Sharpening Sharpe Ratios
AbstractIt 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 has a truncated right tail and a fat left tail. We also derive dynamic 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 punctuated by occasional crashes. Our evidence suggests that the "peso problem" may be ubiquitous in any investment management industry that rewards high Sharpe ratio managers.
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Bibliographic InfoPaper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm273.
Date of creation: 22 Mar 2002
Date of revision:
Sharpe Ratio; Hedge Funds; Derivatives;
Other versions of this item:
- William Goetzmann & Jonathan Ingersoll & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," NBER Working Papers 9116, National Bureau of Economic Research, Inc.
- William N. Goetzmann & Jonathan E. Ingersoll, Jr. & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," Yale School of Management Working Papers ysm29, Yale School of Management.
- G1 - Financial Economics - - General Financial Markets
- G2 - Financial Economics - - Financial Institutions and Services
- G0 - Financial Economics - - General
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