Sharpening Sharpe Ratios

It is now well known that the Sharpe ratio and other related reward-to-risk measures may be manipulated with option-like strategies. In this paper we derive the general conditions for achieving the maximum expected Sharpe ratio. We derive static rules for achieving the maximum Sharpe ratio with two or more options, as well as a continuum of derivative contracts. The optimal strategy rules for increasing the Sharpe ratio. Our results have implications for performance measurement in any setting in which managers may use derivative contracts. In a performance measurement setting, we suggest that the distribution of high Sharpe ratio managers should be compared with that of the optimal Sharpe ratio strategy. This has particular application in the hedge fund industry where use of derivatives is unconstrained and manager compensation itself induces a non-linear payoff. The shape of the optimal Sharpe ratio leads to further conjectures. Expected returns being held constant, high Sharpe ratio strategies are, by definition, strategies that generate regular modest profits punctunated by occasional crashes. Our evidence suggests that the 'peso problem' may be ubiquitous in any investment management industry that rewards high Sharpe ratio managers.

Risk management under Omega measure

We prove that the Omega measure, which considers all moments when assessing portfolio performance, is equivalent to the widely used Sharpe ratio under jointly elliptic distributions of returns. Portfolio optimization of the Sharpe ratio is then explored, with an active-set algorithm presented for markets prohibiting short sales. When asymmetric returns are considered we show that the Omega measure and Sharpe ratio lead to different optimal portfolios

Losing money with a high Sharpe ratio

A simple example shows that losing all money is compatible with a very high Sharpe ratio (as computed after losing all money). However, the only way that the Sharpe ratio can be high while losing money is that there is a period in which all or almost all money is lost. This note explores the best achievable Sharpe and Sortino ratios for investors who lose money but whose one-period returns are bounded below (or both below and above) by a known constant.Comment: 6 page

Methodology of measuring performance in alternative investment

The development of alternative investment has highlighted the limitations of standard performance measures like the Sharpe ratio, primarily because alternative strategies yield returns distributions which can be far from gaussian. In this paper, we propose a new framework in which trades, portfolios or strategies of various types can be analysed regardless of assumptions on payoff. The proposed class of measures is derived from natural and simple properties of the asset allocation. We establish representation results which allow us to describe our set of measures and involve the log-Laplace transform of the asset distribution. These measures include as particular cases the squared Sharpe ratio, Stutzer's rank ordering index and Hodges' Generalised Sharpe Ratio. Any measure is shown to be proportional to the squared Sharpe ratio for gaussian distributions. For non gaussian distributions, asymmetry and fat tails are taken into account. More precisely, the risk preferences are separated into gaussian and non-gaussian risk aversions.Alternative investment, performance measure, additive independence condition, generalised Sharpe ratio, portfolio optimization.

The Returns to Currency Speculation

Currencies that are at a forward premium tend to depreciate. This `forward premium-depreciation anomaly' represents an egregious deviation from uncovered interest parity. We document the returns to currency speculation strategies that exploit this anomaly. The first strategy, known as the carry trade, is widely used by practitioners. This strategy involves selling currencies forward that are at a forward premium and buying those that are at a forward discount. The second strategy relies on a particular regression to forecast the payoff to selling currencies forward. We show that these strategies yield high Sharpe ratios which are not a compensation for risk. However, these Sharpe ratios do not represent unexploited profit opportunities. In the presence of microstructure frictions, spot and forward exchange rates move against traders as they increase their positions. The resulting `price pressure' drives a wedge between average and marginal Sharpe ratios. We argue that marginal Sharpe ratios are zero even though average Sharpe ratios are positive. We display a simple microstructure model that simultaneously rationalizes `price pressure' and the forward premium-depreciation puzzle. The central feature of this model is that market makers face an adverse selection problem that is less severe when, based on public information, the currency is expected to appreciateuncovered interest parity, BGT regressions, price pressure

Pricing kernels and dynamic portfolios

We investigate the structure of the pricing kernels in a general dynamic investment setting by making use of their duality with the self financing portfolios. We generalize the variance bound on the intertemporal marginal rate of substitution introduced in Hansen and Jagannathan (1991) along two dimensions, first by looking at the variance of the pricing kernels over several trading periods, and second by studying the restrictions imposed by the market prices of a set of securities. The variance bound is the square of the optimal Sharpe ratio which can be achieved through a dynamic self financing strategy. This Sharpe ratio may be further enhanced by investing dynamically in some additional securities. We exhibit the kernel which yields the smallest possible increase in optimal dynamic Sharpe ratio while agreeing with the current market quotes of the additional instruments.pricing kernel; Sharpe ratio; self financing portfolio; variance-optimal hedging

Stochastic Dominance Analysis of iShares

Country indices as represented by iShares exhibit non-normal return distributions with both skewness and kurtosis. Davidson and Duclos (2000) and Memmel (2003) provide procedures for determining the statistical significance of stochastic dominance measures and the Sharpe Ratio, respectively. This study uses these refinements to compare the performance of 18 country market indices. The iShares are indistinguishable when using the Sharpe Ratio as no significant differences are found. In contrast, stochastic dominance procedures identify dominant iShares. Although the results vary over time, stochastic dominance appears to be both more robust and discriminating than the CAPM in the ranking of the iShares.Stochastic dominance; Sharpe ratio; skewness; country index funds