Question

You want to create a portfolio that generates an expected return of 13.5% and a beta of 1.1 by investing in two stocks (P and Q) and a risk-free asset with a sure rate of 4%. The beta of Stock P is 1.3, and its expected return is 16%. The beta of Stock Q is 0.9, and its expected return is 10.0%. What is the weight on Stock P in your portfolio?

A. 48.29%

B. 35.00%

C. 51.71%

D. 65.00%

Answer 1

Portfolio Beta = Beta of stock P * Wp + Beta of stock Q * Wq

1.1 = 1.3 * Wp + 0.9 * Wq (Eq 1)

Erp = Rp * Wp + Rq * Wq

0.135 = 0.16 * Wp + 0.10 * Wq (Eq 2)

Subtract Eq2 from Eq1

1.1 - 0.135 = Wp (1.3 - 0.16) + Wq * (0.9 - 0.10)

0.965 = Wp 1.14 + Wq * 0.8

Wp + Wq = 1

Wq = 1 - Wp

0.965 = Wp 1.14 + Wq * 0.8

0.965 = Wp 1.14 + (1 - Wp) * 0.8

0.965 = Wp 1.14 + 0.8 - Wp * 0.8

0.965 - 0.8= Wp (1.14 - 0.8)

0.165 = 0.34 Wp

Wp = 0.165/0.34

Wp = 0.4852941176

The weight of Stock P in our portfolio ~ 48.29% (Option A)

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