Should You Judge Performance on Alpha or Sharpe?

People often say they are focused on obtaining the highest risk adjusted return.  I would suggest the highest goal is return, with an eye towards containing risk.  There's a vast difference in the two approaches.

Primarily, we're trying to maximize the mean periodic return of our investments and minimize the variance of those returns.  If we had an unlimited bankroll, minimizing those variances wouldn't matter because the risk of catastrophic loss, defined in this case as the risk of not being able to continue, wouldn't exist (unlimited bankroll, remember).  We would simply shoot for the biggest returns, acting rationally.  But since we have a limit to the losses that can be sustained, we have to constrain our pursuit of return in this way.

Where people often trip up is in thinking that a given investment with an expected return and beta is better than another investment of the same expected return and higher beta.  Not necessarily, because beta is a backward looking and inherently fuzzy measure.  Even when evaluating a stream of observed returns, the observed volatility is not the same as risk.  Its is the portion of risk that is realized, with possibly much more risk that wasn't observed but still existent.  Just because risk didn't rear its ugly head doesn't mean it wasn't there.

So when someone says they have a sharpe ratio of this or that, consider their alpha as the more important measure.  Higher sharpe may or may not be better, whereas higher alpha is always better.  It's the one that is accurate to the penny, whereas all other measures are fuzzy.  You can't feed your family on sharpe!