Volatility (standard deviation) is the standard and widely accepted definition of investment risk. Last week, we wrote a blog post on the Top 6 Reasons to Trade Volatility. While we think volatility is a great asset class to trade, we believe it is a terrible measure of risk (again, in this case, we mean standard deviation). In turn, any performance measurement based on volatility (like the popular sharpe ratio) is misleading. We'll explain why, give you our definition of risk, and show you our favorite ways to measure investment performance.

**Why Volatility is a Poor Measure of Risk**

**1. There are two sides to volatility - upside volatility and downside volatility**

Upside volatility is the volatility of positive returns; downside volatility is the volatility of negative returns. Investors should welcome *high* upside volatility (possibility for large gains) and seek low downside volatility (controlled losses). However, high upside volatility (and high downside volatility) penalize investment managers on a "risk-adjusted" basis, creating a disincentive to achieve high returns.

**2. Again, there are two sides to volatility**

More specifically, volatility is a *symmetrical* statistic. Thus, volatility is an unbiased statistic only for symmetrical return distributions, and in turn, does not accurately describe asymmetrical return distributions. This is problematic. The best investment opportunities have asymmetrical return distributions.

**3. Volatility (standard deviation) can be misleading**

**.**

A simple example will make this clear. Consider the returns of the three hypothetical investment strategies below. Strategy 1 loses 10% per year. The difference between Strategy 2 and Strategy 3 is that Strategy 3 had an extremely high *positive* return in Year 3. This leads to significantly higher volatility than Strategy 2. In fact, based on volatility, Strategy 3 is considered the riskiest strategy, even though it had the highest compound annual growth rate (OTCPK:CAGR)! Worse yet, Strategy 1 is considered *riskless* (volatility is 0), even though it consistently loses 10% per year! Clearly, volatility (standard deviation) can be misleading.

**4. Volatility (standard deviation) can be "gamed"**

Investment managers can "game" volatility to make it appear lower than it really is. This can be done in numerous ways, but here are a few: lengthening the measurement period (ex. annualized monthly returns are usually lower than annualized daily returns), writing out of the money options on a portfolio (this can increase returns over many periods before taking a loss, thus hiding underlying risks within a portfolio), infrequent marking to market certain assets, etc.

__Better Ways to Measure Performance__First, let's define what risk *really* is. To us, risk is simply not achieving your goal (the whole purpose of investing/trading in the first place!)

Here are our favorite ways to measure performance:

**1. CAGR**

**(this is an**

*absolute*measure of performance)The CAGR (compound annual growth rate), also referred to as geometric return, describes the average *growth* *rate* of a portfolio. It should not be confused with average (arithmetic) return. As an example, if a portfolio earns -50% in Year 1, then 100% in year 2, the average (arithmetic) return is 25%, while the CAGR or growth rate is 0% (assuming the portfolio started with $100, it has $50 after year 1, then $100 after year 2, for a growth rate of 0%). What makes the CAGR so great is that it summarizes all risk, return, and distribution (skew and kurtosis) characteristics into one number. That one number cannot be manipulated (unlike many other performance measurement metrics, including the Sharpe Ratio), and is an apples to apples comparison across all strategies, regardless of return distribution characteristics (you don't have to assume symmetry). In addition, evaluating performance using CAGR becomes a simple success/failure metric. If the CAGR is high enough to reach your investment goal: success; Otherwise: failure.

**2. Gain/Loss Ratio (this is a**

*relative*measure of performance)While the CAGR is the best way to determine if you're reaching your investment/trading goal, the Gain/Loss Ratio tells you how well you are controlling your risk/reward ratios and return profile relative to other strategies.

The Gain/Loss Ratio is:

**-[(number of winning months / number of losing months) * (average % gain for winning months / average % loss for losing months)].**

That appears uglier than it really is. The Gain/Loss Ratio simply compares both the frequency and magnitude of gains relative to losses. The higher and more frequent gains are relative to losses, the higher the Gain/Loss Ratio, and the better the performance (this eliminates the penalty for high upside volatility).

**Conclusion**Volatility is a great asset class to trade, but not a great way to measure risk. To us, risk is simply not achieving your investment goal. The sharpe ratio, and other measures of performance based on volatility, are misleading. The CAGR and Gain/Loss Ratio are much better ways to measure performance.

**See how VIX Strategies' CAGR and Gain/Loss ratio stack up against their benchmark (an XIV buy & hold approach).**

**Disclosure:** I am/we are long XIV.