[2008]Topic 63: Investors and Risk Management相关习题 investment, currently, companies, between, percent

nayizhenfeng

 

AIM 1: Describe how the covariance/correlation of returns between securities affects the returns distribution of a portfolio of securities.

 

1、Mital Tiene’s investment portfolio currently consists of stocks in two companies, 40 percent in Drysdahl Banking and the remaining amount in Clampett Oil. Performance measurement information for these two stocks is given in the table below:  

Stock	Expected Return	Standard Deviation
Drysdahl Banking	10.50%	8.5%
Clampett Oil	16.55%	25.0%

The covariance between the two stocks is 0.001. Tiene is considering adding a third stock, Hilbilee Investors. Hilbilee Investor’s correlation coefficient with the current portfolio is 0.38.

Which of the following statements is least accurate?

A) With Hilbilee added to the portfolio, the variance could be 0.026.  

B) As Tiene diversifies, he will reduce the portfolio's unsystematic risk. 

C) The standard deviation of returns for the current portfolio is 15.5%.  

D) The expected return of Tiene's current portfolio is approximately 14.1%.

nayizhenfeng

 

The correct answer is A

 

Since Hilbilee’s correlation coefficient with the existing portfolio is less than 1, there are benefits to diversification, and adding it to the existing portfolio would reduce the variance below the current level of 0.024. (See calculations below). The other choices are correct.

ER_Portfolio = (w_Drysdahl × ER_Drysdahl) + (w_Clampett × ER_Clampett) = (0.40 × 10.5%) + (0.60 × 16.55%) = 14.13%.

The equation for the standard deviation = σ_1,2 = [(w₁²)(σ₁²) + (w₂²)(σ₂²) + 2w₁w₂σ₁σ₂ρ_1,2]^1/2,

Here stock 1 = Drysdahl and stock 2 = Clampett, and r_1,2 = cov_1,2 / (σ₁ × σ₂) = 0.001 / (0.085 × 0.25) = 0.047

σ_Portfolio = [(0.40² × 0.085²) + (0.60² × 0.25²) + (2 × 0.40 × 0.60 × 0.085 × 0.25 × 0.047)]^1/2 = 0.024^1/2, or 0.155 = 15.5%. (The variance is 0.024).

nayizhenfeng

 

2、 investor owns the following three-stock portfolio today.

Stock                       Market Value                 Expected Annual Return 

K                         $4,500                                       14% 

L                         $6,300                                        9% 

M                        $3,700                                        12%  

The expected portfolio value two years from now is closest to:

A) $16,150.  

B) $14,960. 

C) $17,975. 

D) $17,870.

nayizhenfeng

 

The correct answer is C

 

The easiest way to approach this problem is to determine the value of each stock two years in the future and to sum up the total values of each stock.

Stock           Market Value  ×       Expected Annual Return     =   Total

K                 $4,500   ×               1.14 × 1.14       =   5,848.20

L                  $6,300   ×               1.09 × 1.09       =   7,485.03

M                 $3,700   ×               1.12 × 1.12       =   4,641.28

                                                   Total                =   17,974.51

nayizhenfeng

 

3、If the correlation between assets is less than one, the portfolio variance is less than the weighted average of the variances of the individual securities. This is an example of the:

A) benefits of diversification.  

B) limits of VAR. 

C) variance mapping effect. 

D) variance/covariance effect.

nayizhenfeng

 

The correct answer is A

 

The reduction in variance through the combination of instruments with a correlation of less than one is an example of the benefits of diversification.

nayizhenfeng

 

4、Which of the following statements regarding risk is FALSE? The:

A) expected return for a portfolio is calculated as a weighted average where the weights are based on percentage of asset allocation in each security.  

B) standard deviation of a portfolio is calculated as a weighted average of individual standard deviations where the weights are based on the percentage of asset allocation in each security. 

C) risk for the portfolio is based on dispersion of returns around the expected return.  

D) portfolio's variance or standard deviation is a good measure of total risk.

nayizhenfeng

 

The correct answer is B

 

The standard deviation of a portfolio is calculated using the Markowitz equation. Security correlations are the key to diversification benefits. For a two-asset portfolio the expected return for the portfolio is simply based on the weighted-average return and is a linear relationship based on the percentage allocated in each asset. However, if two assets are not perfectly correlated, the standard deviation or total risk for the portfolio will be reduced based on how the assets are correlated with each other.

nayizhenfeng

 

AIM 2: Describe the efficient frontier and the asset allocation decision both with and without the presence of a riskless asset.

1、All portfolios on the capital market line are:

A) distinct from each other.  

B) unrelated except that they all contain the risk-free asset. 

C) perfectly negatively correlated.  

D) perfectly positively correlated. 

nayizhenfeng

 

The correct answer is D

 

The introduction of a risk-free asset changes the Markowitz efficient frontier into a straight line. This straight efficient frontier line is called the capital market line (CML). Since the line is straight, the math implies that any two assets falling on this line will be perfectly, positively correlated with each other. Note: When ra,b = 1, then the equation for risk changes to sport = WAsA + WBsB, which is a straight line.