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The market portfolio has an expected return of 11 percent and a standard deviation of 19...

The market portfolio has an expected return of 11 percent and a standard deviation of 19 percent. The risk-free rate is 3.2 percent.

a. What is the expected return on a well-diversified portfolio with a standard deviation of 27 percent

b. What is the standard deviation of a well-diversified portfolio with an expected return of 15 percent?

Solutions

Expert Solution

a.

Beta of portfolio = Standard deviation of portfolio/Standard deviation of market

                             = 27 %/19 % = 0.27/0.19 = 1.42105263157895

As per CAPM model,

Expected return = Risk-free rate + Beta (Return on market - Risk-free rate)

                           = 3.2 % + 1.42105263157895 (11 % - 3.2 %)

                             = 0.032 + 1.42105263157895 (0.11 – 0.032)

                             = 0.032 + 1.42105263157895 x 0.078

                             = 0.032 + 0.110842105263158

                            = 0.142842105263158 or 14.28 %

Expected return on portfolio is 14.28 %

b.

Using CAPM model we can compute beta of portfolio as:

Expected return = Risk-free rate + Beta (Return on market - Risk-free rate)

Beta = (Expected return - Risk-free rate)/ (Return on market - Risk-free rate)

          = (15 % - 3.2 %)/ (11 % - 3.2 %)

         = (0.15 – 0.032)/ (0.11 – 0.032)

          = 0.118 / 0.078

          = 1.51282051282051

As the portfolio is well diversified,

Portfolio standard deviation = Beta x Market standard deviation

                                   = 1.51282051282051 x 19 %

                                   = 1.51282051282051 x 0.19

                                   = 0.287435897435897 or 28.74 %

Standard deviation of the portfolio is 28.74 %

jeff jeffy answered 1 month ago
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