mouse123

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 = 0.04666; Standard Deviation = 21.60%.

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

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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.
0.038360.5 = 0.1959 or 19.59%.

mouse123

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

A) The beta of each asset.

B) Each asset’s standard deviation.

C) Each asset weight in the portfolio.

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The formula for calculating the variance of a two-asset portfolio is:
σp2 = WA2σA2 + WB2σB2 + 2WAWBCov(a,b)

mouse123

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) 0.5795.

C) 0.3400.

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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

mouse123

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

• σA = 55%
• σB = 85%
• CovarianceA,B = 0.09
• WA = 70%
• WB = 30%

The variance of the portfolio is closest to:

A) 0.25

B) 0.39

C) 0.54

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

s2 = [WA2σA2 + WB2σB2 + 2WAWBσAσBrA,B]

Since σAσBrA,B = CovA,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.

mouse123

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 + 2W1W2σ1σ2r1,2], or [(0.15)2(0.0071) + (0.85)2(0.0008) + (2)(0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007.

mouse123

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

• σA = 20%
• σB = 15%
• rA,B = 0.32
• WA = 70%
• WB = 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 = [WA2sA2 + WB2sB2 + 2WAWBsAsBrA,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 = 0.02565701/2 = 0.1602, or approximately 16.0%.

mouse123

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) 0.151.

B) 0.426.

C) 0.370.

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σ portfolio = [W12σ12 + W22σ22 + 2W1W2σ1σ2r1,2]1/2 given r1,2 = +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

mouse123

Which one of the following statements about correlation is NOT correct?

A) The covariance is equal to the correlation coefficient times the standard deviation of one stock times the standard deviation of the other stock.

B) Positive covariance means that asset returns move together.

C) If two assets have perfect negative correlation, it is impossible to reduce the portfolio's overall variance.

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This statement should read, "If two assets have perfect negative correlation, it is possible to reduce the portfolio's overall variance to zero."

mouse123

A portfolio currently holds Randy Co. and the portfolio manager is thinking of adding either XYZ Co. or Branton Co. to the portfolio. All three stocks offer the same expected return and total risk. The covariance of returns between Randy Co. and XYZ is +0.5 and the covariance between Randy Co. and Branton Co. is -0.5. The portfolio's risk would decrease:

A) most if she put half your money in XYZ Co. and half in Branton Co.

B) more if she bought Branton Co.

C) more if she bought XYZ Co.

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In portfolio composition questions, return and standard deviation are the key variables. Here you are told that both returns and standard deviations are equal. Thus, you just want to pick the companies with the lowest covariance, because that would mean you picked the ones with the lowest correlation coefficient.
σportfolio = [W12 σ12 + W22 σ22 + 2W1 W2 σ1 σ2 r1,2]½ where σRandy = ΥBranton = σXYZ so you want to pick the lowest covariance which is between Randy and Branton.

mouse123

A portfolio manager adds a new stock that has the same standard deviation of returns as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1. Adding this stock will have what effect on the standard deviation of the revised portfolio's returns? The standard deviation will:

A) increase.

B) decrease.

C) decrease only if the correlation is negative.

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If the correlation coefficient is less than 1, there are benefits to diversification. Thus, adding the stock will reduce the portfolio's standard deviation.