# 16. Equation 8.9 can be modified to compute the risk of a three-security portfolio as follows: a p ¼

16.      Equation 8.9 can be modified to compute the risk of a three-security portfolio as follows:

ap  ¼ qﬃwﬃﬃﬃ2ﬃﬃﬃaﬃﬃﬃ2ﬃﬃﬃþﬃﬃﬃﬃwﬃﬃﬃﬃ2ﬃﬃﬃaﬃﬃ2ﬃﬃﬃﬃþﬃﬃﬃﬃﬃwﬃﬃﬃ2ﬃﬃﬃaﬃﬃﬃ2ﬃﬃﬃþﬃﬃﬃﬃﬃ2ﬃﬃwﬃﬃﬃﬃﬃwﬃﬃﬃﬃﬃﬃﬃpﬃﬃﬃﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃﬃþﬃﬃﬃﬃﬃ2ﬃﬃwﬃﬃﬃﬃﬃﬃwﬃﬃﬃﬃﬃﬃﬃpﬃﬃﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃﬃþﬃﬃﬃﬃﬃ2ﬃﬃwﬃﬃﬃﬃﬃwﬃﬃﬃﬃﬃﬃﬃpﬃﬃﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃﬃaﬃﬃﬃﬃﬃ

A     A           B    B           C    C

A    B      AB     A     B

A     C AC A C

B     C BC B C

You have decided to invest 40 percent of your wealth in Security A, 30 percent in Security B, and 30 percent in Security C. The following information is available about the possible returns from the three  securities:

Security A                                             Security B                                       Security C

 Return Probability Return Probability Return Probability 10% 0.25 13% 0.30 14% 0.40 12 0.50 16 0.35 18 0.30 14 0.25 19 0.35 22 0.30

Compute the expected return of the portfolio and the risk of the portfolio if the cor-

 AB

relations between returns from the three securities are   p

¼ 0.70; pAC

¼ 0.60; and

pBC  ¼ 0.85.