A $100,000 portfolio is invested in a risk-free security and two stocks. The bet

Question

A $100,000 portfolio is invested in a risk-free security and two stocks. The beta of stock A is 1.80 while the beta of stock B is 0.20. One-half of the portfolio is invested in the risk-free security. How much is invested in stock A if the beta of the portfolio is 0.75? A $100,000 portfolio is invested in a risk-free security and two stocks. The beta of stock A is 1.80 while the beta of stock B is 0.20. One-half of the portfolio is invested in the risk-free security. How much is invested in stock A if the beta of the portfolio is 0.75?

Explanation / Answer

P = 0.75 = [A/$100000][1.80] + [($100000 - A - $50000)/$100000)][0.20] + [0][0.50]

0.75 = 1.8A/100000 + 50000-A / 100000 (.20)

.75 *100000 = 1.8A + 50000*.20 – 0.2A

75000 = 1.6A +10000

65000/1.6 = A

A = $40625

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