sources and Nature of Long-Term Dependence in the Business Cycle2001
This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, and focuses on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-term dependence, a consequence of aggregation in the presence of real business cycles. We derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data, and discuss how fiscal policy may alter their stochastic behavior. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test is robust to short-term dependence, and is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle.
Asset Allocation and Derivatives2001
The fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets suggests the possibility of constructing buy-and-hold portfolios of options that mimic certain dynamic investment policies, e.g., asset-allocation rules. We explore this possibility by solving the following problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon which will come closest to the optimal dynamic investment policy. We solve this problem for several combinations of preferences, return dynamics, and optimality criteria, and show that under certain conditions, a portfolio consisting of just a few options is an excellent substitute for considerably more complex dynamic investment policies.