# The Good and Bad of Volatility

Investment volatility or as it’s known on the street as “vol,” is often measured by the standard deviation. Investors frequently use the standard deviation as a proxy for risk. But is the standard deviation a proxy for risk or a proxy for dispersion around the mean?

Mathematically, the standard deviation is the dispersion of data around the mean as the data points move farther from the mean (towards the distribution tails), the standard deviation increases. In a normal (bell-shaped) curve, one standard deviation should capture about 68% of the possible movement around the mean. A two-standard deviation move captures approximately 95%, and three standard deviations should capture an estimated 99.7% of the distribution. Therefore, volatility is both above and below the mean.

Investors often talk about volatility when portfolio’s are losing value. For example, you probably won’t hear much discussion about the stock market being volatile when it rallies. That discussion usually occurs when stocks decline. However, when an investment has profitable returns, it is still technically defined as volatility, sometimes known as upside volatility or positive volatility. Investors are usually accepting of the upside vol, as it implies the investment experiences positive returns. It’s the downside vol investors are often losing value as that is the tail risk they are usually trying to reduce. To paraphrase from my paper, “Skewing Your Diversification” (Shore, 2005), volatility is comparable to cholesterol. There is good and bad volatility.

The traditional view perceives higher standard deviation equating to higher risk. But is that always the case? As I often tell the students in my managed futures class, you should understand if the volatility derives more from the positive returns or the negative returns. If derived more from the positive side of the distribution, that is the dispersion of the positive gains that is inflating the standard deviation. If the volatility is derived more from the negative volatility than it is the dispersion from the negative returns and is the tail risk, that usually concerns investors.

Modern portfolio theory assumes a normal return (bell-shaped) distribution. However, distributions may be skewed (asymmetrical curve) to the right causing positive volatility or skewed to the left, causing negative volatility. The negatively skewed distribution may cause increased tail risk and losses, as noted in Figure 1.

Understanding how an investment’s allocation impacts the portfolio’s skewness helps understand the behavior of the allocation relative to the portfolio. Does it expand the skewness to the left or the right? This concept is also known as co-skewness (Harvey & Siddique, 2000). In other words, an investment with a high standard deviation but more volatility coming from the upside could potentially reduce a portfolio’s volatility when the investment is allocated to a portfolio. It sounds counter-intuitive for a high standard deviation investment to reduce a portfolio’s standard deviation, but it’s the positive volatility that is offering the benefits to the portfolio to reduce the tail risk and downside vol.

An investment with a high standard deviation derived from positive skewness and coupled with a low or non-correlation to the portfolio may increase the added value of the allocation. It’s also possible for an investment with a low standard deviation, but more volatility attributed to the downside increasing the portfolio’s tail risk.

Therefore, only accounting for a standard deviation to be high or low is not enough. Drilling down to understand where the volatility is good or bad is an essential factor to consider. If the tail risk can be more efficiently controlled, than the portfolio’s drawdowns may also be reduced.

References:

Harvey, C. R., & Siddique, A. (2000). Conditional Skewness in Asset Pricing Tests. The Journal of Finance,55(3), 1263-1295.

Shore, M. (2005) “Skewing Your Diversification” Gregoriou, G., Hübner, G., Papageorgiou, N., & Rouah, F. Hedge funds: Insights in performance measurement, risk analysis, and portfolio allocation(Wiley finance). Hoboken, NJ: John Wiley & Sons.

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