Risk Management: Foundations for a Changing Financial World

CHAPTER 17

THE SECOND MOMENT^q

Don Ezra

This brief article discusses the statistical “second moment” that measures the variability in a distribution. Over the years, society’s focus has expanded from looking only at first moments to considering second moments. A consideration of second moments of the distributions of an array of economic variables can aid in understanding societal concerns about outcomes and risk tolerance following the recent global financial crisis. Such an understanding provides a basis for interpreting the use of various mechanisms, including prudent asset allocation, options, regulation of the freedom to make contracts, state participation in markets, and taxation.

This article is not about a moment in time. It is about the statistical second moment, the one that measures the variability in a distribution. And it is a conceptual, not mathematical, treatment.

For many years, I have noticed that society’s focus has expanded from looking only at first moments to considering second moments. In 1952, Harry Markowitz drew our attention to the importance of the second moment of investment return distributions and, in particular, to the tension between increasing the first moment and reducing the second moment. His discovery was a revelation and earned him a Nobel Prize. I believe that second moments of the distributions of other economic variables are equally worthy of attention. So, we look, for example, not only at the average wage but also at the distribution ...