A stock has a beta of 19.5 and an expected return of 12%. A risk free asset curr

Question

A stock has a beta of 19.5 and an expected return of 12%. A risk free asset currently earns 3.8%. (please show your calculation and formula used, thanks)

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

b) If portfolio of the two assets has a beta of .78, what are the portfolio weights?

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

d) Ifa portfolio of the two assets has a beta of 3.9, what are the portfolio weights?

Explanation / Answer

Solution-a

E(Rp) = 0.5(12) + 0.5(3.8)

E(Rp) = 7.9%

Solution-b

p = 0.78 = wS(19.5) + (1 – wS)(0)

0.78 = 19.5wS + 0 – 0wS

wS = 0.78/19.5

wS = .04

So,

The weight of the risk-free asset is:

wRf = 1 – .04

wRf =0.96

Solution-c

E(Rp) = .10 = .12wS+ .038(1 – wS)

.10 = .12wS+ .038– .038wS

wS= .0.7560

So, the of the portfolio will be:

p= 0.7560(19.5) + (1 – 0.2440)(0)

p = 14.74

Solution-d

p = 3.9 = wS(19.5) + (1 – wS)(0)

wS = 3.9/19.5

wS = 0.2

wRf = 1 – 0.2

wRf = 0.8

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