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

/in /by

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.

 

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