An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 5%, and she puts 30% in a Treasury bill that pays 5%. Her portfolio’s expected rate of return and standard deviation are __________ and __________ respectively. Multiple Choice 10.00%; 6.75% 12.00%; 22.40% 12.00%; 15.65%1 10.00%; 35.65%
To calculate the investor’s portfolio’s expected rate of return and standard deviation, we can use the weighted average of the returns and variances of the two assets in which she has invested. Let’s break down the calculation step by step.
The investor has allocated 70% of her wealth to a risky asset with an expected rate of return of 15% and 30% to a Treasury bill with a rate of return of 5%. To find the expected rate of return for the entire portfolio, we can calculate the weighted average:
Expected Rate of Return = (Weighted Return from Risky Asset) + (Weighted Return from Treasury Bill)
Expected Rate of Return = (0.70 * 15%) + (0.30 * 5%) Expected Rate of Return = 10.5% + 1.5% Expected Rate of Return = 12.00%
So, the portfolio’s expected rate of return is 12.00%.
To calculate the portfolio’s standard deviation, we need to consider both assets’ variances and their correlation. Since no correlation information is provided, we will assume these assets are uncorrelated for simplicity. In that case, the formula for the standard deviation of a portfolio is:
Portfolio Standard Deviation = √[(Weighted Variance of Risky Asset) + (Weighted Variance of Treasury Bill)]
Portfolio Standard Deviation = √[(0.70 * 5%) + (0.30 * 0%)] Portfolio Standard Deviation = √[3.50% + 0%] Portfolio Standard Deviation = √3.50% Portfolio Standard Deviation ≈ 1.87%
So, the portfolio’s standard deviation is approximately 1.87%.
Therefore, the investor’s portfolio’s expected rate of return is 12.00%, and its standard deviation is approximately 1.87%. None of the provided multiple-choice options match these calculations exactly. However, the closest option is “12.00%; 15.65%.”
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