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标题: Reading 50: An Introduction to Portfolio Management LOS e习题 [打印本页]

作者: honeycfa 时间: 2010-4-21 14:16 标题: [2010]Session 12-Reading 50: An Introduction to Portfolio Management LOS e习题

LOS e: List the components of the portfolio standard deviation formula.

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)
decrease.

B)
increase.

C)
decrease only if the correlation is negative.

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

作者: honeycfa 时间: 2010-4-21 14:17

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.

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)

作者: honeycfa 时间: 2010-4-21 14:17

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.

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

作者: honeycfa 时间: 2010-4-21 14:17

As the correlation between the returns of two assets becomes lower, the risk reduction potential becomes:

A)
greater.

B)
smaller.

C)
decreased by the same level.

Perfect positive correlation (r = +1) of the returns of two assets offers no risk reduction, whereas perfect negative correlation (r = -1) offers the greatest risk reduction.

作者: honeycfa 时间: 2010-4-21 14:18

Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?

A)
0.00.

B)
+1.00.

C)
+0.50.

Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio.

作者: honeycfa 时间: 2010-4-21 14:18

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

σ_A = 55%
σ_B = 85%
Covariance_A,B = 0.9
W_A = 70%
W_B = 30%

The variance of the portfolio is closest to:

A)
0.39

B)
0.59

C)
0.54

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 × 0.9)] = [0.14822 + 0.06502 + 0.378] = 0.59124, or approximately 0.59.

作者: honeycfa 时间: 2010-4-21 14:18

An investor’s portfolio currently consists of 100% of stocks that have a mean return of 16.5% and an expected variance of 0.0324. The investor plans to diversify slightly by replacing 20% of her portfolio with U.S. Treasury bills that earn 4.75%. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio?

ER_Portfolio

σ_Portfolio

A)

14.15%

14.40%

B)

14.15%

2.59%

C)

10.63%

2.59%

Since Treasury bills (T-bills) are considered risk-free, we know that the standard deviation of this asset and the correlation between T-bills and the other stocks is 0. Thus, we can calculate the portfolio expected return and standard deviation.

Step 1: Calculate the expected return
Expected Return_Portfolio = (w_T-bills × ER_T-bills) + (w_Stocks × ER_Stocks)
= (0.20) × (0.0475) + (1.00-0.20) × (0.165) = 0.1415, or 14.15%.

Step 2: Calculate the expected standard deviation
When combining a risk-free asset and a risky asset (or portfolio or risky assets), the equation for the standard deviation, σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂ σ₁ σ₂ρ_1,2]^1/2, reduces to: σ_1,2 = [(w_Stocks)(σ_Stocks)] = 0.80 × 0.0324^1/2 = 0.14400, or 14.40%. (Remember to convert variance to standard deviation).

作者: honeycfa 时间: 2010-4-21 14:19

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)
0.0007.

C)
0.0026.

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.

作者: honeycfa 时间: 2010-4-21 14:19

Which of the following equations is least accurate?

A)
Real Risk-Free Rate = [(1 + nominal risk-free rate) / (1 + expected inflation)] ? 1.

B)
Required Return_nominal = [(1 + Risk Free Rate_real) × (1 + Expected Inflation) × (1 + Risk Premium)] ? 1.

C)
Standard Deviation_{2-Stock Portfolio} = [(w₁² × σ₁²) + (w₂² × σ₂²) + (2 × w₁ × w₂ σ₁σ₂ × ρ_1,2)].

This is the equation for the variance of a 2-stock portfolio. The standard deviation is the square root of the variance. The other equations are correct.

作者: honeycfa 时间: 2010-4-21 14:19

Stock A has a standard deviation of 4.1% and Stock B has a standard deviation of 5.8%. If the stocks are perfectly positively correlated, which portfolio weights minimize the portfolio’s standard deviation?

Stock A Stock B

A)

100% 0%

B)

63% 37%

C)

0% 100%

Because there is a perfectly positive correlation, there is no benefit to diversification. Therefore, the investor should put all his money into Stock A (with the lowest standard deviation) to minimize the risk (standard deviation) of the portfolio.

作者: honeycfa 时间: 2010-4-21 14:20

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)
0.0256.

C)
0.1600.

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%.

作者: honeycfa 时间: 2010-4-21 14:20

Kendra Jackson, CFA, is given the following information on two stocks, Rockaway and Bridgeport.

Covariance between the two stocks = 0.0325
Standard Deviation of Rockaway’s returns = 0.25
Standard Deviation of Bridgeport’s returns = 0.13

Assuming that Jackson must construct a portfolio using only these two stocks, which of the following combinations will result in the minimum variance portfolio?

A)
50% in Bridgeport, 50% in Rockaway.

B)
80% in Bridgeport, 20% in Rockaway.

C)
100% in Bridgeport.

First, calculate the correlation coefficient to check whether diversification will provide any benefit.

_{Bridgeport, Rockaway}

_Bridgeport

_Rockaway

Since the stocks are perfectly positively correlated, there are no diversification benefits and we select the stock with the lowest risk (as measured by variance or standard deviation), which is Bridgeport.

作者: honeycfa 时间: 2010-4-21 14:20

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.

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

σ = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ_₁σ_₂]^1/2 = (W₁σ₁ + W₂σ₂)²]^1/2

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

作者: honeycfa 时间: 2010-4-21 14:20

Which one of the following statements about correlation is FALSE?

A)
Potential benefits from diversification arise when correlation is less than +1.

B)
If the correlation coefficient were 0, a zero variance portfolio could be constructed.

C)
If the correlation coefficient were -1, a zero variance portfolio could be constructed.

A correlation coefficient of zero means that there is no relationship between the stock's returns. The other statements are true.

作者: honeycfa 时间: 2010-4-21 14:21

There are benefits to diversification as long as:

A)
the correlation coefficient between the assets is less than 1.

B)
there is perfect positive correlation between the assets.

C)
there must be perfect negative correlation between the assets.

There are benefits to diversification as long as the correlation coefficient between the assets is less than 1.

作者: honeycfa 时间: 2010-4-21 14:21

Stock A has a standard deviation of 0.5 and Stock B has a standard deviation of 0.3. Stock A and Stock B are perfectly positively correlated. According to Markowitz portfolio theory how much should be invested in each stock to minimize the portfolio's standard deviation?

A)
100% in Stock B.

B)
30% in Stock A and 70% in Stock B.

C)
50% in Stock A and 50% in Stock B.

Since the stocks are perfectly correlated, there is no benefit from diversification. So, invest in the stock with the lowest risk.

作者: honeycfa 时间: 2010-4-21 14:21

Which of the following statements about portfolio theory is least accurate?

A)
Assuming that the correlation coefficient is less than one, the risk of the portfolio will always be less than the simple weighted average of individual stock risks.

B)
For a two-stock portfolio, the lowest risk occurs when the correlation coefficient is close to negative one.

C)
When the return on an asset added to a portfolio has a correlation coefficient of less than one with the other portfolio asset returns but has the same risk, adding the asset will not decrease the overall portfolio standard deviation.

When the return on an asset added to a portfolio has a correlation coefficient of less than one with the other portfolio asset returns but has the same risk, adding the asset will decrease the overall portfolio standard deviation. Any time the correlation coefficient is less than one, there are benefits from diversification. The other choices are true.

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