Chartered Financial Analyst Level 1
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A portfolio comprises two securities with the following attributes:
Expected Return Standard Deviation of Returns
Security 1 17% 24%
Security 2 6% 12%
Given the portfolio's expected return of 12.6% and uncorrelated returns between the two securities, the portfolio's standard deviation is closest to:
A portfolio comprises two securities with the following attributes: Expected Return Standard Deviation of Returns Security 1 17% 24% Security 2 6% 12% Given the portfolio's expected return of 12.6% and uncorrelated returns between the two securities, the portfolio's standard deviation is closest to:
Explanation:
Explanation:
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Option A (13.4%) is incorrect because it assumes an equally weighted portfolio (50% each) rather than deriving the weights based on the portfolio's expected return. The calculation for an equally weighted portfolio with uncorrelated returns (correlation = 0) would yield a standard deviation of 13.4%, but this does not align with the given expected return of 12.6%.
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Option B (15.2%) is correct. The weights of the securities are calculated by solving for the portfolio return equation:
Rp = W1 * R1 + W2 * R2 12.6% = W1 * 17% + (1 - W1) * 6% W1 = 0.6, W2 = 0.4The portfolio variance for uncorrelated returns (Cov(R1, R2) = 0) is:
σp² = (W1 * σ1)² + (W2 * σ2)² σp² = (0.6 * 0.24)² + (0.4 * 0.12)² σp² = 0.0207 + 0.0023 = 0.0230 σp = √0.0230 ≈ 15.2% -
Option C (19.2%) is incorrect because it incorrectly assumes the portfolio standard deviation is the weighted average of the individual securities' standard deviations. This would only hold true if the correlation between the securities were 1, which is not the case here.