30 September 2013

** “What is Vol? Baby don’t hurt me, don’t hurt me…no more.” **— Haddaway

** Disclaimer: Lyrics slightly modified, but still just as catchy and relevant.*

** Random Trivia: **Haddaway is a Trini!*

But what does the word actually *mean*? (Yes, that was a bad pun.) More importantly, how should it be incorporated into analyzing risk?

There are many different variations, but the core definition of volatility is the standard deviation of the returns of a security. “Standard what?” some of you may be asking. **Standard deviation.** It’s a sort of fancy term for a number that describes how much variation from the average there is within a set of numbers (in this case, returns).

The lower the amount of variation from the mean there is, the lower the standard deviation— and the lower the volatility. The converse is also true: the higher the amount of variation, the higher the standard deviation.

**High volatility is supposed to be bad. Low volatility is supposed to be good.** At least, that’s what they say.

**AN EXAMPLE OF VOLATILITY IN ACTION**

Which of these securities would you rather invest in? I am asking answers here: Security A is up 60% while Security B is down almost 40%. Security A is clearly more desirable—if you believe past performance is indicative of future performance. Surely, Security B must be the more ‘volatile,’ scary option, and therefore must be avoided?

However, both securities have the same standard deviation, or volatility. This is because they have the same returns, but with different signs—Security A has positive returns while Security B has negative returns, but the numbers are exactly the same, as outlined in the table and bar chart below.

Because of how standard deviation is calculated—variation or deviation from the average—if two securities have the same or similar returns, they will have similar or identical averages, with similar variations from that average.

This is one of the problems with volatility: it does not measure or take into account the direction of variation. A security that only goes up but has large swings in the amount it goes up by is going to come across as an extremely volatile security, even though it only goes up. That’s good vol, and it is important to know the difference.

Many investors have strict volatility criteria that end up excluding securities that are outperforming while including securities that may be underperforming. This is due to the erroneous belief that all volatility is bad.

Most investors don’t care about when a security goes up. What most investors *really* care about is when, how often and how much the security goes down.

**MEASURING AND MANAGING**

** “If you can’t measure it, you can’t manage it.” **— Peter Drucker, Management Guru

We’ve seen that traditional volatility measurement has at least one major shortcoming. So what should we also be paying attention to beside volatility? Luckily there are a few metrics that help capture and measure downside risk.

**Downside Deviation** measures the standard deviation only of periods when the security goes down past a certain threshold. To focus on negative returns only, the threshold could be made zero. This number is useful because it provides a snapshot of how dispersed subpar or negative returns are compared to their average, while not penalizing positive returns.

**Maximum Drawdown** essentially assumes that you bought in at the price’s peak and sold out at its lowest price following that peak, over a specified period. It is the difference between the highest price and the subsequent lowest price in a time series. While a bit extreme it is still useful to understand the full implications.

**Average True Range (ATR)** is also a useful metric that captures opening gaps in securities, which volatility ignores. (A gap occurs when a security opens substantially higher or lower than its closing price from the previous day.) True Range is calculated as highest possible range for a security during a period—the highest of the following three: the high minus the low, the high minus the close, or the low minus the close. By selecting between the highest of those three options for a particular period, it encapsulates the full range of price action, while volatility typically only focuses on the difference between closing prices from one period to the next. ATR is then calculated as the average of the True Range for a specified period of time—the most commonly used timeframe is 14 periods.

**Up Down Ratio** is simply the number of days that a security went up divided by the number of days that it went down. If the number is higher than 1 it means there is a tendency for the security to go up more than it goes down. If the number is lower than 1 it means there is a tendency for it to go down more than up. Of course, this information is based on past or historical returns, and the ratio could change substantially going into the future.

**Skew** and **Kurtosis **are two statistical measures that help describe the shape of the distribution, or variations, in returns. A security with a negative skew has more negative returns than positive returns, while a positive skew would have more positive returns than negative. Kurtosis is a bit more complicated but in essence it manages how many extreme values there are across returns. The higher the kurtosis number, the more likely it is that there could be an extreme value. However, Kurtosis does not distinguish between positive extreme events and negative extreme events; therefore it may be useful to calculate a Kurtosis number for the downside only.

We won’t go into the math here but luckily Skewness and Kurtosis are easily calculable in Microsoft Excel and Google Spreadsheets using the *SKEW* and *KURT* functions, respectively.** **

**RISK ADJUSTED PERFORMANCE: WHAT REALLY MATTERS**

There are also measures that are designed to determine the performance of a security relative to the volatility risk. The two most popular are the Sharpe Ratio and the Sortino Ratio.

The **Sharpe Ratio** was originally calculated as the return of a security or portfolio over a period of time, minus the ‘risk free rate’ (usually a US treasury obligation with a maturity corresponding to the period being analyzed), divided by the standard deviation or volatility of the security over that period. However, the Sharpe Ratio was updated in the mid-1990s and its calculation can include either the risk free rate or the return of a benchmark, such as the S&P 500 or the Barclays Aggregate Bond Index.

The Sharpe Ratio can also be calculated using expected or projected returns for the security, risk free rate and / or the volatility.

The **Sortino Ratio** is similar to the Sharpe Ratio, but with two key differences: it uses a Minimum Acceptable Return instead of the risk free rate or benchmark, and it uses Downside Deviation as the denominator.

*The Minimum Acceptable Return can be the same as the Downside Deviation or can be entirely at the discretion of the investor.*

**CONCLUSION**

Understanding the nature of volatility, downside risk metrics, and risk adjusted performance metrics is extremely important because it helps investors avoid throwing the baby out with the bathwater.

Volatility, as traditionally defined and measured, and when used in isolation, can lead to distortions that end up proving costly. By focusing not only on volatility, but how much return is generated per unit of risk, an investor is in a much better position to objectively evaluate the merits and drawbacks of an investment.

Of course, volatility and downside risk are not the only metrics investors should rely on either. You also have to contend with correlation, asset allocation, overall market health and sentiment, and a number of other factors which will be explored in subsequent Risk Aware to Risk Averse instalments.

Firstline has developed tools to help investors of all kinds evaluate volatility and downside risks in their portfolios, or on specific securities. We will also be hosting our first webinar soon, the first of what we hope to be a series of webinars covering the topics in this and other Risk Averse to Risk Aware instalments.

We welcome any questions, suggestions or requests for information at info@nullfirstlinesecurities.com or by phone at 1-868-628-1175.

**Michael J. Cooper**

**Consultant**** **

^{1}*Jumbie – a West Indian term for a ghost or spirit that may have been derived from the Kongo language word zumbi.*