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Abstract:
This paper attempts to evaluate the out-of-sample performance of an improved estimator of the covariance structure of hedge fund index returns, focusing on its use for optimal portfolio selection. Using data from CSFB-Tremont hedge fund indices, we find that ex-post volatility of minimum variance portfolios generated using implicit factor based estimation techniques is between 1.5 and 6 times lower than that of a value-weighted benchmark, such differences being both economically and statistically significant. This strongly indicates that optimal inclusion of hedge funds in an investor portfolio can potentially generate a dramatic decrease in the portfolio volatility on an out-of-sample basis. Differences in mean returns, on the other hand, are not statistically significant, suggesting that the improvement in terms of risk control does not necessarily come at the cost of lower expected returns.

Abstract:
While there has been a significant amount of research on the predictability of traditional asset classes, very little is known about the predictability of returns emanating from alternative vehicles such as hedge funds. This is perhaps surprising, given that significant attempts at structuring the alternative investment markets have occurred over the last decade which now allow investors to implement dynamic trading strategies in hedge fund indexes. This paper attempts to fill this gap by documenting evidence of predictability in hedge fund index returns, focusing on their use for tactical style allocation decisions. Using data from nine CSFB-Tremont hedge fund indexes, we find that there is strong evidence of very significant predictability in hedge fund returns. We also find that the benefits in terms of tactical style allocation portfolios are potentially very large. Even more spectacular results are obtained both for an equity-oriented portfolio mixing traditional and alternative investment vehicles, and for a fixed-income oriented portfolio mixing traditional and alternative investment vehicles. These results do not seem to be significantly affected by the presence of reasonably high transaction costs.

Abstract:
An investment horizon is in practice not frequently known with certainty at the initial investment date. This paper addresses the problem of pricing and hedging a random cash-flow received at a random date in a general stochastic environment. We first argue that specific timing risk is induced by the presence of an uncertain time-horizon if and only if the random time under consideration is not a stopping time of the filtration generated by prices of traded assets. In that context, we provide an explicit characterization of the set of equivalent martingale measures, as well as a necessary and sufficient condition for a convenient separation between adjustment for market risk and timing risk. These results allow us to clarify the definition of the market price for timing risk, and lead to general pricing formulae and explicit hedging strategies for random cash-flows in the presence of timing risk. Potential applications are the valuation of employee stock options, real options, catastrophe insurance contracts, credit derivatives, callable and convertible bonds, mortgage-backed securities, as well as any other asset featuring an embedded prepayment option.

Abstract:
While there are now a number of empirical studies on the subject, very little is known on the market price for default risk from a theoretical perspective. This paper is a first step in the direction of an equilibrium model for the pricing of defaultable securities in an incomplete market setup. We first provide an explicit characterization of the set of equivalent martingale measures consistent with no arbitrage in the presence of default risk, as well as a necessary and sufficient condition for a convenient separation between adjustments for market risk and default risk. That result allows us to spell out an unambiguous definition of the market price for default risk as the logarithm of the ratio of the risk-adjusted probability of default to the original probability of default. It also suggests the following question: how should the original probability of default be adjusted to account for agents' risk-aversion? We address this question in a dynamic continuous-time equilibrium setup, and obtain a defaultable version of a standard consumption-based capital asset pricing model. In particular, we confirm the intuition that the correlation between default risk and market risk is a key ingredient of the equilibrium price for default risk, and obtain a quantitative estimate of the magnitude of the effect. Our model is consistent with empirical findings in that it predicts that the term structure of credit spreads can be upward sloping with a non-zero intercept. The theory is illustrated by an application to the valuation of employee compensation packages, which may be regarded as peculiar, yet natural, examples of defaultable securities.

Abstract:
In the presence of transaction costs, a risk-return trade-off exists between the quality and the cost of a replicating strategy. In that context, I show how to expand the set of all possible time-based strategies through the introduction of a multi-scale class of strategies, which consist in rebalancing different fractions of an option portfolio at different time frequencies. The method, based on time-scale diversification, is to dynamic replication what investment in diversified portfolios is to static portfolio selection: in a dynamic context, one may enjoy the benefits of diversification by using different time scales in trading the same asset.

Abstract:
Executive compensation packages are often valued in an inconsistent manner: while employee stock options (ESOs) are typically valued ex-ante, i.e., before uncertainties are resolved, cash bonuses are valued ex-post, i.e., by discounting the realized cash grants. Such a lack of consistency can, potentially, distort empirical results. A related, yet mostly overlooked, problem is that when ex-post valuation is used pay-performance measures cannot be well defined. Consistent use of ex-ante valuation for all components of a compensation package would simultaneously resolve both of these problems and provide a natural framework for the analysis of agency problems.

