Question

You want your portfolio beta to be 1.30. Currently, your portfolio consists of $100 invested in stock A with a beta of 1.4 and $300 in stock B with a beta of .6. You have another $400 to invest and want to divide it between an asset with a beta of 1.8 and a risk-free asset. How much should you invest in the risk-free asset?

Answer 1

Let new stock be “C” and Risk-free security be “D”

Portfolio beta = Weight of stock A x Beta of stock A + Weight of stock B x Beta of stock B + Weight of stock C x Beta of stock C + Weight of stock D x Beta of stock D

1.3 = 100/800 x 1.4 + 300/800 x 0.6 + Weight of stock C x 1.8 + Weight of stock D x Beta of stock D

Risk free security has beta of 0 hence;

1.3-0.4 = Weight of stock C x 1.8 + Weight of stock D x 0

1.3-0.4 = Weight of stock C x 1.8

Weight of stock C = 0.90/1.8

Weight of stock C = 50%

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Weight of C = 50%; Weight of A = 100/800 = 17.5%; Weight of C = 300/800 = 22.5%

Weight of D = 1-50%-17.5%-22.5% = 0

So, nothing is invested in Risk free security;

Investment in Risk-free security = 0