A stock has a beta of 1.25 and an expected return of 12.3 percent. A risk-free a

Question

A stock has a beta of 1.25 and an expected return of 12.3 percent. A risk-free asset currently earns 4.05 percent. Required: (a) What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return % (b) If a portfolio of the two assets has a beta of 0.85, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) Weight of the stock Weight of the risk-free asset (c) If a portfolio of the two assets has an expected return of 11.5 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Beta (d) If a portfolio of the two assets has a beta of 2.45, what are the portfolio weights? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).) Weight of the stock Weight of the risk-free asset

Explanation / Answer

a) Expected return on portfolio = (Es *Ws) +(Ea* Wa)

= (12.3 * .5) +(4.05 * .5 )

= 6.15 + 2.025

Expected return on portfolio = 8.175%

b) Let weight of Stock be "X"

Weight of risk free asset = 1 -X

Beta of risk free asset = 0 ,as no risk is involved

Beta of portfolio = (Bs * Ws) +(Ba * Wa)

0.85 =   (1.25 * X ) + (0 * [1-x)]

0 .85 = 1.25X + 0

          X =0 .85 / 1.25

                 = 0.68

Weight of stock = 0.68

weight of risk free asset = 1-.68 = 0.32

c) Expected return of portfolio = (Es *Ws) +(Ea* Wa)

      11.5   = (12.3 *X) + [4.05 (1-X)]

               = 12.3X + 4.05 - 4.05X

               = 8.25 X +4.05

   11.5 -4.05 = 8.25X

     7.45 = 8.25X

       X (Weight of stock ) = 7.45 / 8.25

weight of stock = 0.9030

weight of risk free asset = 1 -.9030 =0 .0970

beta of portfolio = (1.25 * 0.9030) +(0*0 .0970)

                           = 1.13 + 0

Beta of portfolio = 1.13

d)Let weight of Stock be "X"

Weight of risk free asset = 1 -X

Beta of risk free asset = 0 ,as no risk is involved

Beta of potfolio = (Bs * Ws) +(Ba * Wa)

2.45 = (1.25 *X) + [ 0* (1-X)]

             = 1.25X + 0

   X = 2.45 /1.25

Weight of stock = 1.96

weight of risk free asset = 1- 1.96 = -0.96

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