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.)23.32%24.20%22.24%25.30%

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.)23.32%24.20%22.24%25.30%

BlackTom AI · Accepted Answer

To tackle this question, start by determining the portfolio weights from the given monetary amounts. The investor has $40,000 in Microsoft and $60,000 in Apple, so the total investment is $100,000. Therefore, the weight of Microsoft (w1) is 40,000 / 100,000 = 0.40, and the weight of Apple (w2) is 60,000 / 100,000 = 0.60.
Now apply the two‑stock portfolio standard deviation formula: 
Portfolio SD = sqrt( w1^2 * sigma1^2 + w2^2 * sigma2^2 + 2 * w1 * w2 * rho * sigma1 * sigma2 ).
Plugging in the numbers: sigma1 = 0.22, sigma2 = 0.30, rho = 0.45, w1 = 0.40, w2 = 0.60.
Compute each term:
- w1^2 * sigma1^2 = (0.40)^2 * (0.22)^2 = 0.16 * 0.0484 = 0.007744.
- w2^2 * sigma2^2 = (0.60)^2 * (0.30)^2 = 0.36 * 0.09 = 0.0324.
- 2 * w1 * w2 * rho * sigma1 * sigma2 = 2 * 0.40 * 0.60 * 0.45 * 0.22 * 0.30.
  First compute 2 * 0.40 * 0.60 = 0.48. Then 0.45 * 0.22 * 0.30 = 0.0297. Multiply: 0.48 * 0.0297 = 0.014256.
Sum of the three terms: 0.007744 + 0.0324 + 0.014256 = 0.0544.
Take the square root to obtain the portfolio standard deviation: sqrt(0.0544) ≈ 0.2334, i.e., about 23.34%.
Now compare to the answer choices:
- 23.32%: This is a close approximation to the computed 23.34% and aligns with rounding differences in intermediate steps.
- 24.20%: This would require a larger contribution from the cross‑term or different weights; not matching the calculation here.
- 22.24%: This would imply smaller combined risk than computed, suggesting errors in either weights, variances, or the correlation term.
- 25.30%: This is noticeably higher than the calculated value and indicates overestimation of any component.
Thus, the option closest to the precise calculation is 23.32%, which matches the expected result when carrying typical rounding at intermediate steps.

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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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