4. you own a portfolio that is invested 43 percent in stock a, 16 percent in stock b, and 41 percent in stock c. the "expected returns" on stocks a, b, and c are: 9.1 percent, 16.7 percent, and 11.4 percent, respectively. a.) what is the "expected return" of the portfolio? b.) what is the "variance" of the portfolio? c.) what is the "standard deviation" of the returns on this stock?

A.) The "Expected Return" of the Portfolio is 11.26%

B.) The "Variance" of the Portfolio is 6.749238

C.) The  "Standard Deviation" of the Returns on this Stock is 2.5979%

Explanation:

A.) Expected return on portfolio = 0.43x9.10 + 0.16x16.70 + 0.41x11.40

                                                     = 11.26%

Therefore, The "Expected Return" of the Portfolio is 11.26%

B.)  

"Variance" of the Portfolio = probability*(deviation)^2

Stock A:

probability = 0.43

(deviation)^2 =  (9.1 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4))^2

                      = (9.1 - (3.913 + 2.672 + 4.674))^2

                      = (9.1 - 11.259)^2

                      = (-2.159)^2

                      = 4.6613

Stock B:

probability = 0.16

(deviation)^2 =  (9.1 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4))^2

                      = (16.7 - (3.913 + 2.672 + 4.674))^2

                      = (16.7 - 11.259)^2

                      = (5.441)^2

                      = 29.6045

Stock C:

probability = 0.41

(deviation)^2 =  (11.4 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4))^2

                      = (11.4 - (3.913 + 2.672 + 4.674))^2

                      = (11.4 - 11.259)^2

                      = (0.141)^2

                      = 0.0199

"Variance" of the Portfolio = 0.43x4.6613 + 0.16x29.6045 + 0.41x0.0199

                                                  = 2.004359 + 4.73672 + 0.008159

                                                   = 6.749238

Therefore, The "Variance" of the Portfolio is 6.749238

C.) "Standard Deviation"  = square root of variance

Stock A = 1.4158

Stock B = 2.1764

Stock C = 0.0906

"Standard Deviation" of the Returns on this Stock = 1.4158 + 2.1764 + 0.0906

= 2.5979%

Therefore, The  "Standard Deviation" of the Returns on this Stock is 2.5979%

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