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By Salil Mehta, statistician and blogger at (Statistical Ideas)



) -- There is more risk in less-risky asset classes than one may think. Let's looks at the major equity and fixed-income asset classes, both in the U.S. as well as internationally. We'll look at two decades of data, from 1990 to 2010.

A higher-order measure of risk, named kurtosis (also called the volatility of volatility), is designed to look at the relative thickness or thinness of the tail-ends of the distribution. A "higher-order" risk term looks at the largest swings in financial market performance, which is more of an emphasis on these large swings than what we would see if we only looked at the popular standard deviation measure.

The aforementioned "distribution" is simply the collection of all of the performance results of an asset class over time. If we hear in the news that a stock had yesterday made a 52-week closing high, for example, then the distribution is the past 52 weeks of closing prices (of which yesterday's was the highest).

Kurtosis can be used to look at the tail risk of an asset class, vs. what we would see if it were normally distributed. A normal distribution is a common probability distribution of things as they naturally occur. We'll look at how to calculate Kurtosis later.

Many market participants simply use this distribution to look at technical analysis levels, or financial market returns. Evidence of this is when one speaks of financial market returns in terms of standard deviations, or risk measures such as value-at-risk, when talking about probabilities of an event occurring.

However, this is the wrong way to think about financial market returns, as it is not a conservative enough of an assumption, and it underestimates the number of once-in-a-lifetime risk events that we have seen in the past decade.

Now only some market participants know that financial market data do not follow a normal distribution, and even for those who do, it is a common mistake to then not throw out a common assumption about the underlying kurtosis of the return distributions.

Then when we see kurtosis levels of, say four or five, for the risky assets (i.e., U.S. large value, non-U.S. developed stocks, U.S. large growth stocks, emerging market stocks), we know that there has been very heavy distribution in the tails.

These risky assets include the

SPDR S&P 500 Value ETF


and the

SPDR S&P 500 Growth ETF

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. And while kurtosis doesn't distinguish between the upper tail and the lower tail, similar to the standard deviation measure, it should be noted that skew was negative for all of the asset classes shown here but for the non-U.S. bonds (for which skewness was virtually nonexistent).

Since we see risky assets having this excess kurtosis in its return distribution, how does this relate to what we see in less risky asset classes (i.e., U.S. bonds, and non-U.S. bonds)? In the U.S., this would be similar to the

iShares Barclays U.S. Treasury Bond


. And we see that the typical risk measure of standard deviation is about 1/3 that for risky assets (~5% vs. ~17%).

We might say this makes sense for bonds to have this lower risk, by the standard deviation measure. But what happens to those bonds on the higher-order, kurtosis statistic?

So to be sure, kurtosis is less for bonds than for stocks, regardless of geography. Though not by a lot. Bonds still have a higher degree of kurtosis than would be proportionally assumed by either the normal distribution, let alone the reduction in standard deviation risk of a non-normal distribution.

In other words, there is greater tail risk from these "less risky" instruments than most investors appreciate until after their downturn. This is likely further evidence that statistical aberrations in the markets are creating simultaneous, correlated inefficiencies from multiple asset classes.

In order to best diversify against an inevitable slowdown in the economy and markets, do not simply allocate funds from equities to fixed income. It is better to appreciate and have a small cash allocation, which can help cushion any risk and provide liquidity, during financial stress, which may be used to purchase equities, fixed income, or both.

As mentioned earlier, Kurtosis is calculated by taking the typical "return dispersion" to the fourth power, or ^4. For examples, if we have a sample of four returns (in percent): -2, 0, 1, 1. Then to the naked eye these returns average 0, and seem close enough together. Yet by taking this sample to the 4th power we see that they are now -2^4, 0^4, 1^4, 1^4 -- which equals 16, 0, 1, 1! We also see that by taking the 4th power, both positive and negative deviations become positive, and higher values take on significantly greater weight.

Kurtosis is important, as it applies to stocks and bonds, as it helps investors see beyond the financial calculations generally reported.

Written by Salil Mehta, creator of the Statistical Ideas blog.

At the time of publication, the author held no positions in any of the stocks mentioned, although positions may change at any time.

This article is commentary by an independent contributor, separate from TheStreet's regular news coverage.

This commentary comes from an independent investor or market observer as part of TheStreet guest contributor program. The views expressed are those of the author and do not necessarily represent the views of TheStreet or its management.