Standard deviation is widely relied on to assess risk by measuring the volatility and dispersion of returns. Despite this popularity, the statistic is often misused or its shortcomings ignored, resulting in invalid conclusions. Some applications of standard deviation are ambiguous even within the Global Investment Performance Standards (GIPS) framework.
The author reviews the fundamental characteristics of standard deviation, including applications that are prone to misinterpretation or misunderstanding. Three areas of ambiguity he addresses are using asset-weighted standard deviations, assigning standard deviations to composite returns, and annualizing standard deviations.
How Is This Research Useful to Practitioners?
Standard deviation should be measured against a normally distributed population, and when there are 30 or more returns in the distribution, it is expected that 68% of the distribution falls within one standard deviation of the mean and 95% of the distribution falls within two standard deviations of the mean. In practice, ignoring the fact that returns are typically not normally distributed and using a distribution of fewer than 30 samples may cause invalid conclusions to be drawn from the standard deviation statistic.
Asset-weighting standard deviations was suggested by performance presentation standards that predate the Global Investment Performance Standards (GIPS®) based on the rationale that the measure of risk should be asset-weighted due to the composite return being asset-weighted. Whereas an equal-weighted standard deviation gives prospective investors information about the range of actual portfolio returns and the degree of dispersion around those returns, the asset-weighted standard deviation is difficult to interpret because of the theoretical nature of an asset-weighted mean.
The GIPS standards require a measure of dispersion when a composite has six or more accounts present for the full period. Calculating the standard deviation in this instance provides information about the average return of accounts present for the full period, which should not be confused with the composite return even though the difference is suggested to be immaterial. Because the GIPS standards prohibit annualizing partial period returns, there is no real alternative.
Annualizing standard deviation based on 36 months of data per GIPS-compliant reporting provides little interpretive value because it reduces the sample size to three. Standard deviation is a stand-alone tool for measuring risk and is the basis for such other popular risk statistics as the Sharpe ratio and the information ratio. The popularity and importance of this tool in assessing risk mean a review of its shortcomings should appeal to a broad audience of practitioners, particularly those working with GIPS-compliant reporting.
How Did the Author Conduct This Research?
Seemingly hypothetical yet plausible data are presented that adhere to GIPS requirements. A composite with eight accounts present for the full year provides an equal-weighted standard deviation calculation of 1.64% versus an asset-weighted one of 1.75%. Although this difference may or may not be significant, the issue remains that asset-weighted standard deviation is more complicated and not comparable with the distribution. The GIPS standards require firms to report 36-month annualized ex post standard deviations on an annual basis; as such, 36 months of composite returns are presented to show cumulative, annualized, and average returns, as well as the monthly and annualized standard deviations for the full period. From these data, 19 of the 36 months fall within the average monthly return plus or minus one standard deviation, whereas 24 months would be expected in this range if the population were normally distributed. Changing the sequential ordering of monthly returns would not affect the monthly average but could result in many different combinations of annualized returns—in this case, ranging from 8.46% to 108.13%. When these returns are annualized, the sample size decreases from 36 to 3; all 3 happen to fall within plus or minus one standard deviation.
Asset-weighting standard deviations may emphasize a return outlier when that outlier is a relatively large account, but some might prefer this method because it minimizes return outliers of very small accounts. The author feels strongly that annualized standard deviations should not be reported, but this process is unlikely to change because prospective investors are highly concerned with annual returns and much less so with monthly performance. Standard deviation remains a primary tool for assessing risk and has a lasting place in the GIPS framework. Therefore, practitioners should be aware of its proper applications.