Investment risk means many different things to different people. Yet for decades the investment world has relied primarily on one particular measure of risk, standard deviation, which I believe doesn't apply very well to today's markets. Many of the violent swings that we've seen would never have been predictable under traditional standard deviation calculations. Let me show you why and introduce you to another risk measurement concept that may more accurately reflect reality.

Today's standardized risk metric took hold in the 1950s when top economists from major academic institutions, such as Maurice Kendall (London School of Economics); Paul Samuelson (MIT); Harry Markowitz (University of Chicago); and William Sharpe (UCLA) observed that over the long term, changes in security prices plotted on a histogram chart resembled the shape of the symmetrical bell curve.

The plot of the data in Figure 1 shows that most days prices were barely up or down from the long-term, mean-average price movement, while large changes in price occurred far less frequently. "Long term" generally refers to 40 or more years of daily prices.

Since the data approximately fit a familiar bell curve (that came with well-developed mathematical tools), it was tempting for the early researchers to adopt it as a good fit. The ease of plotting a bell curve made the chore of estimating and interpreting risk easy: The wider the bell-i.e., the wider the variance or average distance from the mean-the greater the risk.

This variance is measured using the standard deviation calculation-the same method your teachers used to score your tests back in school. The assumption is that 68.3% of returns will fall under one standard deviation (1σ), 95.4% of returns will fall under 2σ and 99.7% will occur within 3σ. Low-volatility securities, like short-term bonds, have very low standard deviations, such as 2%, whereas volatile securities, like emerging-market stocks, will have large standard deviations, such as 24%.

In the theoretical world where security returns can be described by a normal bell curve, you might assume that the expected return of a specific security is 8% per year and its standard deviation is 4% (see Figure 2). Then you would expect your daily returns to be between 4% and 12%, 68.3% of the time; and between 0% and 16%, 95.4% of the time; the returns will fall between -4% and 20% 99.7% of the time. Furthermore, a 1σ event should occur every six days; a 2σ event once a month, a 3σ event once every 1.5 years, and a 4σ occurrence once every 63 years.

In the 1950s, Harry Markowitz took the concept a step further. Realizing that most investors are concerned with the probability of losing money, he focused on downside risk, by examining just the left side of the frequency distribution. This concept (Figure 3) is called semi-variance because it measures only the half of the variance with losses. With semi-variance the probability that a loss will be more than 1σ is 15.9%; more than 2σ is 2.3%; more than 3σ is 0.14%; and more than 4σ only 0.003%.

In the 1980s, risk modeling really took off, along with the introduction of Modern Portfolio Theory, which uses standard deviation as the foundation of its asset allocation methodology. Much of the impetus came from bank and insurance companies that were trying to manage risk in the wake of the savings & loans crisis. ERISA laws and compliance regulations were also spurring brokerage firms to find better ways to mitigate their liability.

In 1993, two J.P. Morgan analysts realized that banks were less concerned about small losses caused by a house fire, flood or cracked foundation. Their clients were concerned about catastrophic losses. They wanted to know the financial effects of a natural disaster such as a hurricane or an earthquake.

To calculate the odds of such worst-case scenarios, they took the concept of semi-variance and moved the marker toward the far left tail of the distribution. They typically measured the last 1% of the distribution, located at about 2.6. They coined this risk method "VaR" to signify how much "Value" they would have "at Risk" in their portfolios should the worst occur. With VaR (Figure 4), a risk manager would cite a 1% chance of losing x% on a given day.

WRONG TURN
But there is a common limitation to all of these risk methods (standard deviation, semi-variance and VaR). They all assume that distributions are normally distributed. But distributions tend to be lopsided in one direction or another, a tendency called "skewness" in the world of statistical modeling. Normal distributions and standard deviations describe many, but not all, natural phenomena and they tend to work well in low-volatility markets. But these measurements don't apply to the more recent, complicated behavior of the securities markets. In nature almost anything you can measure can fit into an idea of random variables, which tend to follow a bell curve, the exceptions, like hurricanes, can be applied to commodities, which relate to seasons.