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You have $100,000 to invest in a portfolio containing Xantus shares and Yak shares
You have $100,000 to invest in a portfolio containing Xantus shares and Yak shares. Your goal is to create portfolio that has an expected return of 10.6%. Xantus has an expected return of 11.4% and a beta of 1.25. Yak has an expected return of 8.68% and a beta of 0.85,
a) How much money will you invest in Yak shares?
b) What is the beta of your portfolio?
Expert Solution
a) Computation of the investment in Yak shares:-
Portfolio return = (Weight of Xantus shares * Return of Xantus shares) + (Weight of Yak shares * Return of Yak shares)
10.6% = (WX * 11.4%) + ((1-WX) * 8.68%)
10.6% = (WX * 11.4%) + 8.68% - (WX * 8.68%)
10.6% - 8.68% = WX * 2.72%
WX = 1.92% / 2.72%
= 0.7059
Weight of Xantus shares = 0.7059
Weight of Yak shares = 1 - WX = 1 - 0.7059
= 0.2941
Investment in Xantus shares = $100,000 * 0.7059
= $70,588.24
Investment in Yak shares = $100,000 * 0.2941
= $29,411.76
b) Computation of the beta of portfolio:-
Portfolio beta = (Weight of Xantus shares * Beta of Xantus shares) + (Weight of Yak shares * Beta of Yak shares)
= (0.7059 * 1.25) + (0.2941 * 0.85)
= 0.88 + 0.25
= 1.13
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