EXAMPLE 5 Investing 101

We have discussed examples about income. Here is an example about what to do with it once you’ve earned it. One of the first principles of investing is that taking more risk brings higher returns, at least on the average in the long run. People who work in finance define risk as the variability of returns from an investment (greater variability means higher risk) and measure risk by how unpredictable the return on an investment is. A bank account that is insured by the government and has a fixed rate of interest has no risk—its return is known exactly. Stock in a new company may soar one week and plunge the next. It has high risk because you can’t predict what it will be worth when you want to sell.

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Investors should think statistically. You can assess an investment by thinking about the distribution of (say) yearly returns. That means asking about both the center and the variability of the pattern of returns. Only naive investors look for a high average return without asking about risk, that is, about how variable the returns are. Financial experts use the mean and standard deviation to describe returns on investments. The standard deviation was long considered too complicated to mention to the public, but now you will find standard deviations appearing regularly in mutual funds reports.

Here by way of illustration are the means and standard deviations of the yearly returns on three investments over the second half of the twentieth century (the 50 years from 1950 to 1999):

You can see that risk (variability) goes up as the mean return goes up, just as financial theory claims. Treasury bills and bonds are ways of loaning money to the U.S. government. Treasury bills are paid back in one year, so their return changes from year to year depending on interest rates. Bonds are 30-year loans. They are riskier because the value of a bond you own will drop if interest rates go up. Stocks are even riskier. They give higher returns (on the average in the long run) but at the cost of lots of sharp ups and downs along the way. As the stemplot in Figure 12.7 shows, stocks went up by as much as 50% and down by as much as 26% in one year during the 50 years covered by our data.