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 the risk-free asset? A. 28.32% B. 8.71% C. 65.00% D. 6.67%

Answer 1

Answer to the Question is Option "D" i.e "6.67%"

Let Weight of Portfolio "P" be X

Let Weight of Portfolio "Q" be Y

So, Weight of Risk-Free Rate will be "1-X-Y"

Now, Using Expected Return of Portfolio

E{Rport} = Wp * Rp + Wq * Rq + Wrf * Rf

13.50% = X*16.00% + Y*10.00% + (1-X-Y)*4.00%

Y = (9.50% - 12.00%X)/6.00% (Equation - 1)

Now, Using Beta of Portfolio

Bport = Wp * Bp + Wq * Bq

1.10 = 1.30X + 0.90Y

Using Value of Y from First Equation

1.10 = 1.30X + 0.90*((9.50% + 12.00%X)/6.00%)

1.10 = 1.30X + (0.0855 - 0.108X)/6.00%

0.066 = 0.078X + 0.0855 - 0.108X

X = 0.0195 / .03

X = 0.650 or 65.00%

Using, Value of X in Equation - 1

Y = (9.50% - (12.00%X))/6.00%

Y = (9.50% - 7.80%)/6.00%

Y = 1.70%/6.00%

Y = 28.33%

Now, let's calculate the value of Weight of Risk-Free Asset

Wrf = 1 - X - Y

Wrf = 1 - 65.00% - 28.33%

Wrf = 1 - 93.33%

Wrf = 6.67%

Weight of Risk-Free Asset = 6.67%