What the Sharpe ratio does is: give you a dimensionless score to compare similar investments that may vary both in riskiness and returns without needing to know the investor’s risk tolerance. It does this by separating the task of valuing an investment (which can be made independent of the investor’s risk tolerance) from the task of allocating/valuing a portfolio (which must depend on the investor’s preferences).
Having worked in finance I am a public fan of the Sharpe ratio. I have written about this here and here.
One thing I have often forgotten (driving some bad analyses) is: the Sharpe ratio isn’t appropriate for models of repeated events that already have linked mean and variance (such as Poisson or Binomial models) or situations where the variance is very small (with respect to the mean or expectation). These are common situations in a number of large scale online advertising problems (such as modeling the response rate to online advertisements or email campaigns).
This is an elementary mathematical finance article. This means if you know some math (linear algebra, differential calculus) you can find a quick solution to a simple finance question. The topic was inspired by a recent article in The American Mathematical Monthly (Volume 117, Number 1 January 2010, pp. 3-26): “Find Good Bets in the Lottery, and Why You Shouldn’t Take Them” by Aaron Abrams and Skip Garibaldi which said optimal asset allocation is now an undergraduate exercise. That may well be, but there are a lot of people with very deep mathematical backgrounds that have yet to have seen this. We will fill in the details here. The style is terse, but the content should be about what you would expect from one day of lecture in a mathematical finance course.
The current state of the global financial markets has gotten more people than usual worrying about the technical aspects of finance. One method for reasoning about investment returns and risk is a tool called the Sharpe Ratio. It is well worth reviewing this measure and seeing how, if used properly, it doesn’t favor any of the mistakes that underly our current financial crisis. Continue reading A Quick Appreciation of the Sharpe Ratio