When one is evaluating systems (or a manager), it’s advisable to measure both the return and the risk associated with it. Often the volatility of the return stream, which isn’t necessarily the same thing as its risk, is thought of as synonymous with risk and substituted for risk in the measurement. The Sharpe ratio is one metric often used for measuring return in relation to risk; the Sortino ratio is another.

There are at least four different ways of conceptualizing the Sharpe ratio; I will list them, along with my thoughts on each:

(1) Maximizing the Sharpe ratio maximizes compounded returns.

Only if the distribution of returns is symmetric. Are returns distributed symmetrically? Not in THIS universe. To paraphrase Rodney Dangerfield’s character in “Back To School,” speaking to his business professor, maybe we should base our funds in Fantasyland, home of exclusively Gaussian distributions!

The good folks who popularized the Sortino ratio have kindly posted a proof which shows that a modified Sortino ratio has maximizing properties if returns are asymmetric. Here’s another paper, by Ashraf Chaudhry and Helen Johnson, with a similar finding on the superiority of Sortino vs. Sharpe, when return distributions are skewed.

It’s painfully obvious to all but the oblivious that many systems and styles of trading produce significantly skewed returns. Often these pay off like long options or long-term trend-following - positive skewness - or like scalping pennies (the “glorified market-making” world of high-frequency spurious correlation trades) or short options - negative skewness. Using the Sharpe ratio on a positively skewed strategy may lead you to discard it unnecessarily, whereas using the Sharpe ratio on a negatively skewed strategy may lead you to discard your assets (and those of your investors) unnecessarily.

For my money, I ignore the mathturbational “proof” process and satisfy myself (pun intended) that the Sortino is better for evaluating competing systems than the Sharpe ratio is, because the Sortino ratio doesn’t punish upside volatility. Bill likey upside vol.

(2) The Sharpe ratio measures the probability that a given return stream is significantly different from the “Risk Free” rate of return.

This is the pure stats way of thinking about it; a one-tailed hypothesis test and the Sharpe ratio is the glorified Z-score, asking the eternal question, “This actual mean is how many standard deviations away from the expected mean?”

Here I’d like to make an important note on annualizing Sharpe ratios – many managers use shorter timeframes (weekly, etc) for the return evaluation, and annualize the returns to develop a Sharpe ratio that they THINK is on common ground with everyone else’s Sharpe ratio. Don’t forget that the Sharpe is a ratio, and both terms, the return and the standard deviation, would need to be annualized. How one annualizes the standard deviation of a sample says a lot about what that person believes the underlying distribution is; and the manager doing the analysis is probably dead-ass wrong in their assumption about the distribution, because the standard solution is back in Fantasyland.

My take – don’t trust any comparison of Sharpe or Sortino ratios across different systems, unless both systems have their metric analyzed on the same timeframe. As an example, if system one is “Sharped” on daily bars, annualized, and system two is “Sharped” on monthly bars, annualized, then to compare the two Sharpe ratios is mildly mistaken at best, dangerously foolish at worst. Grab the actual data streams yourself, and compute the metrics on common time units. When comparing Sharpes (or Sortinos) in this manner, there’s no need to annualize the metrics in order to preference rank the systems, because they’ll be on the same basis.

Oh, and don’t forget to ask what Risk Free rate was used in calculating the Sharpe ratio!

(3) When using an interest rate as the Risk Free rate, the Sharpe ratio measures the probability that a given system would be profitable, if it were executed on borrowed money.

For retail hacks, this fits the other actuarial definition of IBNR - “interesting but not relevant.”

(4) Sharpe ratios are essential marketing tools.

This is pretty self-explanatory. If you’re after other people’s money, it makes sense to dance like a monkey and show them whatever ratio they like, whether or not you personally might think there are better metrics to use, and you should annualize it, regardless of how improper the treatment of the denominator, simply because every other fund manager does.

Think about it, though; if the potential investor was worth their weight in dollar bills, they wouldn’t trust your metrics anyway! They would ask for a return stream and metric it themselves. Then they would put a small amount of money with you for several months, or a year, and then, finally, fully seed you – but I digress.

Bottom line -

I no longer calculate Sharpe ratios for my own use, and I present a Sharpe ratio, when I do, purely for other people’s enjoyment. No single metric, whether it be Sharpe, Sortino, whatever, captures enough about any distribution of returns to be worth using in isolation. The key in my opinion is to use multiple metrics. When I’m evaluating systems for my personal use, I use long backtests and start with two hurdles in the neighborhood of 20% each, one hurdle for maximum drawdown and one hurdle for minimum annual compounding rate. Then I try to maximize the ratio of annual compounding to maxmum drawdown, which is kinda-sorta like Seykota’s Bliss ratio, but not exactly.

I’ve written about the Sharpe ratio before.

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