You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.06?

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Quizplus · Accepted Answer

To achieve a portfolio with a specific standard deviation (in this case, 0.06) when combining a risk-free asset (with a standard deviation of 0) and a risky asset, we use the formula for the standard deviation of a portfolio. The standard deviation of the portfolio is proportional to the amount invested in the risky asset because the risk-free asset has a standard deviation of 0. To achieve a standard deviation of 0.06 when the risky asset has a standard deviation of 0.15, the proportion of the investment in the risky asset must be 0.06 / 0.15 = 0.4 or 40%. Therefore, 60% must be invested in the risk-free asset.

You Invest $100 in a Risky Asset with an Expected