bre44380_ch08_192-220.indd 193 09/30/15 12:45 PM
Chapter 8 Portfolio Theory and the Capital Asset Pricing Model 193The result is typical: When measured over a short interval, the past rates of return on any
stock conform fairly closely to a normal distribution.^2
Normal distributions can be completely defined by two numbers. One is the average or
expected value; the other is the variance or standard deviation. Now you can see why in
Chapter 7 we discussed the calculation of expected return and standard deviation. They are
not just arbitrary measures: if returns are normally distributed, expected return and standard
deviation are the only two measures that an investor need consider.
Figure 8.2 pictures the distribution of possible returns from three investments. A and B
offer an expected return of 10%, but A has the much wider spread of possible outcomes. Its
standard deviation is 15%; the standard deviation of B is 7.5%. Most investors dislike uncer-
tainty and would therefore prefer B to A.
Now compare investments B and C. This time both have the same standard deviation, but
the expected return is 20% from stock C and only 10% from stock B. Most investors like high
expected return and would therefore prefer C to B.Combining Stocks into Portfolios
Suppose that you are wondering whether to invest in the shares of Johnson & Johnson (J&J) or
Ford. You decide that J&J offers an expected return of 8.0% and Ford offers an expected return
of 18.8%. After looking back at the past variability of the two stocks, you also decide that(^2) If you were to measure returns over long intervals, the distribution would be skewed. For example, you would encounter returns
greater than 100% but none less than –100%. The distribution of returns over periods of, say, one year would be better approximated
by a lognormal distribution. The lognormal distribution, like the normal, is completely specified by its mean and standard deviation.
You would also find that the distribution of price changes has a longer tail than the normal and lognormal distributions. Extreme
events or “black swans” crop up with alarming frequency.
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Utility theory
◗ FIGURE 8.1 Daily price changes for IBM are approximately normally distributed. This plot spans 1994 to 2013.
% of days
Daily price changes, %
0
2
1
3
4
5
6
7
2 9.
0
2 7.
8
2 6.
5
2 5.
2
2 3.
9
2 2.
7
2 1.
4
2 0.
(^1) 1.2 2.4 3.7 5.0 6.3 7.5 8.8