## Wednesday, February 10, 2010

### The gain-loss spread as an intuitive measure of risk

Today’s post relies on a paper written by Javier Estrada for the Fall 2009 issue of the Journal of Applied Corporate Finance, a Morgan Stanley publication. It is entitled “The Gain-Loss Spread: A New and Intuitive Measure of Risk.”

Estrada seeks to replace standard deviation as the benchmark way to quantify risk with a metric that is intuitive and that is based on numbers that investors consider relevant when assessing risk. “This measure is the gain-loss spread (GLS), which takes into account the probability of a loss, the average loss, and the average gain.” Estrada shows that the GLS provides basically the same kind of information as the standard deviation of returns but in a much clearer way. “Furthermore, the evidence shows that: (1) the GLS is more correlated with mean returns than both the standard deviation and beta, thus providing a tighter link between risk and return; and (2) it is better able to discriminate between high-return and low-return portfolios than beta and equal to or better than the standard deviation, and therefore is a useful tool for portfolio selection.”

The GLS is very easy to calculate. You start with annual percentage returns for an index over a specified period of time. Estrada uses the MSCI World Index for the 20-year period 1988 to 2007. During five of those years the index delivered negative returns, so the probability of a loss is 25%. Next calculate the average annual loss, in this case -13.9%. The expected annual loss is the product of these two numbers: 25% * -13.9% = -3.5%. Similar calculations will yield the expected annual gain of the asset, in this case 75% * 18.9% = 14.2%. The gain-loss spread is the difference between the expected gain and the expected loss: 14.2% - (-3.5%) = 17.6%. As risk measurements go, that’s as easy as it gets.

Can such a simple risk measurement be useful? Estrada here relies on statistical tests that are too technical for this post; the interested reader can go to the original paper. The answer (refer back to the second paragraph of this post) is clearly yes. GLS may not satisfy investors who have learned to worry about fat tails, but I consider it wonderful, even close to miraculous, that a model that requires such rudimentary arithmetical skills can compete with those that have been the provenance of statisticians.