1215

What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

A) 6.20%.

B) 0.38%.

C) 6.83%.

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The standard deviation of the portfolio is found by:

[W₁² σ₁² + W₂² σ₂² + 2W₁W₂σ₁σ₂r_1,2]^0.5, or [(0.30)²(0.046)² + (0.70)²(0.078)² + (2)(0.30)(0.70)(0.046)(0.078)(0.45)]^0.5 = 0.0620, or 6.20%.

1215

An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

• σ_R = 34%
• σ_S = 16%
• r_R,S = 0.67
• W_R = 80%
• W_S = 20%

A) 7.8%.

B) 29.4%.

C) 8.7%.

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The formula for the standard deviation of a 2-stock portfolio is:

s = [W_A²s_A² + W_B²s_B² + 2W_AW_Bs_As_Br_A,B]^1/2

s = [(0.8² × 0.34²) + (0.2² × 0.16²) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]^1/2 = [0.073984 + 0.001024 + 0.0116634]^1/2 = 0.0866714^1/2 = 0.2944, or approximately 29.4%.