The implied Sharpe ratio
Abstract
In an incomplete market, including liquidlytraded European options in an investment portfolio could potentially improve the expected terminal utility for a riskaverse 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 statedependent coefficients in a nonlinear partial differential equation, we also establish the behaviour of the implied Sharpe ratio with respect to an investor's riskaversion parameter. In a series of numerical studies, we compare the investment attractiveness of different European options by studying their implied Sharpe ratio.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.04837
 Bibcode:
 2019arXiv190804837A
 Keywords:

 Quantitative Finance  Mathematical Finance
 EPrint:
 22 pages, 6 figures