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You manage a risky portfolio with an expected rate of return of 18%, and standard deviation of 28%. The risk-free rate (US Treasuries) is 8%. Consider the following: a) Your client chooses to invest 70% in the risky portfolio and 30% in the risk-free rate. What is the expected return and standard deviation of her portfolio

Question

You manage a risky portfolio with an expected rate of return of 18%, and standard deviation of 28%. The risk-free rate (US Treasuries) is 8%. Consider the following:

a) Your client chooses to invest 70% in the risky portfolio and 30% in the risk-free rate. What is the expected return and standard deviation of her portfolio

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Solution

a) The expected return and standard deviation of the portfolio can be calculated as follows:

Expected Return: The expected return of the portfolio is the weighted average of the expected returns of the risky portfolio and the risk-free rate.

Expected Return = (Weight of Risky Portfolio * Expected Return of Risky Portfolio) + (Weight of Risk-Free Rate * Expected Return of Risk-Free Rate)

Expected Return = (0.70 * 18%) + (0.30 * 8%) = 12.6% + 2.4% = 15%

So, the expected return of the portfolio is 15%.

Standard Deviation: The standard deviation of the portfolio is the square root of the weighted average of the variances of the risky portfolio and the risk-free rate. However, since the risk-free rate has a standard deviation of zero (it's risk-free), the standard deviation of the portfolio is simply the standard deviation of the risky portfolio multiplied by the weight of the risky portfolio in the portfolio.

Standard Deviation = Weight of Risky Portfolio * Standard Deviation of Risky Portfolio

Standard Deviation = 0.70 * 28% = 19.6%

So, the standard deviation of the portfolio is 19.6%.

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