Reading 52: Portfolio Risk and Return: Part I-LOS e 习题精选 invest

1215

Session 12: Portfolio Management
Reading 52: Portfolio Risk and Return: Part I

LOS e: Calculate and interpret portfolio standard deviation.

 

 

Two assets are perfectly positively correlated. If 30% of an investor's funds were put in the asset with a standard deviation of 0.3 and 70% were invested in an asset with a standard deviation of 0.4, what is the standard deviation of the portfolio?

A) 0.370.

B) 0.151.

C) 0.426.

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σ portfolio = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂r_1,2]^1/2 given r_1,2 = +1

σ = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂]^1/2 = (W₁σ₁ + W₂σ₂)²]^1/2

σ = (W₁σ₁ + W₂σ₂) = (0.3)(0.3) + (0.7)(0.4) = 0.09 + 0.28 = 0.37

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Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40% invested in A, the portfolio standard deviation is closest to:

A) 0.3742.

B) 0.3400.

C) 0.5795.

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The portfolio standard deviation = [(0.4)²(0.25) + (0.6)²(0.4) + 2(0.4)(0.6)1(0.25)^0.5(0.4)^0.5]^0.5 = 0.5795

1215

An investor has a two-stock portfolio (Stocks A and B) with the following characteristics:

• σ_A = 55%
• σ_B = 85%
• Covariance_A,B = 0.09
• W_A = 70%
• W_B = 30%

The variance of the portfolio is closest to:

A) 0.39

B) 0.25

C) 0.54

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

s² = [W_A²σ_A² + W_B²σ_B² + 2W_AW_Bσ_Aσ_Br_A,B]

Since σ_Aσ_Br_A,B = Cov_A,B, then

s² = [(0.7² × 0.55²) + (0.3² × 0.85²) + (2 × 0.7 × 0.3 × 0.09)] = [0.1482 + 0.0650 + 0.0378] = 0.2511.

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What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04?

A) 0.0020.

B) 0.0026.

C) 0.0007.

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The variance of the portfolio is found by:

[W₁² σ₁² + W₂² σ₂² + 2W₁W₂σ₁σ₂r_1,2], or [(0.15)²(0.0071) + (0.85)²(0.0008) + (2)(0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007.

1215

Betsy Minor is considering the diversification benefits of a two stock portfolio. The expected return of stock A is 14 percent with a standard deviation of 18 percent and the expected return of stock B is 18 percent with a standard deviation of 24 percent. Minor intends to invest 40 percent of her money in stock A, and 60 percent in stock B. The correlation coefficient between the two stocks is 0.6. What is the variance and standard deviation of the two stock portfolio?

A) Variance = 0.02206; Standard Deviation = 14.85%.

B) Variance = 0.03836; Standard Deviation = 19.59%.

C) Variance = 0.04666; Standard Deviation = 21.60%.

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(0.40)²(0.18)² + (0.60)²(0.24)² + 2(0.4)(0.6)(0.18)(0.24)(0.6) = 0.03836.

0.03836^0.5 = 0.1959 or 19.59%.

1215

Which of the following measures is NOT considered when calculating the risk (variance) of a two-asset portfolio?

A) Each asset’s standard deviation.

B) The beta of each asset.

C) Each asset weight in the portfolio.

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The formula for calculating the variance of a two-asset portfolio is:

σ_p² = W_A²σ_A² + W_B²σ_B² + 2W_AW_BCov(a,b)

1215

An investor calculates the following statistics on her two-stock (A and B) portfolio.

• σ_A = 20%
• σ_B = 15%
• r_A,B = 0.32
• W_A = 70%
• W_B = 30%

The portfolio's standard deviation is closest to:

A) 0.1832.

B) 0.1600.

C) 0.0256.

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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 = [(0.7² × 0.2²) + (0.3² × 0.15²) +( 2 × 0.7 × 0.3 × 0.2 × 0.15 × 0.32)]^1/2 = [0.0196 + 0.002025 + 0.004032]^1/2 = 0.0256570^1/2 = 0.1602, or approximately 16.0%.