York University

ADMD 4501

CHAPTER 8

AN INTRODUCTION TO ASSET PRICING MODELS

TRUE/FALSE QUESTIONS

1)One of the assumptions of capital market theory is that investors can borrow or lend at the risk free rate.

 

 2                           Since many of the assumptions made by the capital market theory are unrealistic, the theory is not applicable in the real world.

 

 3                           A risk-free asset is one in which the return is completely guaranteed, there is no uncertainty.

 

 4                           The market portfolio consists of all risky assets.

 

 5                           The introduction of lending and borrowing severely limits the available risk/return opportunities.

 

 6                           The capital market line is the tangent line between the risk free rate of return and the efficient frontier.

 

 7                           The portfolio on the capital market line are combinations of the risk-free asset and the market portfolio.

 

 8                           If you borrow money at the RFR and invest the money in the market portfolio, the rate of return on your portfolio will be higher than the market rate of return.

 

 9                           Studies have shown that a well diversified investor needs as few as five stocks.

 

 10                         Beta is a measure of unsystematic risk.

 

 11                         The betas of those companies compiled by Value Line Investment Services tend to be almost identical to those compiled by Merrill Lynch.

 

 12                         Securities with returns that lie above the security market line are undervalued.

 

 13                         Securities with returns that lie below the security market line are undervalued.

 

 14                         Under the CAPM framework, the introduction of lending and borrowing at differential rates leads to a non-linear capital market line.

 

 15                         Correlation of the market portfolio and the zero-beta portfolio will be linear.

 16                         There can be only one zero-beta portfolio.

 

                17           The existence of transaction costs indicates that at some point the additional cost of diversification relative to its benefit would be excessive for most investors.

 

 18                         Studies have shown the beta is more stable for portfolios than for individual securities.

 

 19                         If the market portfolio is mean-variance efficient it has the lowest risk for a given level of return among the attainable set of portfolios.

 

 20                         Using the S&P index as the proxy market portfolio when evaluating a portfolio manager relative to the SML will tend to underestimate the manager's performance.

 

 21                         If an incorrect proxy market portfolio such as the S&P index is used when developing the security market line, the slope of the line will tend to be underestimated.

 

 22                         Since the market portfolio is reasonable in theory, therefore it is easy to implement when testing or using the CAPM.

 

 23                         The planning period for the CAPM is the same length of time for every investor.

 

 

 

 

MULTIPLE CHOICE PROBLEMS

 

2. 1                      Calculate the expected return for A Industries which has a beta of 1.75 when the risk free rate is 0.03 and you expect the market return to be 0.11.

a)            11.13%

b)            14.97%

c)            16.25%

d)            22.25%

e)            17.0%

(c) 2                       Calculate the expected return for B Services which has a beta of 0.83 when the risk free rate is 0.05 and you expect the market return to be 0.12.

a)            14.96%

b)            16.15%

c)            10.81%

d)            17.00%

e)            15.25%

 

(c) 3                       Calculate the expected return for C Inc. which has a beta of 0.8 when the risk free rate is 0.04 and you expect the market return to be 0.12.

a)                 8.10%

b)                 9.60%

c)               10.40%

d)              11.20%

e)              12.60%

 

(e) 4                      Calculate the expected return for D Industries which has a beta of 1.0 when the risk free rate is 0.03 and you expect the market return to be 0.13.

a)             8.6%

b)             9.2%

c)           11.0%

d)          12.0%

e)          13.0%

 

(d) 5                      Calculate the expected return for E Services which has a beta of 1.5 when the risk free rate is 0.05 and you expect the market return to be 0.11.

a)            10.6%

b)            12.1%

c)            13.6%

d)            14.0%

e)            16.2%

 

 

(c) 6                       Calculate the expected return for F Inc. which has a beta of 1.3 when the risk free rate is 0.06 and you expect the market return to be 0.125.

a)            12.65%

b)            13.55%

c)            14.45%

d)            15.05%

e)            16.34%

 

 

USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS

 

Rates of Return

Year                            RA Computer                  Market Index 1                                 13                                      17

