Question at position 9 (5 marks, difficulty level: Easy/Medium) A portfolio consists of two stocks, Microsoft and Apple. The investor holds $40,000 in Microsoft and $60,000 in Apple. Microsoft has a standard deviation of 22%, Apple has a standard deviation of 30%, and the correlation between the two stocks is 0.45. Calculate the standard deviation of this two-stock portfolio. (Hint: Calculate the portfolio weights for each stock first.)22.24%25.30%23.32%24.20%

Question

Question at position 9 (5 marks, difficulty level: Easy/Medium) A portfolio consists of two stocks, Microsoft and Apple. The investor holds $40,000 in Microsoft and $60,000 in Apple. Microsoft has a standard deviation of 22%, Apple has a standard deviation of 30%, and the correlation between the two stocks is 0.45. Calculate the standard deviation of this two-stock portfolio. (Hint: Calculate the portfolio weights for each stock first.)22.24%25.30%23.32%24.20%

BlackTom AI · Accepted Answer

Begin by identifying the portfolio weights from the given values. The total investment is 40,000 + 60,000 = 100,000, so w_Microsoft = 40,000/100,000 = 0.40 and w_Apple = 60,000/100,000 = 0.60.
Next, recall the formula for the standard deviation of a two-asset portfolio: SD_p^2 = (w1^2)(σ1^2) + (w2^2)(σ2^2) + 2(w1)(w2)(σ1)(σ2)(ρ).
Plug in the numbers: w1 = 0.40, σ1 = 0.22, w2 = 0.60, σ2 = 0.30, ρ = 0.45.
Compute each term step by step:
- w1^2 σ1^2 = (0.40)^2 × (0.22)^2 = 0.16 × 0.0484 = 0.007744.
- w2^2 σ2^2 = (0.60)^2 × (0.30)^2 = 0.36 × 0.09 = 0.0324.
- Cross term = 2 × w1 × w2 × σ1 × σ2 × ρ = 2 × 0.40 × 0.60 × 0.22 × 0.30 × 0.45.
  Evaluate the inner product: 0.22 × 0.30 = 0.066; 0.066 × 0.45 = 0.0297.
  Then multiply by 2 × 0.40 × 0.60 = 0.48: 0.0297 × 0.48 = 0.014256.
Add the three components: 0.007744 + 0.0324 + 0.014256 = 0.0544.
Thus, SD_p = sqrt(0.0544) ≈ 0.2334, which is about 23.34% when expressed as a percentage.
Comparing to the provided options, 23.32% is the closest and aligns with the calculation, while the other figures (22.24%, 25.30%, 24.20%) do not match the computed value and would be incorrect interpretations of the same inputs.

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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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