Currently, the risk-free rate is 5 percent and the market risk premium is 6 perc

Question

Currently, the risk-free rate is 5 percent and the market risk premium is 6 percent.  You have your money invested in three assets: an index fund that has a beta of 1.0, a risk-free security that has a beta of 0, and an international fund that has a beta of 1.5. You want to have 20 percent of your portfolio invested in the risk-free asset, and you want your overall portfolio to have an expected return of 11 percent. What portion of your overall portfolio should you invest in the inter-national fund?

Explanation / Answer

Rf = Risk free rate = 5%

Rm = Return on market = 5 + 6 = 11%

Rif = Return on International Fund = 5 + 1.5 * 6 = 14%

Now Let X the portion of your overall portfolio you invest in International fund

Then portion invested in Index fund = 0.80 - X

Return on Portfolio = 14 ( X ) + 11 (0.80 - X) + 5 * (0.20) = 11 ....... given

14X - 11X + 8.80 + 1 = 11

3X = 1.20

X = 0.40 or 40% is the portion investable in Inter National fund

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