Valeri Zakamouline

Portfolio Performance Evaluation with Generalized Sharpe Ratios: Beyond the Mean and Variance

This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investors preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.

Portfolio performance evaluation with loss aversion

In this paper we consider a loss-averse investor equipped with a specific, but still quite general, utility function motivated by behavioral finance. We show that, under certain concrete assumptions concerning the form of this utility, one can derive closed-form solutions for the investors portfolio performance measure. We investigate the effects of loss aversion and demonstrate its important role in performance measurement. The framework presented in this paper also provides a sound theoretical foundation for all known performance measures based on partial moments of the distribution.

Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs

One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other well-known strategies and find that our strategy outperforms all the others.

On the Consistent Use of VaR in Portfolio Performance Evaluation: A Cautionary Note

The portfolio performance measures based on the Value at Risk (VaR) concept have gained widespread popularity and are often used in empirical studies. In the majority of empirical studies, however, a VaR-based performance measure is inconsistently used. In this article, Zakamouline emphasizes how to consistently use VaR in portfolio performance evaluation. He also elaborates on a simple framework that allows the derivation of a general formula for a portfolio performance measure that is not limited to the use of VaR-based reward and risk measures, but is valid for all reward and risk measures that satisfy a few plausible properties.

Block Bootstrap Methods and the Choice of Stocks for the Long Run

Financial advisors commonly recommend that the investment horizon should be rather long in order to benefit from the ‘time diversification’. In this case, in order to choose the optimal portfolio, it is necessary to estimate the risk and reward of several alternative portfolios over a long-run given a sample of observations over a short-run. Two interrelated obstacles in these estimations are lack of sufficient data and the uncertainty in the nature of the return generating process. To overcome these obstacles researchers rely heavily on block bootstrap methods. In this paper we demonstrate that the estimates provided by a block bootstrap method are generally biased and we propose two methods of bias reduction. We show that an improper use of a block bootstrap method usually causes underestimation of the risk of a portfolio whose returns are independent over time and overestimation of the risk of a portfolio whose returns are mean-reverting.

The Best Hedging Strategy In The Presence Of Transaction Costs

Considerable theoretical work has been devoted to the problem of option pricing and hedging with transaction costs. A variety of methods have been suggested and are currently being used for dynamic hedging of options in the presence of transaction costs. However, very little was done on the subject of an empirical comparison of different methods for option hedging with transaction costs. In a few existing studies the different methods are compared by studying their empirical performances in hedging only a plain-vanilla short call option. The reader is tempted to assume that the ranking of the different methods for hedging any kind of option remains the same as that for a vanilla call. The main goal of this paper is to show that the ranking of the alternative hedging strategies depends crucially on the type of the option position being hedged and the risk preferences of the hedger. In addition, we present and implement a simple optimization method that, in some cases, improves considerably the performance of some hedging strategies.

A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components

In this paper we present a multi‐factor continuous‐time autoregressive moving‐average (CARMA) model for the short and forward interest rates. This models is able to present a more adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provide closed‐form solutions to bond and bond option prices, bond yields, and the forward rate volatility term structure. We demonstrate the capabilities of our model by calibrating it to market data and show that it can reproduce rather complex shapes of the empirical volatility term structure. In particular, a three‐factor CARMA model can easily capture the dynamics of the level, slope, and curvature factors widely documented in term structure models.