2	9	15
3	-11	6
4	10	8
5	11	10
6	6	12

 

(c) 7                       Compute the beta for RA Computer using the historic returns presented above. a)               0.7715

b)               1.2195

c)                1.3893

d)               1.1023

e)               -0.7715

 

(c)           8              Compute the correlation coefficient between RA Computer and the Market Index.

a)             -0.32

b)              0.78

c)               0.66

d)              0.58

e)              0.32

(a) 9                      Compute the intercept of the characteristic line for RA Computer. a)             -9.41

b)              11.63

c)               4.92

d)             -4.92

e)             -7.98

 

 

 

 

(c) 10                    The equation of the characteristic line for RA is a)            R_RA = 11.63 + 1.2195R_MI

b)            R_RA = -7.98 + 1.1023R_MI

c)            R_RA = -9.41 + 1.3893R_MI

d)            R_RA = - 4.92 – 0.7715R_MI

e)            R_RA = 4.92 + 0.7715R_MI

 

1. 11                                   If you expected return on the Market Index to be 12%, what would you expect the return on RA Computer to be?

a)               7.26%

b)               6.75%

c)                8.00%

d)               9.37%

e)               -3.29%

 

USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS

 

You expect the risk-free rate (RFR) to be 3 percent and the market return to be 8 percent. You also have the following information about three stocks.

 

STOCK	BETA	CURRENT PRICE	EXPECTED PRICE	EXPECTED DIVIDEND
X	1.25	$ 20	$ 23	$ 1.25
Y	1.50	$ 27	$ 29	$ 0.25
Z	0.90	$ 35	$ 38	$ 1.00

 

2. 12                   What are the expected (required) rates of return for the three stocks (in the order X, Y, Z)?

a)            16.50%, 5.50%, 22.00%

b)            9.25%, 10.5%, 7.5%

c)            21.25%, 8.33%, 11.43%

d)            6.20%, 2.20%,  8.20%

e)            15.00%, 3.50%, 7.30%

 

(a) 13                    What are the estimated rates of return for the three stocks (in the order X, Y, Z)?

a)            21.25%, 8.33%, 11.43%

b)            6.20%, 2.20%,  8.20%

c)            16.50%, 5.50%, 22.00%

d)            9.25%, 10.5%, 7.5%

e)            15.00%, 3.50%, 7.30%

 

 

 

 

5. 14                   What is your investment strategy concerning the three stocks?
   1. Buy X and Y, sell Z.
   2. Sell X, Y and Z.
   3. Sell X and Z, buy Y.
   4. Buy X, Y and Z.
   5. Buy X and Z, sell Y.

 

2. 15                   Recently you have received a tip that the stock of Bubbly Incorporated is going to rise from $57 to $61 per share over the next year. You know that the annual return on the S&P 500 has been 9.25% and the 90-day T-bill rate has been yielding 3.75% per year over the past 10 years. If beta for Bubbly is 0.85, will you purchase the stock?
   1. Yes, because it is overvalued.
   2. No, because it is overvalued.
   3. No, because it is undervalued.
   4. Yes, because it is undervalued.
   5. Yes, because the expected return equals the estimated return.

2. 16                   Your broker has advised you that he believes that the stock of Brat Inc. is going to rise from $20 to $22.15 per share over the next year. You know that the annual return on the S&P 500 has been 11.25% and the 90-day T-bill rate has been yielding 4.75% per year over the past 10 years. If beta for Brat is 1.25, will you purchase the stock?
   1. Yes, because it is overvalued
   2. No, because it is overvalued
   3. No, because it is undervalued
   4. Yes, because it is undervalued
   5. Yes, because the expected return equals the estimated return

 

4. 17                   Recently you have received a tip that the stock of Buttercup Industries is going to rise from $76.00 to $85.00 per share over the next year. You know that the annual return on the S&P 500 has been 13% and the 90-day T-bill rate has been yielding 3% per year over the past 10 years. If beta for Buttercup is 1.0, will you purchase the stock?
   1. Yes, because it is overvalued.
   2. Yes, because it is undervalued.
   3. No, because it is undervalued.
   4. No, because it is overvalued.
   5. Yes, because the expected return equals the estimated return.

