Financial Risk Manager Part 1

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Raul Perez, a portfolio manager, created the following portfolio:

Security	Security Weight (%)	Expected Standard deviation(%)
A	40	7
B	60	12

If the covariance of returns between the two securities is -0.004, then what is the expected standard deviation of the portfolio?

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TTanishq

6.36%

6.56%

8.14%

6.10%

Explanation:

The portfolio standard deviation is calculated using the portfolio variance formula:

$\sigma_P^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2 \text{Cov}(R_1, R_2)$

Given:

w₁ = 0.4, σ₁ = 7% = 0.07
w₂ = 0.6, σ₂ = 12% = 0.12
Cov(R₁, R₂) = -0.004

Calculation: $\sigma_P^2 = (0.4)^2(0.07)^2 + (0.6)^2(0.12)^2 + 2(0.4)(0.6)(-0.004)$ $= (0.16)(0.0049) + (0.36)(0.0144) + (0.48)(-0.004)$ $= 0.000784 + 0.005184 - 0.00192$ $= 0.004048$

$\sigma_P = \sqrt{0.004048} = 0.063624 = 6.36\%$

The negative covariance reduces the portfolio variance, resulting in a lower standard deviation than the weighted average of the individual standard deviations._

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