The implied Sharpe ratio

Agarwal, A. and Lorig, M. (2020) The implied Sharpe ratio. Quantitative Finance, 20(6), pp. 1009-1026. (doi: 10.1080/14697688.2020.1718194)

Abstract

In an incomplete market, including liquidly-traded European options in an investment portfolio could potentially improve the expected terminal utility for a risk-averse investor. However, unlike the Sharpe ratio, which provides a concise measure of the relative investment attractiveness of different underlying risky assets, there is no such measure available to help investors choose among the different European options. We introduce a new concept – the implied Sharpe ratio – which allows investors to make such a comparison in an incomplete financial market. Specifically, when comparing various European options, it is the option with the highest implied Sharpe ratio that, if included in an investor’s portfolio, will improve his expected utility the most. Through the method of Taylor series expansion of the state-dependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor’s risk-aversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Agarwal, Dr Ankush
• Authors: Agarwal, A., and Lorig, M.
• Subjects: H Social Sciences > HB Economic Theory; H Social Sciences > HG Finance
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Quantitative Finance
• Publisher: Taylor & Francis
• ISSN: 1469-7688
• ISSN (Online): 1469-7696
• Published Online: 19 February 2020
• Copyright Holders: Copyright © 2020 Informa UK Limited, trading as Taylor and Francis Group
• First Published: First published in Quantitative Finance 20(6):1009-1026
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Related URLs

• Pre-print