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OptimalPortoliosWhenThereIsARiskFreeAsset

# OptimalPortoliosWhenThereIsARiskFreeAsset - Optimal...

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Optimal portfolios when there is a riskfree asset 1 How does the set of possible portfolios change when you have access to a riskfree asset? We will conside the problem in two steps. 1. One riskfree asset and one risky asset 2. One riskfree asset and multiple risky assets As we learned in our section on bond valuation, the riskfree asset is the zero-coupon bond whose maturity equals the length of your holding period. For concreteness, we will assume a one-year holding period, so the riskfree asset will be a one-year Treasury Bill. 1. One riskfree asset and one risky asset Suppose the risky asset is a mutual fund. We will call this mutual fund “M”, and the riskfree asset “f”. The return on the mutual fund will therefore be called R M , while the return on the riskfree asset will be called R f . Using our formulas for the mean and the variance, the mean of the portfolio that puts weight X f in the riskfree asset and weight X M in the risky asset equals ¯ R p = X f R f + X M ¯ R M Note that R f = ¯ R f because the riskfree asset is, by definition, without risk. Thus its

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OptimalPortoliosWhenThereIsARiskFreeAsset - Optimal...

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