You have a $1,250 portfolio which is invested in Stocks A and B plus a risk-free asset.$350 is invested in Stock A which has a beta of 1.36 and Stock B has a beta of .84.How much needs to be invested in Stock B if you want a portfolio beta of .95?
A)$803
B)$951
C)$782
D)$847
E)$791

Question

Quizplus · Accepted Answer

Let X be the amount invested in Stock B.

We know that the total portfolio amount is $1,250:

$350 is invested in Stock A, so the remaining amount invested in Stock B and a risk-free asset is $1,250 - $350 = $900.

We also know that the portfolio beta is 0.95:

0.95 = ((0.84)(X) + (1.36)(350)) / 1250

0.95(1250) = 0.84X + 1.36(350)

1187.5 = 0.84X + 476

0.84X = 711.5

X = 711.5 / 0.84 = $846.43

Therefore, the amount that needs to be invested in Stock B is $847 (rounded to the nearest dollar). The answer is D.

You Have a $1,250 Portfolio Which Is Invested in Stocks