Working Paper: NBER ID: w9116
Authors: William Goetzmann; Jonathan Ingersoll; Matthew Spiegel; Ivo Welch
Abstract: 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.
Keywords: Sharpe Ratio; Performance Measurement; Investment Management; Hedge Funds; Derivatives
JEL Codes: G0; G1; G2
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| manipulation of the Sharpe ratio through derivative strategies (G40) | increased expected Sharpe ratio (G11) |
| using out-of-the-money calls and puts (G13) | favorable return distribution for achieving high Sharpe ratios (C46) |
| these strategies (L10) | higher expected Sharpe ratio (G19) |
| hedge fund managers' nonlinear compensation structures (J33) | employment of derivative strategies (G13) |
| derivative trading strategies (G13) | artificially inflate performance metrics (C43) |