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Risk Analysis With Standard Deviation

03/26/02 03:53:00 PM PST
by Sean Moore

Investments are risky. So how do you minimize the risks?

All investments have an element of risk associated with them, some more than others. You've probably heard that the more potential an investment has for large returns, the greater the risk. Anybody who invested in an Internet stock prior to the dotcom bubble-burst can attest to the validity of this statement. If we've learned our lesson from the boom and bust, the next time a bull rally starts to emerge, instead of buying all the high-flyers — whatever they happen to be — we'll be more likely to take the time to assess the risk.


By analyzing risk you'll be better equipped to make decisions on specific investments, since you'll gain insight into what you can expect in terms of price fluctuations. Being equipped with this information beforehand will help you prepare for the upturns and downturns in the markets that will ultimately affect your returns.

Risk analysis is extremely important for both short- and long-term investors. If you're a short-term investor, you can't afford poor returns, because time is not on your side. If you're a long-term investor, you may be uncomfortable with volatility or have a difficult time making a final choice among a few carefully selected investments. Risk analysis can help you overcome these hurdles. One of the simplest ways to assess risk is with the statistical measurement known as standard deviation.

The term standard deviation may sound boring, or it may sound like something that involves complex calculations. But it's really one of the easiest risk measurements to calculate. Statistically speaking, standard deviation is a popular measure of variation that helps determine how accurate your average (or mean) is. If a fund or stock has an average annual return of 15% with a standard deviation of 3%, you can assume that the average of 15% is fairly stable. If, on the other hand, a fund has an average annual return of 15% with a standard deviation of 20%, you know that the performance has been very volatile: down 10% one year, up 40% the next, perhaps. Like performance figures, standard deviation becomes a more accurate measurement as you accumulate more data. A standard deviation of the last 10 years would be a more accurate measurement than a standard deviation of the last three years.

Figure 1 shows a display of the three-year standard deviation taken from for three different Vanguard bond funds. You can see that the long-term bond fund is more volatile than the intermediate-term fund, which in turn is more volatile than the short-term fund. Comparing different funds will help you select a fund or investment that best meets your needs. The long-term fund does have a higher average annual return, but is it enough to make up for the extra risk?

Figure 1: Using standard deviation as a measure of risk to compare three bond funds.


If you have access to annual performance figures, you can easily calculate standard deviation with software like Microsoft Excel. For a mutual fund, you can obtain annual performance figures from the fund prospectus or from a mutual fund website such as I selected a couple of funds from my watchlist for a quick comparison: the Clipper Fund (CFIMX) and the Vanguard Standard & Poor's 500 index fund (VFINX). I went to each company's website and obtained the annual return figures from each fund's prospectus. I entered these return figures into an Excel spreadsheet and calculated the average and standard deviation for each fund. The resulting spreadsheet can be seen in Figure 2. Excel has preprogrammed functions for many statistical measurements, including average and standard deviation. To calculate the average for VFINX, the following was entered in cell C14:


To calculate the standard deviation, the following was entered in cell C16:


From the comparison you can see that the Clipper Fund has a higher average annual return and a lower standard deviation than the Vanguard S&P 500 fund, making the Clipper fund an attractive investment. Both funds are no-load funds with low expense ratios and reasonable minimum investment requirements, as shown in Figure 2.

Figure 2: Comparing the average annual return and standard deviation for two mutual funds, VFINX and CFIMX.


It is not uncommon for the standard deviation of a stock or mutual fund to be higher than its average. When you're contemplating a new investment or evaluating an old one, it's a good idea to look closely at the risk involved. Standard deviation is a great measurement to use for quick comparisons and basic risk analysis.

Sean Moore may be reached at

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Sean Moore Staff Writer.

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