Why Standard Deviation Won’t Serve to Classify the Risk of a Portfolio

by David Ranson

This report reviews some important reasons why investment managers and their regulators should not rely on standard deviation when they assess the riskiness of investment products.

There are many ways in which standard deviation may produce an irrelevant or misleading impression of the risk assumed when an asset is purchased. Volatility is one element of risk, but often only a subsidiary.

Investors care a great deal whether most of the volatility straying tends to occur on the upside or the downside, and whether extreme divergence from the average is frequent or rare.

Tail risk is much more of a deterrent for investors if it occurs on the downside rather than being evenly distributed between the downside and the upside.

The stand-alone volatility of the investment is not a measure of that. The increase (or reduction) in the investor’s vulnerability is measured by what the investment adds to (or subtracts from) the investor’s overall portfolio volatility.

That is also why the risk of an investment is a function of its covariance (or correlation) with other assets, and not merely its stand-alone volatility.

If an investor diversifies their portfolio to include an asset that is roughly uncorrelated with stocks (such as investment-grade bonds), or has an inverse correlation with stocks (such as gold), they will tend to lower overall risk, regardless of the volatility of the investment itself.

Gold, with its inverse correlation to stocks, is low risk. In this sense, the risk of a gold investment may well be negative.

The riskiness of an investment product cannot be represented by the standard deviation (volatility) of its historical returns, or by any other single statistic. On a real risk scale, cash could be assessed as risky and gold as safe.

A common example is where upside volatility is substantially different from downside volatility. Any investor will rightly regard an investment where the downside is substantially greater than the upside as far riskier than one where the reverse is the case.

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