Rating the Stock Market Performance through Zero-Investment Strategies

The central aim of this work is to find a method for rating the performance of stock market indices. Although stock market indices are the most frequent benchmark for portfolio performance measurement, there is no benchmark for them except its own history and other market indices. Comparing the present performance with the past or with other markets means to introduce the variables time and distance into the analysis, which leads to compare different contexts. This arouses the question whether we can measure the stock market performance putting aside time and distance. We find a positive answer by means of options that have the index as their underlying asset. Properly chosen, these options create thresholds that classify the performance level on each period according to a systematic scale. To this end, we develop an option based zero-investment strategy that interacts a long call and short put that capture the market risk premium at their maturity. The notional return on this strategy can be taken as a performance measure that enables us to rate the market performance according to four categories depending on its capacity of overcoming or not the cost of protecting a long position with a put or a short position with a call. We prove that our measure adds a new interpretation to the Sharpe ratio because it is quasi-proportional to it for the usual values of volatility. The paper includes an application to the historical performance of S&P 500 (1959-2013).Â