The opportunity set: Market opportunities and the effective breadth of a portfolio

The opportunity set (OS) is an ex post measure of the maximum Sharpe ratio for a given universe of assets. As the authors show, the average value of the OS is approximately equal to the square root of portfolio breadth, or the number of assets in a portfolio.The authors thus suggest an interpretation of the OS to be the effective breadth of a portfolio. Effective breadth is higher when the volatility of asset returns is high because such an environment offers investors more opportunities for generating returns, which is tantamount to having greater portfolio breadth. When asset return volatility is lower, the opposite is true; that is, effective breadth is lower and investors are hard-pressed to generate excess returns at any risk level.