sharath-sury

Risk Measurement - A Multi-Dimensional Concept!

By Sharath Sury

For the past 50 years, many financial economists and professional investment managers relied upon the concept of "mean variance optimization (MVO)" to design investment portfolios. The principle was simple: maximize mean return subject to a certain variance (risk); or minimize variance subject to a certain mean return.

While the MVO technique is well-intentioned, it suffers from an incomplete definition of risk. It has long been known that asset classes can be described using various degrees of specificity, sometimes known as "moments of the distribution." For example, the first moment of the return distribution of an asset class is its mean return. The second moment is known as variance. For a normally distributed asset class with well behaved properties, a variety of analytical techniques can be applied and conclusions drawn based upon these two moments alone (mean and variance).

Unfortunately, many asset classes do not behave according to what the normal distribution would suggest. Further, asset classes that exhibit "normality" for one time period may not exhibit it during other time periods. The incorporation of alternative asset classes (e.g., hedge funds, real estate, private equity) increases the likelihood that an overall portfolio will exhibit degrees of non-normality.

As a result, it is often important to consider at least two other "higher order" moments of the return distribution. The third moment is known as "skew" or asymmetry. It reflects the degree to which an asset class may have a higher proportion of negative (or positive) returns. Some hedge fund strategies are built and marketed explicitly on this notion: while they may exhibit low levels of variance (or standard deviation), they concomitantly exhibit high levels of negative skew (or returns which are asymmetrically biased to the downside).

The fourth moment of a return distribution is referred to as "kurtosis," or more colloquially as "fat tails." Kurtosis reflects the degree to which the return distribution may be subject to extreme events. Thus, the "fat tails" refer to the graphic representation of the returns as exhibiting a higher probability of extreme results than the normal distribution would suggest. As an example, higher levels of geopolitical uncertainty can increase the kurtosis of particular asset classes.

Thus, investment managers and asset allocators who rely solely upon the popularly employed MVO techniques may be missing key risk factors that can adversely affect a portfolio and may therefore provide solutions that are incomplete with respect to skew and kurtosis.

New methods for dealing with the shortcomings of MVO include the use of other constraints in the optimization. For example, the so-called "mean-conditional value at risk (MCVaR)" is a methodology which seeks to incorporate skew and kurtosis. CVaR essentially relates to the "area of the return profile" below which an investor is "at risk."

By maximizing mean return subject to an acceptable level of CVaR, an investment manager may be better able to capture the important risks of the portfolio. Recent (and repeated) empirical research has shown that-in hedge fund portfolios alone-the MVO methodology has underestimated the amount of risk (as defined by CVaR) by as much as 50%!

In the past few years, CVaR has been joined by other risk measures, such as "Omega," to help broaden the traditional definition of risk beyond the confines of simple variance or standard deviation. In the end, more complete definitions of risk should lead to more robust portfolio optimization solutions.