A Common Sense Approach to Portfolio Theory
Contents
Introduction
Traditional portfolio theory employs an optimization strategy that involves maximizing a expected portfolio’s Sharpe Ratio given asset Sharpe Ratios and a correlation matrix. Levy and Duchin (2009), however, demonstrate that optimal weights don’t significantly outperform a naive 1/N optimization strategy.
The problem with weights is that they are heavily dependent on Sharpe Ratio estimatation. If a stock has a 0.99 correlation versus the market and has the highest Sharpe Ratio amongst all assets under consideration, then portfolio optimization would suggest that 100% of the portfolio should be in that single asset. If, however, another 0.99 correlation asset in actuality had the highest Sharpe Ratio, then 0% of the portfolio should be in that asset.
In other words, there is an implicit assumption in portfolio theory that Sharpe Ratio estimates have 0 standard error, which of course is ridiculous. A correct portfolio theory must account for Sharpe Ratio estimation error. And to the best of my knowledge, no such theory currently exists.
An alternative approach is simply to consider whether an asset belongs in a portfolio in general. It turns out that the decision criteria is based on the following formula: $$ MSR_a = SR_a - \rho SR_m $$
where MSR means Marginal Sharpe Ratio. If an asset’s Marginal Sharpe Ratio is greater than zero, then an asset has some place in our portfolio. Moreover, assuming Sharpe Ratios estimates are roughly the same for all assets, a higher MSR implies a greater confidence that the asset belongs in our portfolio.
References
Author David Rashty
LastMod 2020-09-03