You want your portfolio beta to be 1.112. Currently, your portfolio consists of

Question

You want your portfolio beta to be 1.112. Currently, your portfolio consists of $200 invested in stock A with a beta of 1.7 and $300 in stock B with a beta of .5. You have another $400 to invest and want to divide it between an asset with a beta of 1.7 and a risk-free asset. How much should you invest in the risk-free asset?

Explanation / Answer

as portfolio beta = w1*beta1 +w2 beta2 +w3 beta3 +w4 beta4 => 200/900*1.7 + 300/900*0.5+ x/900*1.7+0*(400-x)/900 =1.12 => 340+150+1.7x+400-x =1008 =>0.7x =118 => x =$168.57 so 400-x should be inveted in risk free asset => 400-168.57 =$231.43(appx)

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