Question

A stock has a beta of 1.6 and an expected return of 14 percent. A risk-free asset currently earns 4 percent.

a) What is the expected return on a portfolio that is equally invested in the two assets?

b) If a portfolio of the two assets has a beta of 0.8, what are the portfolio weights?

c) If a portfolio of the two assets has an expected return of 10 percent, what is its beta?

d) If all assets in the economy are correctly priced, what is the expected return on the market portfolio?

Answer 1

a)Expected return on a portfolio that is equally invested in the two assets = [expected return of stock * weight of stock]+ [return of risk free asset * weight of risk free asset]

     = [14 * .50 ] +[4*.50]

      = 7 +2

        = 9%

b)Beta of risk free asset is 0 as it is risk free .let weight of stock be "X" ,weight of risk free asset = 1-x

Portfolio beta = [Beta of stock * weight of stock ] + [Beta of risk free asset * weight of risk free asset]

   .8 = [1.6 *x]+ [0 * (1-x)]

.8 = 1.6x +0

x = .8/1.6 =.50

weight of stock = .50

weight of risk free asset = 1-.50 =.50

c)let weight of stock be "X" ,weight of risk free asset = 1-x

    10 = [14*x] +[4*(1-x)]

    10 = 14x + 4- 4x

     10 = 10x +4

      10- 4 = 10x

        6 = 10x

         x= 6/10 = .60

weight of stock = .60

weight of risk free asset = 1-.60 = .40

Beta of portfolio = [1.6*.60]+[0*.40]

             = .96 +0

               = .96

d)Beta of market is 1 ,so beta of portfolio should be equal to 1. Let the weight of stock be X, weight of risk free asset = (1-x)

1= [1.6* x] +[0*(1-x)]

1 = 1.6x +0

x = 1/1.6 = .625

weight of stock = .625 or 62.5%

weight of risk free asset = 1-.625 = .375 or 37.5%

Expected return of market protfolio = [14*.625]+[4*.375]

         = 8.75+ 1.5

           = 10.25%