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

**SPDR S&P 500 Value ETF**( SPYV) and the

**SPDR S&P 500 Growth ETF**( SPYG). 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).

**iShares Barclays U.S. Treasury Bond**( GOVT). 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.*