The current convention for estimating annual volatility is to estimate daily standard deviation and then multiply the result by the square root of the number of business days in a year. This method requires that the returns be uncorrelated with one another from day to day. If the returns are correlated, the risk estimates are biased.

The authors show that equity returns tend to exhibit positive autocorrelation (correlation between the time series of equity returns and a lagged version of the same time series over subsequent time intervals), whereas commodity trading adviser (CTA) returns tend to exhibit negative autocorrelation. As a result, the standard square-root-of-time rule produces biased results. The authors demonstrate that the expected maximum drawdown with the positive autocorrelation shown by equities is nearly double that of an asset with the negative autocorrelation of CTA returns.

The use of autocorrelation estimates to detect biases in standard volatility measures can be a valuable tool. Accounting for the autocorrelated returns will provide managers with a better idea of the riskiness of various assets in their portfolios. The authors demonstrate that it is possible to improve risk-adjusted returns with autocorrelation estimates. For return series with positive autocorrelation, a rule that reduces position sizes when losing money and increases position sizes when making money will improve risk-adjusted returns.

The authors also reveal that CTAs represent an important asset class with lower risk than originally estimated. A natural extension of this research would be to amend the manager evaluation reports to reflect the new drawdown model and to include some information about autocorrelation in each manager’s return.

When the drawdown model is used with a broad range of large, prominent CTAs, the authors find that the realized maximum drawdowns for trend-following CTAs are significantly smaller than what the model predicts. Drawdown is defined as the percentage change in a manager’s net asset value from a high-water mark to the next low-water mark. The authors use monthly returns from 1990 through July 2012 for the 67 CTAs who appear in the Newedge CTA index. These are among the largest and most successful CTAs in the industry.

The authors transform the return series for both asset classes (global equity and CTAs) so that they exhibit the same mean return (5%) and the same annualized volatility (15%). Using Monte Carlo simulations, they find that the holding period and volatility are positively related, whereas the volatility is inversely related to the maximum drawdown. They also find that skewness and kurtosis have no effect on the maximum drawdowns.

By plotting the expected and observed maximum drawdowns for the two components (trend-following and non-trend-following managers) of the Newedge CTA index, the authors find that realized maximum drawdowns of trend-following CTAs are smaller than what the model predicts. The trend-following CTA managers’ returns have a significantly negative autocorrelation. After autocorrelation is accounted for in the model, the trend followers’ maximum drawdown values are in line with the model’s predictions.

This article is very interesting. The authors suggest that autocorrelation is an important variable in addition to risk and return. Hence, a simple method of calculating daily standard deviation and then multiplying the result by the square root of the number of business days in a year is not the appropriate method when autocorrelations are presented in the data series. The evidence provided is very convincing.