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

Given that,

A portfolio need to generated with expected return Rr = 13.5%

Beta Br = 1.1

Risk free rate Rf = 4%

Beta of of stock P Bp = 1.3

Expected return on stock P, Rp = 16%

Beta of of stock Q Bq = 0.9

Expected return on stock Q, Rq = 10%

Let weight of stock P be Wp, stock Q be Wq, then weight of risk free security = 1-Wp-Wq

So, Beta of portfolio is weighted average beta of its stock,

=> Br = Wp*Bp + Wq*Bq

=> 1.1 = Wp*1.3 + Wq*0.9

=> 11= 13Wp + 9Wq

Expected return on portfolio is weighted average return on its stock

So, Rr = Wp*Rp + Wq*Rq + (1-Wp-Wq)*Rf

=> 13.5 = 16Wp + 10Wq + 4(1-Wp-Wq)

=> 9.5 = 12Wp + 6Wq

From the two equation, Wp = 0.65

So, weight of stock P in portfolio is 65%

Option D is correct.