Equally Weighted Rebalancing as the Average of All Investment Strategies

In a performance evaluation, it is important for both sponsors and portfolio managers to estimate the opportunity set of possible performances. In this regard, we investigate the average performance of all possible strategies and how performance varies across strategies. We show that the average is equal to the performance of the equally-weighted rebalancing strategy and that the standard deviation of all the performances during a period is approximately equal to that of all the investment assets' performances divided by the square root of the sum of the number of the assets and one, given certain conditions