Sortino – More than a small Italian Townrtino


New York – One issue with incorporating risk into an assessment of research recommendations is that process is thought to be a simple statistical one. Harry Markowitz’s model became the standard approach to assessing the investment decision to be a mean-variance decision.

In a risk management sense we normally associate specific probabilities (usually from the normal distribution) to the expected excess return results. This is generally expressed as a level of confidence, expressed in standard deviations, within which we expect returns to vary within.

Standard deviations of excess returns are a solid measure of potential for problems and to compare one asset class to another in terms of riskiness, but once a recommendation has been made, one only cares about risk is one direction. The fact
remains that the decision to rate a stock as a buy or a sell changes the game somewhat.

The game changes from a mean-variance decision (a la Markowitz) to a mean- semivariance one. The Sortino ratio is a measure of risk-adjusted return that utilizes semivariance and is therefore at least theoretically appropriate to use after a recommendation has been made. This means that may be  appropriate for all performance measurement systems.

The Sortino Ratio for a buy recommendation is:

S = (R – T)/DR

R is the asset’s return
T is a target return – e.g. the S&P 500, or a particular bogey
DR is the downside risk or the square root of the semi-variance

The semivariance is actually an intertemporal measure of risk.  Rather than summing the squared deviations from the mean, we use the squared deviations of the differences from a lagged value of the returns. This provides a measure of only the downside risk.

Although the measurement of research recommendation performance is still a thorny issue, the Sortino ratio may offer a better estimate of risk than the classical Sharpe ratio. 


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