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Updated Aug. 27, 2007 11:59 p.m. ET

ON A PERFECTLY ORDINARY DAY in February, the Dow Jones Industrial Average dropped 416 points, or 3.47%. Investors shouldn’t have been particularly surprised by the drop or the market’s subsequent movement. The losses were wiped out by gains over the next several months; now those gains are eroding again. The market, as they say, fluctuates.

Since 1990 there have been 13 days with drops of more than 400 points, and one-day drops of 3% or more have occurred on average 1.5 times a year. History shows, and the market has again validated, that such large price moves tend to clump together.

The market’s behavior should convince investors that even a rising market holds significant risk. For those who are sensitized to investment risk, history also suggests that they shouldn’t depend on Wall Street to provide them with useful measures of risk.

Quantitative risk measures are not new. As early as the 17th century it became possible to measure risk in certain wagers. Sir Isaac Newton, for example, worked on probability theory to help his acquaintance Samuel Pepys have success at dice. In the early 20th century The Theory of Games and Economic Behavior. a book by John von Neumann and Oskar Morgenstern, raised the theory to a science. And in 1952, Harry Markowitz’s classic paper Portfolio Selection showed how to minimize one dimension of risk for a specified level of expected portfolio return.

Wall Street professionals know that risk must be treated as a co-equal to return, and they use a variety of quantitative tools to evaluate it. However, little of their work has made its way to average investors. This has significant implications for these investors’ success. For example:

• Investors are regularly exposed to articles and analysts’ reports that predict a given stock’s price will skyrocket. Almost none provide more than a cursory acknowledgment that there’s a risk the stock’s price might decline.
• Mutual-fund families have many offspring, some with lower risk than the general market and others with higher risk. The latter funds tend to outperform in rising markets, the former in falling markets. However, without a quantitative knowledge of their relative risk, an investor in a rising market might buy the high-risk fund because he believes its out-performance is the result of better portfolio management.

Investors’ best interests require them to be more self-reliant in evaluating risk. While the most sophisticated tools on Wall Street are not available to them, average investors can evaluate some dimensions of risk.

One is the sensitivity of a security or a portfolio to market movements as measured by beta. The market’s beta is defined as one. If the market moves by 2%, a security or a portfolio with a beta of 1.5 would on average move 3% and one with a beta of .5 would move about 1%. Or put another way: A security or portfolio with a high beta has more risk than one with a low beta.

Current estimates of beta for individual securities are easily found on financial Websites. Barron’s Online’s stock screener, for instance, allows users to search for stocks of particular betas, high or low. The beta of a portfolio of stocks is the weighted average of the individual stocks, using their dollar value for the weights.

Another dimension of risk is uncertainty of return. This is measured by standard deviation, also known as volatility and denoted by sigma. Sigma measures how widely the returns on an asset differ from their average. Most investors seeking a long-term average return of, say, 10% prefer that their annual returns cluster close to 10% rather than jump from minus 20% one year to plus 40% the next. In other words, they’d like a small sigma.

There are free Websites that provide a security’s standard deviation, including www.morningstar.com for mutual funds and www.cboe.com for individual stocks. There are software products for sophisticated investors that, among other tasks, calculate the sigma of a portfolio. Closely related to sigma and more useful for portfolio-risk analysis is RiskMetrics Group’s concept of a RiskGrade. It measures an asset’s or portfolio’s risk due to volatility relative to the global-equity market’s volatility. Free and relatively comprehensive risk analysis is available at www.RiskGrades.com .

Of course, these only scratch the surface. Many investors don’t consider simple volatility to be as important a risk factor as the chance of an investment’s losing money or not meeting some preset return goal.

Frank Sortino’s book Managing Downside Risk in Financial Markets (and a related Website, www.sortino.com ) are helpful in assessing the chance of falling short of a financial goal. The book contains a CD that allows investors to investigate this risk for individual securities or for complete portfolios.

Still another approach is Value-at-Risk (VAR), a process for estimating the worst loss a security or portfolio is likely to incur over a specified time interval with a specified confidence level.

An investor might ask, What’s the largest monthly loss I could expect to see from my portfolio over, say, a 20-month period? (That would work out to about 5% of the time.) There are fee-based Websites that perform VAR calculations online; www.finportfolio.com is one. But just about anyone can do a poor man’s VAR analysis of a simple portfolio.

First, gather historical price data (which finance.yahoo.com provides) and construct a sequence of monthly percentage returns for the portfolio over, for example, 120 months. Then order the 120 returns from worst to best. You can eliminate the six worst months (or 5% of 120) because they are likely to occur roughly 5% of the time, and instead use the seventh worst month. Multiply that return by the value of the portfolio for a back-of-the-envelope estimate.

Risk analysis is a critical component in the investing process. Investors shouldn’t put their capital into play without an understanding of risk. To do otherwise is a recipe for financial disappointment — or much worse.

ROBERT STEPLEMAN, who has a Ph.D. in mathematics, is a principal at Portfolio Consulting Services. His e-mail: rsstepl@tampabay.rr.com