I've been thinking about how to rate investment opportunities using historical performance. What do you good people think of the following?Good points:1) The Sharpe ratio falls naturally out of a reasonable and tractable mean-variance formalism as a thing to be maximized.2) It's an intuitively reasonable thing to maximize - "excess return per unit risk" (sweeping aside skew, fat tails, all other non-normality, etc. for the moment)3) It's leverage-independent (because of 2). This makes it possible to compare a highly levered CTA, say, with a risk-averse "T-bills plus a few percent" fund.Bad points:1) It's dimensionful (has units of 1/sqrt(time)) and therefore you can't, e.g., directly compare the Sharpes of two funds that have been around for different amounts of time -- a fund with a Sharpe of 1 over 10 years should be seen to be "better than" a fund with a Sharpe of 1 over only 1 year, ceteris paribus.2) It doesn't know about or correct for realized or hypothetical skew - e.g. the writer of deep out puts looks great (i.e. high Sharpe) until he gets blown out and the negative skew may take years to show up in a given sample realization.How to fix it:1) The first bad point can be fixed by using instead of the Sharpe ratio another quantity which is Sharpe ratio * sqrt(time). This is just the t-statistic for rejecting the hypothesis that the excess return is zero - another intuitiively good thing to maximize! Now the 10y Sharpe=1 strategy is "sqrt(10) times as good" as the 1y Sharpe=1 strategy, other things being equal. One can also think of maximizing a quantity Q = Sharpe ratio - constant * sampling uncertainty in Sharpe ratio, but I like the t-stat better...2) The second bad point can be fixed by realizing that the t-stat is really supposed to be Sharpe*sqrt(number of independent observations). So, if we choose some reasonable way to define an autocorrelation time scale then the right thing to maximize becomes Q=Sharpe ratio * sqrt(length of performance history / autocorrelation time scale for strategy). In this way, a given history of a strategy with lots of serial autocorrelation like convert arb (or deep out put writing) will "count less" than an equally long history of a strategy without much serial autocorrelation. By the way, it's apparent upon thinking about it that positive serial autocorrelation of returns and negative skew of the return distribution are inextricably tied together if there's to be no free lunch...Thoughts?

adannenbergAs a firm believer in "dimensional analysis", I agree 100% with your first point. You simply cannot compare dimensional parameters unless you non-dimensionalise them first. There is a general, but elaborate, theory behind all this and anyone who's gone through undergraduate fluid mechanics in college would recognise it as the Buckingham Pi Theorem. Its potential in plotting and analysing data is enormous, but for some strange reason it has been completely left out of finance and economics, where there is a vast amount of data to be sorted out.

After a quick reading on http://scienceworld.wolfram.com/physics ... eorem.html, I must admit that I don't see how the Buckingham Pi Theorem goes beyond standard dimensional analysis or why it's deserving of a separate name?! Perhaps there's more to it than what's written there... Anyway, I can't believe that no one seems to be interested in discussing the pros and cons of performance measures. Do all the risk management types out there only measure risk, or are you also involved in its allocation? If so, on what basis do you allocate capital and/or limits? How do you penalize liquidity risk and capacity constraints? Is it a qualitiative, after-the-fact adjustment of some nominal allocation based on risk-adjusted performance, or is it done quantitatively? What else should be considered?C'mon! I thought I was being original or at least a bit provocative, and all I hear is dead silence ...