Risk Statistics & Risk-Adjusted Statistics

Many investors approach manager selection and analysis with pre-conceived statistical prejudices based on a misunderstanding of statistics. In many cases, it is because they’ve been led to believe that a certain statistic measures something that it does not. Others encounter difficulties trying to use a pre-defined toolkit of investment statistics because they’ve been led to believe that those are the right statistics to choose. It is important to remember, however, that investors have different notions of risk. To some, risk is the uncertainty of achieving an expected return. To others, it is not achieving a minimal acceptable return (MAR). Still others define risk as flat-out losing money. To illustrate this point, let’s look at how many investors use standard deviation to help them identify “strong” investments.

Standard Deviation

Investors sometimes begin a quantitative screening by stating that they want a fund with a “low risk.” Because of the historical ties between risk and standard deviation in the world of traditional investments, they equate high standard deviation with high risk, and then use standard deviation as a comparative statistic. However, in truth, standard deviation is merely a statistic that measures predictability. A high standard deviation means that the fund is volatile, not that the fund is risky or will lose money, while a low standard deviation means a fund is generally consistent in producing similar returns. A fund can have extremely low standard deviation and lose money consistently, or have high standard deviation and never experience a losing period. For example, without looking at the returns the fund in Figure 9 exhibits a return pattern with overall consistency, which results in a low annualized standard deviation of 3.8%.

Figure 9: Standard Deviation at a Risk Statistic - Take I

Is the fund in Figure 9 a good investment? If we assess the same chart with returns plotted on the x-axis, the exact opposite is true. As Figure 10 highlights, this fund, while maintaining a low standard deviation, has a compound annual return of less than 1% (see circled area), and the fund has lost money almost as often as it has generated profits.

Figure 10: Standard Deviation as a Risk Statistic - Take II

Assessing funds based on standard deviation also tends to unjustly penalize funds with high upside volatility. The fund in Figure 11 has a standard deviation of 22.5%, which is generally considered high. However, the monthly returns are skewed to the upside as the result of several months of 15+% returns (see circled area).

Figure 11: Standard Deviation as a Risk Statistic - Take III

One of the main differences between traditional return analysis and absolute return analysis is accepting the fact that volatility is good, provided it is on the upside. Indeed, most investors should be less concerned with upside volatility, and consider downside deviation as a better measure of a fund’s ability to achieve its return goal. For this reason, investors should acquaint themselves with downside deviation. Downside deviation introduces the concept of minimum acceptable return (MAR) as a risk factor. If a retirement plan has annual liabilities of 8%, the plan’s real risk is not earning 8% – not whether it has a high or low standard deviation.

Downside deviation considers only the returns that fall below the MAR, ignoring upside volatility. As Figure 12 illustrates, if the MAR is set at 8%, downside deviation measures the variation of returns below this value.

Figure 12: Minimum Acceptable Return (MAR)

So, with standard deviation out of the equation, what statistics can we use to compare funds? While fund returns may seem useful, they do not consider the investment’s risk. Therefore, investors should always use risk-adjusted statistics such as the Sharpe Ratio, Sortino, Sterling or Calmar ratios.

Investors who are required to select and monitor investment managers should develop a basic understanding of investment statistics. Quantitative tools can provide you with good insight that you can use in your qualitative interviews with managers and when monitoring your investments.