Generalized Sharpe Ratios and Asset Pricing in Incomplete Markets
Review of Finance, 2003, 7(2), 191-233
45 Pages Posted: 5 Oct 2000 Last revised: 30 Sep 2019
Date Written: November 1, 2002
Abstract
The paper presents an incomplete market pricing methodology generating asset price bounds conditional on the absence of attractive investment opportunities in equilibrium. The paper extends and generalises the seminal article of Cochrane and Saa-Requejo who pioneered option pricing based on the absence of arbitrage and high Sharpe Ratios. Our contribution is threefold:
We base the equilibrium restrictions on an arbitrary utility function, obtaining the Cochrane and Saa-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms of Generalised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide a consistent ranking of investment opportunities even when asset returns are highly non-normal. Last but not least, we demonstrate that for Ito processes the Cochrane and Saa-Requejo price bounds are invariant to the choice of the utility function, and that in the limit they tend to a unique price determined by the minimal martingale measure.
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Beyond Arbitrage: 'Good Deal' Asset Price Bounds in Incomplete Markets
-
Beyond Arbitrage: "Good-Deal" Asset Price Bounds in Incomplete Markets
-
Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities
By Jun Liu and Francis A. Longstaff