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发表于 2011-3-24 15:44 | 只看该作者

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

2011, investing, standard, stocks
Session 12: Portfolio Management
Reading 52: Portfolio Risk and Return: Part I

LOS f: Describe the effect on a portfolio's risk of investing in assets that are less than perfectly correlated.

 

 

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)
63% 37%
B)
0% 100%
C)
100% 0%

 

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.

 

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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.

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]? where σRandy = ΥBranton = σXYZ so you want to pick the lowest covariance which is between Randy and Branton.

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发表于 2011-3-24 15:44 | 只看该作者

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.

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发表于 2011-3-24 15:44 | 只看该作者

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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发表于 2011-3-24 15:44 | 只看该作者

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

A)
 If two assets have perfect negative correlation, it is impossible to reduce the portfolio's overall variance.
B)
 The covariance is equal to the correlation coefficient times the standard deviation of one stock times the standard deviation of the other stock.
C)
 Positive covariance means that asset returns move together.

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

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发表于 2011-3-24 15:45 | 只看该作者

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.

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发表于 2011-3-24 15:45 | 只看该作者

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.

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发表于 2011-3-24 15:45 | 只看该作者

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

A)
 If the correlation coefficient were 0, a zero variance portfolio could be constructed.
B)
 Potential benefits from diversification arise when correlation is less than +1.
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.

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发表于 2011-3-24 15:45 | 只看该作者

There are benefits to diversification as long as:

A)
 there is perfect positive correlation between the assets.
B)
 there must be perfect negative correlation between the assets.
C)
 the correlation coefficient between the assets is less than 1.

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

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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)
 30% in Stock A and 70% in Stock B.
B)
 50% in Stock A and 50% in Stock B.
C)
 100% in Stock B.

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

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