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Sep 23

Maximize Sharpe Ratio or Geometric Mean?

Posted by abiao at 14:59 | Others | Comments(3) | Reads(10674)
Markowitz was the first to advocate the focus on mean and variance and the selection of portfolios with the lowest risk for a target level of return, or the highest return for a target level of risk, read Markowitz Efficient Frontier stock portfolio for an example. However, to maximize Sharpe ratio, or to maximize Geometric mean for optimized portfolio construction, that is the question. Both methods have found their positions in industry. But which one should we choose? there seems to be different opinions. Shared with you an interesting working paper Geometric Mean Maximization: An Overlooked Portfolio Approach, although the example doesn't suggest a clear answer to our question, it is still worth reading.

Academics and practitioners usually optimize portfolios on the basis of mean and variance. They set the goal of maximizing risk-adjusted returns measured by the Sharpe ratio and thus determine their optimal exposures to the assets considered. However, there is an alternative criterion that has an equally plausible underlying idea; geometric mean maximization aims to maximize the growth of the capital invested, thus seeking to maximize terminal wealth. This criterion has several attractive properties and is easy to implement, and yet it does not seem to be very widely used by practitioners. The ultimate goal of this article is to explore potential empirical reasons that may explain why this is the case. The data, however, does not seem to suggest any clear answer, and, therefore, the question posed in the title remains largely unanswered: Are practitioners overlooking a useful criterion?

Here's an Excel spreadsheet that finds the investment weights in a Sharpe Optimal Portfolio
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