## Summary

- Not being able to precisely define risk is a problem for both advisors and investors.
- A common definition for risk is standard deviation, or a measure of volatility.
- Unfortunately, two investments with similar standard deviations can experience entirely different distribution of returns.

This is the first of a two part series that aims to define risk. Since we live in a world without crystal balls that allow us to clearly see the future, prudent investing is all about the management of risk and *expected* returns. A problem that both investors and investment advisors face is defining what exactly risk is. As you will see, risk can be many different things, and since risk can be many different things to different people, investors/advisors are faced with deciding which risks are the most important to manage.

## Standard Deviation

The most commonly used academic definition of risk is standard deviation - a measure of volatility. Unfortunately, two investments with similar standard deviations can experience entirely different distribution of returns. While some investments exhibit normal distribution (i.e., the familiar bell curve), others may exhibit characteristics known as kurtosis and skewness. We will first define these terms and then explain why it is important to understand their implications.

## Skewness

Skewness measures asymmetry of a distribution. In other words, the historical pattern of returns doesn't resemble a normal distribution. Negative skewness occurs when the values to the left of (less than) the mean are fewer but *farther* from the mean than are values to the right of the mean. For example: the return series of -30 percent, 5 percent, 10 percent, and 15 percent has a mean of 0 percent. There is only one return less than zero percent, and three higher; but the one that is negative is much further from zero than the positive ones. (Positive skewness occurs when the values to the right of [more than] the mean are fewer but *farther* from the mean than are values to the left of the mean.) Behavioral finance studies have found that, in general, people like assets with positive skewness. This is evidenced by their willingness to accept low, or even negative, expected returns when an asset exhibits positive skewness. The classic example of positive skewness is a lottery ticket. Some examples of assets that exhibit both positive skewness and poor returns are IPOs, "penny stocks," stocks in bankruptcy, and small-cap growth stocks.

On the other hand, in general, investors don't like assets with negative skewness. High-risk asset classes (such as junk bonds, emerging markets) typically exhibit negative skewness. In addition, some investment vehicles, such as hedge funds, also exhibit negative skewness.

## Kurtosis

Kurtosis measures the degree to which exceptional values, much larger or smaller than the average, occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal (bell shaped) distribution. High kurtosis results in exceptional values that are called "fat tails." Fat tails indicate a higher percentage of very low and very high returns than would be expected with a normal distribution. (Low kurtosis results in "thin tails" and wide middle - more values are close to the average than there would be in a normal distribution, and tails are thinner than there would be in a normal distribution.)

It's important for investors/advisors to understand that when skewness and kurtosis are present (the distribution of returns isn't normal), investors looking *only* at the standard deviation of returns may receive a misleading picture as to the riskiness of the asset class - understating the risks. This creates problems for investors/advisors using efficient frontier models to help them determine the correct, or most efficient, asset allocation. The reason is that efficient frontier models are based on mean variance analysis, which assumes that investors care *only* about expected returns and standard deviation. In other words, they don't care about whether an asset exhibits either skewness or kurtosis. If that assumption is correct (investors are not bothered by skewness and fat tails), then indeed, the use of mean variance analysis may be appropriate (though there are other serious problems with the use of efficient frontier models). However, this assumption is too simplistic, as many, if not most, investors do, in fact, care about skewness (especially negative skewness) and kurtosis.

If an asset exhibits non-normal distribution (as do many risky assets), mean variance analysis is only a good first approximation of risk - but it doesn't completely reflect investors' true preferences. Mean variance analysis will underestimate risk, and the result will be an overallocation to the asset class.

Another problem with standard deviation (volatility) as *the* measure of risk is that investors in the real world generally care much more about downside volatility and far less (if at all) about volatility when returns are above average. Thus investors/advisors may want to consider what is called negative semivariance. Positive and negative semivariance are calculated using positive (and respectively negative) deviations from the mean. Since research into behavioral finance has revealed that most investors are risk averse, negative semivariance should be an important consideration in the asset allocation decision.

Another risk measure should be the probability of a negative outcome. This is especially true of risk-averse investors who are more inclined to lose discipline, and stray from a well-thought-out plan, when risk actually shows up.

Next time, we'll look into alternative definitions of risk - like the probability of not achieving your financial objective.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.