 

 

 

 

2. 18                   A friend has some reliable information that the stock of Puddles Company is going to rise from $43.00 to $50.00 per share over the next year. You know that the annual return on the S&P 500 has been 11% and the 90-day T-bill rate has been yielding 5% per year over the past 10 years. If beta for Puddles is 1.5, will you purchase the stock?
   1. Yes, because it is overvalued.
   2. Yes, because it is undervalued.
   3. No, because it is undervalued.
   4. No, because it is overvalued.
   5. Yes, because the expected return equals the estimated return.

 

2. 19                   Recently your broker has advised you that he believes that the stock of Casey Incorporated is going to rise from $55.00 to $70.00 per share over the next year. You know that the annual return on the S&P 500 has been 12.5% and the 90-day T-bill rate has been yielding 6% per year over the past 10 years. If beta for Casey is 1.3, will you purchase the stock?
   1. Yes, because it is overvalued.
   2. Yes, because it is undervalued.
   3. No, because it is undervalued.
   4. No, because it is overvalued.
   5. Yes, because the expected return equals the estimated return.

4. 20                   A friend has information that the stock of Zip Incorporated is going to rise from $62.00 to $65.00 per share over the next year. You know that the annual return on the S&P 500 has been 10% and the 90-day T-bill rate has been yielding 6% per year over the past 10 years. If beta for Zip is 0.9, will you purchase the stock?
   1. Yes, because it is overvalued.
   2. Yes, because it is undervalued.
   3. No, because it is undervalued.
   4. No, because it is overvalued.
   5. Yes, because the expected return equals the estimated return.

 

(a)                          21 Assume that as a portfolio manager the beta of your portfolio is 0.85 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = 0.0475	Rm(proxy) = 0.0975
2)	RK = 0.0325	Rm(true) = 0.0845
a) b) c) d) e)	1.33% higher 2.35% lower 8% lower 1.33% lower 2.35% higher

 

3. 22 Assume that as a portfolio manager the beta of your portfolio is 1.15 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = 0.0625	Rm(proxy) = 0.12
2)	RK = 0.078	Rm(true) = 0.10
a) b) c) d) e)	2.53% lower 3.85% lower 2.53% higher 4.4% higher 3.85% higher

 

1. 1. 23                   Assume that as a portfolio manager the beta of your portfolio is 1.3 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = .08	Rm(proxy) = .11
2)	RK = .07	Rm(true) = .14
a) b) c)	4.2% lower 3.6% lower 3.8% lower

4. 4.2% higher
5. 3.6% higher

 

1. 2. 24                   Assume that as a portfolio manager the beta of your portfolio is 1.2 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = .09	Rm(proxy) = .12
2)	RK = .10	Rm(true) = .13
a) b) c) d) e)	2% lower 1% lower 5% lower 1% higher 2% higher

 

 

 

 

(d) 25                    Assume that as a portfolio manager the beta of your portfolio is 1.1 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = .07	Rm(proxy) = .15
2)	RK = .06	Rm(true) = .12
a) b) c) d) e)	3.2% lower 6.4% lower 4.9% lower 3.2% higher 6.4% higher

 

4. 26                   Assume that as a portfolio manager the beta of your portfolio is 1.4 and that your performance is exactly on target with the SML data under condition 1. If the true SML data is given by condition 2, how much does your performance differ from the true SML?

1)	RFR = .06	Rm(proxy) = .12
2)	RK = .05	Rm(true) = .11
a) b) c) d) e)	2.0% lower 0.5% lower 0.5% lower 1.0% higher 2.0% higher

 

USE THE FOLLOWING INFORMATION FOR THE NEXT SEVEN PROBLEMS

 

Period	Return of Radtron (Percent)	Proxy Specific Index (Percent)	True General Index (Percent)
1	10	12	15
2	12	10	13
3	-10	-8	-8
4	-4	-10	0

 

5. 27                   The average true return is
   1. 1%
   2. 2%
   3. 3%
   4. 4%
   5. 5%

 

