Part 2 of 7:

What is the standard deviation of a Complete Portfolio that invests 40% in Portfolio A and 60% in the risk-free rate?

Round your answer to four decimals. DO NOT use percentage format. E.g. 10.51% should be entered as 0.1051

Question

Part 2 of 7:

What is the standard deviation of a Complete Portfolio that invests 40% in Portfolio A and 60% in the risk-free rate?

Round your answer to four decimals. DO NOT use percentage format. E.g. 10.51% should be entered as 0.1051

BlackTom AI · Accepted Answer

This question asks for the standard deviation of a portfolio that combines a risky asset A and a risk-free asset. The key idea is that the risk-free portion contributes zero variance, so the portfolio's variance comes only from the risky asset portion.

Step 1: Identify the weights. The portfolio allocates 40% to Portfolio A (the risky asset) and 60% to the risk-free asset. Therefore, w_A = 0.40 and w_RF = 0.60.

Step 2: Recognize the variance contribution. Since the risk-free asset has zero standard deviation (sigma_RF = 0), the overall portfolio variance simplifies to (w_A)^2 * (sigma_A)^2, because the cross-term with the risk-free asset is zero and the variance from the risk-free part is zero.

Step 3: Compute the portfolio standard deviation. The standard deviation of the portfolio is sigma_p = w_A * sigma_A, since only the risky asset contributes to risk in this setup.

Step 4: Relate to the given numerical answer. The provided answer is 0.0395. If sigma_p = 0.0395 and w_A = 0.40, then 0.0395 = 0.40 * sigma_A, so sigma_A = 0.0395 / 0.40 = 0.09875.

Step 5: Interpret the result. This means the standard deviation of Portfolio A alone would be 0.09875 (9.875%), and the portfolio’s standard deviation with 40% in A and 60% in the risk-free asset would be 0.0395 (3.975%), as long as the risk-free portion truly has zero variance.

Optional consistency check: If you instead start from sigma_p = w_A * sigma_A, substituting w_A = 0.40 and solving for sigma_p with a known sigma_A would yield the same relationship. The final numeric value for sigma_p depends on the given sigma_A; using the provided final value 0.0395 confirms the implied sigma_A = 0.09875.

Note: If the problem had included any covariance terms or a nonzero variance for the risk-free asset (which is not standard), the calculation would be different. Here, the risk-free asset contributes no risk, so the above straightforward scaling applies.

COMM_V 298 101 102 103 2025W1 Class 14 Practice Quiz

Part 2 of 7: What is the standard deviation of a Complete Portfolio that invests 40% in Portfolio A and 60% in the risk-free rate? Round your answer to four decimals. DO NOT use percentage format. E.g. 10.51% should be entered as 0.1051

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