In this paper, we perform ex-ante valuation of cash bonus contracts as if the executive's performance were measured by the company stock price, demonstrate how the shape of the bonus contract influences the executive's attitude toward risk, and study the pay-performance sensitivity of such contracts. We commence by demonstrating that a typical executive bonus contract with a linear incentive zone has a payoff structure equivalent to a portfolio of standard and binary European call options so that the ex-ante contract value is given by the linear combination of Black and Scholes call and binary call prices, with the strike prices at the boundary points of the incentive zone. Assuming that a risk neutral executive can choose the level of stock price volatility by selecting a set of projects at origination, we show that bonus contract terms can dramatically affect the executive's risk taking behavior and pay-performance incentives. Our results are extended to bonus contracts with non-linear incentive zones, and performance share contracts with vesting risk. Several testable predictions are made, and venues of future research outlined.

Abstract:
This paper provides a joint quantitative analysis of capital structure (debt versus equity) and debt structure (fixed versus floating) decisions in the presence of interest rate and inflation risks. Our analysis shows that debt management decisions have an impact on capital structure decisions. It also suggests that substantial increases in firm value can be generated by optimal debt structure choices.

debt management, capital structure, debt structure

Abstract:
In the context of a dynamic capital structure model with stochastic interest and inflation rates, we obtain analytical expressions for the price of, and optimal allocation to, various forms of liabilities classes, namely fixed-rate bonds, floating-rate bonds and inflation-indexed bonds, in addition to equity. Our analysis shows that debt management decisions have an impact on capital structure decisions. It also suggests that substantial increases in firm value can be generated by optimal debt structure choices.

capital structure, debt management, stochastic interest rates

Abstract:
We derive a closed-form solution for the optimal portfolio of a nonmyopic utility maximizer who has incomplete information about the alphas or abnormal returns of risky securities. We show that the hedging component induced by learning about the expected return can be a substantial part of the demand. Using our methodology, we perform an "ex ante" empirical exercise, which shows that the utility gains resulting from optimal allocation are substantial in general, especially for long horizons, and an "ex post" empirical exercise, which shows that analysts' recommendations are not very useful. (JEL C61, G11, G24)

Abstract:
Following a growing concern among investors about the quality of hedge fund index return data, this paper addresses the question of whether designing hedge fund indices that fulfill the usual requirements (in particular representative and investable) is or not a feasible task, given a variety of features that are specific to that industry. To test whether or not investability should necessarily come at the cost of representativity, we use a well-known methodology in the asset pricing literature based on the concept of factor replicating portfolios. Our results suggest that it is actually possible to construct representative indices based on a limited number of funds that are open to new investments, except perhaps in the case of equity market neutral strategies, provided that: i) these funds are suitably selected and ii) a portfolio is constructed with the objective of replicating the common trend in hedge fund returns for a given strategy. A range of robustness tests are performed that show that high correlation of the factor replicating portfolios with the common factor of returns for each strategy is remarkably stable with respect to modifying the number of funds in the replicating portfolio or changing the frequency of rebalancing.

Abstract:
The focus of this paper is to determine what fraction a myopic risk-averse investor should allocate to investment strategies with convex exposure to stock market returns in a general economy with stochastically time-varying interest rates and equity risk premium. Our conclusion is that typical investors should optimally allocate a sizable fraction of their portfolio to such portfolio insurance strategies, and the associated utility gains are significant. While the fact that static investors would benefit from accessing dynamic investment strategies is in essence not surprising, we have found the size of the rational investment in such structures to be rather remarkable. This strong result is robust with respect to various parametric assumptions, as well as the presence of realistic levels of market frictions and heterogeneous expectations on volatility.

Portfolio insurance, stochastic optimization, dynamic asset allocation

Abstract:
A significant amount of research has been devoted to the predictability of traditional asset classes, but little is known about the predictability of returns emanating from alternative vehicles, such as hedge funds. We attempt to fill this gap by documenting evidence of predictability in hedge fund returns. Using multifactor models for the return on nine hedge fund indexes, for which the factors were chosen to measure the many dimensions of financial risk, we found strong evidence of significant predictability in hedge fund returns. We also found that the benefits of tactical style allocation portfolios are potentially large. We obtained even more spectacular results for an equity-oriented portfolio that mixed traditional and alternative investment vehicles and for a debt-oriented portfolio that mixed traditional and alternative investment vehicles. These results do not seem to have been significantly affected by the presence of reasonably high transaction costs.

Alternative investments, hedge fund strategies, portfolio management, asset allocation