Investors measure risk because they care not only about return on an investment but also about the level of risk taken on to achieve that return. An investment that returns 10% by taking on 20% risk is not as good as an investment that returns 10% by taking on 5% risk, because the former has a lower return to risk ratio. But, how do investors quantify risk? Many investors measure risk with standard deviation. In simple terms, standard deviation measures the level of dispersion of a set of random numbers (i.e. returns) around their average value. As such, a high standard deviation indicates a high level of dispersion, which implies a high level of volatility (risk). This blog questions whether standard deviation is the proper measure of risk for investments, and discusses an alternative measure of risk called downside deviation.
Let’s begin by looking at a diagram of realized returns for a hypothetical security over one month. Black points indicate positive daily returns and orange points indicate negative daily returns.
For illustrative purposes, this example assumes that an investor’s target or required rate of return is 0% (i.e. an investor would consider any return above zero to be acceptable), and that daily returns are scattered above and below this level1. Typically, investors and advisor's would calculate the volatility of the return data shown by using standard deviation. Standard deviation measures the dispersion of returns, and therefore their total volatility, inclusive of both upside (black) and downside (orange) observations. But what if standard deviation is not the best way to quantify risk? What if investors care more about risk on the downside than risk on the upside? Do investors care if a stock price suddenly spikes to the upside? Probably not.
An alternative measure of risk, downside deviation, measures volatility on the downside and therefore captures risk in a way that better aligns with investor preferences. In the context of the exhibit above, downside deviation measures the volatility of only the “bad” (i.e. orange/negative) returns, while standard deviation measures the volatility of both the “good” (i.e. black/positive) and “bad” returns. Accordingly, minimizing downside deviation concentrates on reducing losses, while minimizing standard deviation—a strategy pursued by typical investors—has the unintended side effect of reducing both gains and losses. Therefore, investors that use downside deviation as a measure of risk may be able to construct more optimal portfolios. The father of Modern Portfolio Theory, Harry Markowitz, agrees. He preferred to use semi-variance (which relates to downside deviation) as a measure of risk, but instead chose to use variance (which relates to standard deviation) for ease of calculation. Markowitz stated that “analyses based on semi-variance tend to produce better portfolios than those based on variance.” 2
Another benefit of downside deviation is that it takes into account a more accurate reflection of the historical distribution of equity returns. History shows that equity returns are not normally distributed (which is assumed when one uses standard deviation as a measure of risk). Instead, returns have been negatively skewed, which means that aggregate stock market returns have demonstrated a propensity to generate large negative returns with a higher probability than a normal distribution would suggest. Therefore, a risk measure such as downside deviation that focuses on downside volatility, rather than overall volatility, may better gauge the risk of a security.
A similar discussion is to compare the commonly used Sharpe Ratio to the less-well-known Sortino Ratio. The Sortino Ratio uses downside deviation to penalize returns falling below a user-specified target or required return, while the Sharpe Ratio penalizes upside and downside returns equally (due to using standard deviation). Given investor preferences and given the fact that equity markets have been negatively skewed historically, it is likely that the more accurate ratio and risk measure to use would be the Sortino Ratio and downside deviation respectively.
Ultimately, investors should be aware that there are multiple methods of measuring risk. As compared to standard deviation and the Sharpe Ratio, downside deviation and the Sortino Ratio offer investors an alternative framework for risk management and portfolio optimization. Investor preferences suggest a desire to reduce losses without forfeiting the potential for gains, and minimizing downside deviation aims to do just that.
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