Volatility is a key consideration when evaluating an asset class or an investment manager, yet many endowments and pension funds, and their consultants, are using an inappropriate measure of standard deviation, and consequently they are underestimating their funds' volatility.
A common measure of volatility is the standard deviation of monthly returns annualized, that is, multiplied by the square root of 12, or 3.464. This is a measure critically important to a trader, but by itself it is irrelevant, and even misleading, to a long-term investor. The long-term investor is interested in annual volatility, and that's a different thing, best measured by the standard deviation of rolling 12-month returns.
The difference wouldn't matter if the two measures were roughly the same. But often they aren't, sometimes by a wide margin.
Consider the following 10-year (from 2003 through 2012) standard deviation measures of the MSCI All Country World index:
n16.7% for monthly returns annualized; and
n21% for rolling 12-month returns.
Why such a difference? If the standard deviation of rolling 12-month returns were less than the standard deviation of monthly returns annualized, it would mean monthly returns had a tendency to revert toward the mean. But in the case of the MSCI ACWI, the difference means that monthly returns have tended to trend, or to compound one another.
The 10-year standard deviation of rolling 12-month returns is consistent with the standard deviation of a manager's or index's calendar-year returns, and also consistent with the expected standard deviation one would enter as an assumption in asset optimization models.
The difference between the two methods can be quite wide not only for equity funds but also for hedge funds, many of whose standard deviations are also underestimated. And since the overall portfolios of most endowment and pension funds tend to have a relatively high correlation with the stock market, investors might be underestimating the historic volatility of their portfolios.