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Chapter 8 Portfolio Theory and the Capital Asset Pricing Model 195the standard deviation of returns is 13.2% for J&J and 31.0% for Ford. Ford offers the higher
expected return, but it is more risky.
Now there is no reason to restrict yourself to holding only one stock. For example, in
Section 7-3 we analyzed what would happen if you invested 60% of your money in J&J and
40% in Ford. The expected return on this portfolio is 12.3%, simply a weighted average of
the expected returns on the two holdings. What about the risk of such a portfolio? We know
that thanks to diversification the portfolio risk is less than the average of the risks of the sepa-
rate stocks. In fact, on the basis of past experience the standard deviation of this portfolio is
15.9%.^3
The curved blue line in Figure 8.3 shows the expected return and risk that you could
achieve by different combinations of the two stocks. Which of these combinations is best
depends on your stomach. If you want to stake all on getting rich quickly, you should put all
your money in Ford. If you want a more peaceful life, you should invest most of your money
in J&J, but you should keep at least a small investment in Ford.^4
We saw in Chapter 7 that the gain from diversification depends on how highly the stocks
are correlated. Fortunately, on past experience there is only a modest correlation between
the returns of J&J and Ford (ρ = +.19). If their stocks moved in exact lockstep (ρ = +1),
there would be no gains at all from diversification. You can see this by the gold dotted line in
Figure 8.3. The red dotted line in the figure shows a second extreme (and equally unrealistic)
case in which the returns on the two stocks are perfectly negatively correlated (ρ = –1). If this
were so, your portfolio would have no risk.◗ FIGURE 8.3
The curved line illustrates how expected
return and standard deviation change as
you hold different combinations of two
stocks. For example, if you invest 40% of
your money in Ford and the remainder in
Johnson & Johnson, your expected return
is 12.3%, which is 40% of the way between
the expected returns on the two stocks.
The standard deviation is 15.9%, which is
less than 40% of the way between the stan-
dard deviations of the two stocks. This is
because diversification reduces risk.Expected return (r ), %Standard deviation (σ), %40% in FordJohnson & JohnsonFord024681012141618200510 15 20 25 30 35(^3) We pointed out in Section 7-3 that the correlation between the returns of J&J and Ford has been .19. The variance of a portfolio which
is invested 60% in J&J and 40% in Ford is
Variance = x 2 1 σ 2 1 + x 22 σ^22 + 2 x 1 x 2 ρ 12 σ 1 σ 2
= [ (.6)^2 × (13.2)^2 ] + (^) [ (.4)^2 × (31.0)^2 ] + 2(.6 × .4 × .19 × 13.2 × 31.0)
= 253.8
The portfolio standard deviation is √
253.8 = 15.9%.
(^4) The portfolio with the minimum risk has just over 90% in J&J. We assume in Figure 8.3 that you may not take negative positions in
either stock, that is, we rule out short sales.