Lionel Martellini

Predictability in the Shape of the Term Structure of Interest Rates

Evidence of predictability in the time-varying shape of the U.S. term structure of interest rates is demonstrated using a robust recursive modeling approach based on a Bayesian mixture of multifactor models. Variables such as default spread, equity volatility, and short-term and forward rates can be used to predict changes in the slope of the yield curve and (to a lesser extent) changes in its curvature. Systematic trading strategies based on butterfly swaps reveal that this evidence of predictability in the shape of the yield curve is both statistically and economically significant.

Extending Black-Litterman Analysis Beyond the Mean-Variance Framework

Extension of the Black-Litterman Bayesian approach to portfolio construction in the presence of non-trivial preferences about higher moments of asset return distributions has a particular application to active style allocation decisions in hedge fund investing. Results here suggest that the systematic implementation of active style allocation decisions can add significant value in a hedge fund portfolio, provided implementation of a sound investment process to account for non-normality and parameter uncertainty in hedge fund return distributions.

Toward the Design of Better Equity Benchmarks: Rehabilitating the Tangency Portfolio from Modern Portfolio Theory

Following recent research on the relevance of idiosyncratic risk in asset pricing models, the author proposes using total volatility as a model-free estimate of a stocks excess expected return and analyzes the implications, in terms of design, for improved equity benchmarks. The author finds that maximum Sharpe ratio portfolios are consistent with such expected return proxies and, if built upon improved estimates of the correlation parameters, will significantly outperform market cap–weighted schemes on a risk-adjusted basis. This analysis, which rehabilitates the role of the tangency portfolio from modern portfolio theory, suggests that better equity benchmarks can be designed, provided that a sophisticated portfolio optimization procedure is used that relies on robust estimates of moments and co-moments of stock return distributions. The article has important potential implications for the on-going debate about appropriate weighting schemes for equity indices.

Optimal Allocation to Hedge Funds : An Empirical Analysis

What percentage of their portfolio should investors allocate to hedge funds? The only available answers to the above question are set in a static mean-variance framework, with no explicit accounting for uncertainty on the active managers ability to generate abnormal return, and usually generate unreasonably high allocations to hedge funds. In this paper, we apply the model introduced in Cvitanic et al (2002b Working Paper USC) for optimal investment strategies in the presence of uncertain abnormal returns to a database of hedge funds. We find that the presence of the model risk significantly decreases an investors optimal allocation to hedge funds. Another finding of this paper is that low beta hedge funds may serve as natural substitutes for a significant portion of investor risk-free asset holdings.

Competing Methods for Option Hedging in the Presence of Transaction Costs

Most option pricing models are set in continuous time in order for it to be (theoretically) possible to follow an option replication strategy that continuously rebalances a delta-neutral hedge. One big problem in applying such a model to the real world is that perfect replication theoretically entails trading an infinite amount of the underlying asset. With transactions costs, no matter how small, the cost of this strategy is also infinite. A delta hedge can not be rebalanced continuously, so how should one rebalance periodically to achieve the best replication at minimum cost? Some possibilities are to rebalance at fixed time intervals, or whenever the asset price moves by a preset amount, or when the option’s delta differs from the position’s hedge ratio by a given percentage. Other ideas have also been proposed, but it is still not clear which is best. In this article, Martellini and Priaulet examine this issue in an extensive simulation exercise. Among their results, they find that delta-based rebalancing works best under proportional transactions costs. But adding a fixed component to the transactions cost reduces the effectiveness of that strategy.

Static Mean-Variance Analysis with Uncertain Time Horizon

We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.

Passive Hedge Fund Replication: A Critical Assessment of Existing Techniques

In this article the authors provide a critical analysis of various methodologies involved in “passive replication” of hedge fund returns, a subject that has received renewed interest following recent initiatives by major investment banks. The authors examine from both theoretical and empirical perspectives the benefits and limits of the two different and somewhat competing approaches to hedge fund replication, respectively known as “factor-based replication,” and “payoff distribution replication.” The analysis suggests that only through the introduction of novel econometric techniques allowing for a parsimonious statistical estimation of the dynamic and/or non-linear functions relating underlying factors to hedge fund returns can hedge fund replication be transformed from an attractive concept into a workable investment solution. The authors conclude that hedge fund replication is still very much a work in progress.

Inflation-Hedging Properties of Real Assets and Implications for Asset–Liability Management Decisions

Recent increases in inflation uncertainty have increased investor awareness of the need to hedge against unexpected changes in price levels. Given that the capacity of the inflation-linked securities market is not sufficient to meet the collective demand of institutional and private investors and that the OTC inflation derivatives market suffers from a perceived increase in counterparty risk, investors are now turning to other asset classes to seek inflation protection. Using a vector error correction model that explicitly distinguishes between short-term and long-term dynamics in the joint distribution of asset returns and inflation, the authors show that real estate and commodities have particularly attractive inflation-hedging properties over long horizons and that these properties justify the introduction of these asset classes into pension fund liability-hedging portfolios. These results suggest that novel forms of liability-driven investment solutions, including commodities and real estate in addition to inflation-linked securities, can be designed to decrease the cost of inflation insurance for long-horizon investors.

Diversifying the Diversifiers and Tracking the Tracking Error:Outperforming Cap-Weighted Indices with Limited Risk of Underperformance

A number of quantitative or fundamental weighting schemes have been shown to produce robust outperformance with respect to standard cap-weighted equity indices over long time periods. Over periods ranging from a few months to a few years, however, such alternative weighting schemes can generate substantial downside risk relative to cap-weighted indices, which would be a source of concern for most investment managers or chief investment officers. In this article, the authors focus on two reasonable proxies for well-diversified, efficient frontier portfolios, namely, the maximum Sharpe ratio (MSR) portfolio and the global minimum volatility (GMV) portfolio. They address the question of how to use these building blocks to design an improved equity benchmark while satisfying target levels of average and extreme tracking error with respect to cap-weighted indices. The authors find that robust proxies for the GMV portfolio provide defensive exposure to equity that does well in adverse market conditions, while robust proxies for MSR portfolios provide greater access to the upside of equity markets. Because the relative performance of these two diversification approaches depends on market conditions, they expect a combination of both approaches to lead to a smoother conditional performance and higher probability of outperformance of the cap-weighted index, an intuition that is confirmed in empirical tests. Empirical analysis also suggests that “diversifying the diversifiers” still leads to high levels of relative downside risk, in particular when the performance of cap-weighted indices is unusually strong. In this context, the authors introduce an explicit relative risk control mechanism designed to reduce the consequences of severe short-term underperformance with respect to the cap-weighted index and confirm through out-of-sample empirical tests that “tracking the tracking error” would allow investors to achieve better access to outperformance per unit of extreme relative risk taken. Overall, the results reported in this article suggest that it is possible to achieve robust outperformance versus cap-weighted indices by diversifying model risk and by controlling relative risk compared to the cap-weighted indices.

Revisiting Core-Satellite Investing

Tracking error is not necessarily bad. Good tracking error would be outperformance of a portfolio with respect to the benchmark. If they severely restrict the amounts invested in active strategies as a result of tight tracking error constraints, investors foreclose the opportunity for significant outperformance, especially during market downturns. A new methodology based on an optimal dynamic adjustment of the fractions invested in a passive core versus an active satellite portfolio allows investors to gain full access to good tracking error, while keeping bad tracking error below a given threshold. The method is a natural extension of constant-proportion portfolio insurance techniques.