A random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing

DISTRIBUTION 
OF 
MONTHLY
RETURNS FOR A PORTFOLIO
INVESTED IN THE S&P 500-STOCK
INDEX, JANUARY 1940–JUNE 2010

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Source: Global Financial Data.
For reasonably symmetric distributions such as this one, a
helpful rule of thumb is that two-thirds of the monthly
returns tend to fall within one standard deviation of the
average return and 95 percent of the returns fall within two
standard deviations. Recall that the average return for this

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distribution was close to 1 percent per month. The standard
deviation (our measure of portfolio risk) turns out to be about
4½ percent per month. Thus, in two-thirds of the months the
returns from this portfolio were between +5½ percent and –
3½ percent, and 95 percent of the returns were between 10
percent and –8 percent. Obviously, the higher the standard
deviation (the more spread out are the returns), the more
probable it is (the greater the risk) that at least in some
periods you will take a real bath in the market. That’s why a
measure of variability such as standard deviation is so often
used and justified as an indication of risk.
DOCUMENTING RISK: A LONG-
RUN STUDY
One of the best-documented propositions in the field of
finance is that, on average, investors have received higher
rates of return for bearing greater risk. The most thorough
study has been done by Ibbotson Associates. Their data
cover the period 1926 through 2009, and the results are
shown in the following table. What Ibbotson Associates did
was to take several different investment vehicles—stocks,

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bonds, and Treasury bills—and measure the percentage
increase or decrease each year for each item. A rectangle or
bar was then erected on the baseline to indicate the number of
years the returns fell between 0 and 5 percent; another
rectangle indicated the number of years the returns fell
between 5 and 10 percent; and so on, for both positive and
negative returns. The result is a series of bars showing the
dispersion of returns and from which the standard deviation
can be calculated.