242 Part 3 Financial Assets
8-3b Portfolio Risk
Although the expected return on a portfolio is simply the weighted average of the
expected returns on its individual stocks, the portfolio’s risk, #p, is not the weighted
average of the individual stocks’ standard deviations. The portfolio’s risk is gen-
erally smaller than the average of the stocks’ #s because diversi" cation lowers the
portfolio’s risk.
To illustrate this point, consider the situation in Figure 8-4. The bottom section
gives data on Stocks W and M individually and data on a portfolio with 50% in
each stock. The left graph plots the data in a time series format, and it shows that
the returns on the individual stocks vary widely from year to year. Therefore, the
individual stocks are risky. However, the portfolio’s returns are constant at 15%,
indicating that it is not risky at all. The probability distribution graphs to the right
show the same thing—the two stocks would be quite risky if they were held in iso-
lation; but when they are combined to form Portfolio WM, they have no risk
whatsoever.
If you invested all of your money in Stock W, you would have an expected re-
turn of 15%, but you would face a great deal of risk. The same thing would hold if
you invested entirely in Stock M. However, if you invested 50% in each stock, you
would have the same expected return of 15%, but with no risk whatsoever. Being
rational and averse to risk, you and all other rational investors would choose to
hold the portfolio, not the stocks individually.A B C D E F G
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108Year Stock W Stock M Portfolio WMRate of Return (%)-20% 15% 40%Rate of Return (%)-20% 15% 40%2004
2005
2006
2007
2008
Avg return =
Estimated! =40.00%
-10.00
40.00
-10.00
15.00-10.00%
40.00
-10.00
40.00
15.0015.00%
15.00
15.00
15.00
15.00
15.00%
25.00%15.00%
25.00%15.00%
0.00%
Correlation coe$cient = -1.00Portfolio WMStocks W and M, held separately2004 2005 2006 2007 2008W MRate of Return-15%0%15%30%45%WMReturns With Perfect Negative Correlation, % $ !1.0
F I G U R E 8! 4