Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options

Abstract

We propose a criterion for portfolio selection, implied excess Sharpe ratio. The implied excess Sharpe ratio is intended as an excess Sharpe ratio (versus the underlying stock) that investors can expect to enjoy from portfolios that include options and is a useful ex ante indicator that can be easily calculated. There are a variety of ways to include options in a portfolio, but we theoretically show that the combination that produces the largest implied excess Sharpe ratio is the best way to maximize the short-term Sharpe ratio. The selection process uses implied excess Sharpe ratio, which is easily calculated from stock lending fees implied by stock prices and actual stock lending fee. It does not require historical simulation or prediction of share price average growth rates and is highly transparent as it can be easily reproduced (at a low calculation cost). Hence, the implied excess Sharpe ratio is a simple but effective tool for investors seeking returns in exchange for a certain amount of risk that want to use the options market efficiently. The short-term Sharpe ratio is not necessarily the only criterion, but is a rational benchmark of portfolio performance closely related to criteria such as the long-term Sharpe ratio and maximum drawdown. To examine the benefit of the concept, we construct an investment strategy that automatically selects from multiple candidate portfolios that are made up of combinations of Nikkei futures and Nikkei listed options the portfolio with the largest implied excess Sharpe ratio. Back-testing shows that this investment strategy performs well over the long term as well.