If an investor’s portfolio is composed of an investment in the Magellan fund (with 14% expected return and a 25% standard deviation) and a risk free asset with a 5% return, what is the expected return if the total portfolio has a standard deviation of 20%?

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Quizplus · Accepted Answer

The expected return of a portfolio that combines a risky asset and a risk-free asset can be calculated using the formula: $E(R_p) = wR + (1-w)R_f$, where $E(R_p)$ is the expected return of the portfolio, $w$ is the weight of the risky asset in the portfolio, $R$ is the expected return of the risky asset, and $R_f$ is the return of the risk-free asset. The weight of the risky asset can be determined by the ratio of the portfolio's standard deviation to the standard deviation of the risky asset, since the risk-free asset has a standard deviation of 0. Thus, $w = \frac{20\%}{25\%} = 0.8$. Plugging the values into the formula gives $E(R_p) = 0.8 \times 14\% + 0.2 \times 5\% = 11.2\% + 1\% = 12.2\%$.

If an Investor’s Portfolio Is Composed of an Investment in the Magellan