Classic risk measures (such as volatility) do not consider the path followed by returns and fail to communicate the risk of potential large drawdowns. Using path-dependent measures adds valuable information to any investment decision. We propose a new measure of portfolio risk, the serenity ratio, which estimates both the average and extreme risks carried by an investment. This indicator can be used in a modified version of modern portfolio theory and might assist investors in making prudent investment decisions.
Annualized standard deviation or volatility (the Sharpe ratio being its return-adjusted version) is one of the most widely used measures of the riskiness of an investment. As a reminder, Sharpe ratio = (R-R_f)/Vol. The volatility and Sharpe ratio measures present drawbacks of which investors might not be aware. Both upside and downside changes in prices are used to calculate the volatility of an investment.
Thus, many investors use a modified version of standard deviation that only penalizes the downside risk: downside volatility (the Sortino ratio being its return-adjusted version). Although an improvement, this downside risk measure can be misleading when it comes to fat tail distributions as it does not focus on tail losses and therefore may significantly understate the range of potential losses.
Neither of the above measures consider autocorrelation of returns (i.e., today's return is dependent on yesterday's return).
Consider the three following strategies, all using the same return time series:
- The actual return series of the MSCI World index (the “long” strategy as shown by the black line in Figure 1);
- The return series of the MSCI World index sorted from worst months first to best months last (the “sorted” strategy represented by the orange line);
- The return series of the MSCI World index sorted to minimize the drawdowns — biggest drawdown, followed by biggest runup, followed by second biggest drawdown, followed by second biggest runup, etc. (the “flattened” strategy, blue line).