 

2. 28                   The average proxy return is
   1. 1%
   2. 2%
   3. 3%
   4. 4%
   5. 5%

 

1. 29                   The average return for Radtron is
   1. 1%
   2. 2%
   3. 3%
   4. 4%
   5. 5%

(c) 30                    The covariance between Radtron and the proxy index is a)               57.30

b)              86.50

c)               88.00

d)              92.50

e)            107.90

(b) 31                    The covariance between Radtron and the true index is a)            57.30

b)              86.50

c)               88.00

d)              92.50

e)            107.90

1. 32                   What is the beta for Radtron using the proxy index?

a)            0.87

b)            0.97

c)            1.02

d)            1.15

e)            1.28

 

2. 33                   What is the beta for Radtron using the true index? a)           0.87

b)            0.97

c)            1.02

d)            1.15

e)            1.28

 

 

 

2. 34                                 Consider an asset that has a beta of 1.5. The return on the risk-free asset is 6.5%

and the expected return on the stock index is 15%. The estimated return on the asset is 20%. Calculate the alpha for the asset.

a)               19.25%

b)               0.75%

c)                –0.75%

d)               9.75%

e)               9.0%

 

 

3. 35                                 The variance of returns for a risky asset is 25%. The variance of the error term,

Var(e) is 8%. What portion of the total risk of the asset, as measured by variance,

is systematic?

a)               32%

b)               8%

c)                68%

d)               25%

e)               75%

 

1. 36                                 An investor wishes to construct a portfolio consisting of a 70% allocation to a

stock index and a 30% allocation to a risk free asset. The return on the risk- free

asset is 4.5% and the expected return on the stock index is 12%. The standard deviation of returns on the stock index 6%. Calculate the expected standard deviation of the portfolio.

a)         4.20%

b)               25.20%

c)                3.29%

d)               10.80%

e)               5.02%

 

2. 37                                 An investor wishes to construct a portfolio by borrowing 35% of his original

wealth and investing all the money in a stock index. The return on the risk- free

asset is 4.0% and the expected return on the stock index is 15%. Calculate the expected return on the portfolio.

a)               18.25%

b)               18.85%

c)                9.50%

d)               15.00%

e)               11.15%

 

 

 

 

 

(d) 38                                 An investor wishes to construct a portfolio consisting of a 70% allocation to a

stock index and a 30% allocation to a risk free asset. The return on the risk- free

asset is 4.5% and the expected return on the stock index is 12%. Calculate the expected return on the portfolio.

a)               8.25%

b)               16.50%

c)                17.50%

d)               9.75%

e)               14.38%

 

4. 39                                 A stock has a beta of the stock is 1.25. The risk free rate is 5% and the return on

the market is 6%. The estimated return for the stock is 14%. According to the CAPM you should

1. 1. Sell because it is overvalued.
   2. Sell because it is undervalued.
   3. Buy because it overvalued.
   4. Buy because it is undervalued.
   5. Short because it is undervalued.

 

(b) 40                                 Consider a risky asset that has a standard deviation of returns of 15.

Calculate the

correlation between the risky asset and a risk free asset. a)   1.0

b)               0.0

c)                -1.0

d)                0.5

e)               -0.5

 

(a) 41                                 The expected return for a stock, calculated using the CAPM, is 10.5%.

The

market return is 9.5% and the beta of the stock is 1.50. Calculate the implied risk-free rate.

a)               7.50%

b)               13.91%

c)                17.50%

d)               21.88%

e)               14.38%

 

(e) 42                                 The expected return for a stock, calculated using the CAPM, is 25%.

The risk free

rate is 7.5% and the beta of the stock is 0.80. Calculate the implied return on the

market.

a)               7.50%

b)               13.91%

c)                17.50%

d)               21.88%

e)               14.38%

 

 

(c) 43                                  The expected return for Zbrite stock calculated using the CAPM is 15.5%. The

risk free rate is 3.5% and the beta of the stock is 1.2. Calculate the implied market

risk premium.

a)               5.5%

b)               6.5%

c)                10.0%

d)               15.5%

e)            12.0%