Finance 10 Problems Set

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In a multifactor APT model, the coefficients on the macro factors are often called

systemic risk.

firm-specific risk.

idiosyncratic risk.

factor betas.

Multiple Choice Difficulty: 1 Basic

Consider the multifactor APT with two factors. Stock A has an expected return of 17.6%, a beta of 1.45 on factor 1, and

a beta of .86 on factor 2. The risk premium on the factor 1 portfolio is 3.2%. The risk-free rate of return is 5%. What is

the risk-premium on factor 2 if no arbitrage opportunities exist?

9.26%

3%

4%

7.75%

Multiple Choice Difficulty: 3 Challenge

The exploitation of security mispricing in such a way that risk-free economic profits may be earned is called

arbitrage.

capital asset pricing.

factoring.

fundamental analysis.

None of the options

Multiple Choice Difficulty: 1 Basic

Consider the one-factor APT. The variance of returns on the factor portfolio is 6%. The beta of a well-diversified

portfolio on the factor is 1.1. The variance of returns on the well-diversified portfolio is approximately

3.6%.

6.0%.

7.3%.

10.1%.

Multiple Choice Difficulty: 2 Intermediate

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Consider the multifactor APT with two factors. Stock A has an expected return of 16.4%, a beta of 1.4 on factor 1 and a

beta of .8 on factor 2. The risk premium on the factor 1 portfolio is 3%. The risk-free rate of return is 6%. What is the

risk-premium on factor 2 if no arbitrage opportunities exist?

2%

3%

4%

7.75%

Multiple Choice Difficulty: 3 Challenge

Suppose that two factors have been identified for the U.S. economy: the growth rate of industrial

production, IP, and the inflation rate, IR. IP is expected to be 2%, and IR 2.0%. A stock with a beta of 0.9

on IP and 0.4 on IR currently is expected to provide a rate of return of 6%. If industrial production actually

grows by 4%, while the inflation rate turns out to be 4.0%, what is your revised estimate of the expected

rate of return on the stock? (Do not round intermediate calculations. Round your answer to 1

decimal place. Omit the "%" sign in your response.)

Revised expected rate of

return %

Worksheet Difficulty: 1 Basic

Assume that security returns are generated by the single-index model,

Ri

= ?i

+ ?i

RM + ei

where Ri

is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%.

Suppose also that there are three securities A, B, and C, characterized by the following data:

Security ?i E(Ri

) ?(ei

)

A 1.5 6% 29%

B 1.7 8 15

C 1.9 10 24

a. If ?M = 26%, calculate the variance of returns of securities A, B, and C. (Do not round intermediate

calculations. Round your answers to the nearest whole number.)

Variance

Security A

Security B

Security C

b. Now assume that there are an infinite number of assets with return characteristics identical to those of

A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B,

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and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not

round intermediate calculations. Round your answers to the nearest whole number. Omit the

"%" sign in your response.)

Mean Variance

Security A %

Security B

Security C

Worksheet Difficulty: 2 Intermediate

Consider the following multifactor (APT) model of security returns for a particular stock.

Factor Factor Beta Factor Risk Premium

Inflation 1.0 9%

Industrial production 0.5 10

Oil prices 0.2 8

a. If T-bills currently offer a 8% yield, find the expected rate of return on this stock if the market views the

stock as fairly priced. (Do not round intermediate calculations. Round your answer to 1 decimal

place. Omit the "%" sign in your response.)

Expected rate of return %

b. Suppose that the market expected the values for the three macro factors given in column 1 below, but

that the actual values turn out as given in column 2. Calculate the revised expectations for the rate of

return on the stock once the "surprises" become known. (Do not round intermediate calculations.

Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Factor

Expected Rate of

Change

Actual Rate

of Change

Inflation 8% 8%

Industrial production 4 10

Oil prices 2 0

Expected rate of return %

Worksheet Difficulty: 2 Intermediate

Suppose that the market can be described by the following three sources of systematic risk with

associated risk premiums.

Factor Risk Premium

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Industrial production (I) 8%

Interest rates (R) 4

Consumer confidence (C) 6

The return on a particular stock is generated according to the following equation:

r = 16% + 1.6I + 0.8R + 1.30C + e

a-1. Find the equilibrium rate of return on this stock using the APT. The T-bill rate is 4%. (Do not round

intermediate calculations. Omit the "%" sign in your response.)

Equilibrium rate of return %

a-2. Is the stock over- or underpriced?

Overpriced

Underpriced

Worksheet Difficulty: 2 Intermediate

Assume that security returns are generated by the single-index model,

Ri

= ?i

+ ?i

RM + ei

where Ri

is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%.

Suppose also that there are three securities A, B, and C, characterized by the following data:

Security ?i E(Ri

) ?(ei

)

A 0.8 10% 25%

B 1.0 12 10

C 1.2 14 20

a. If ?M = 20%, calculate the variance of returns of securities A, B, and C. (Do not round intermediate

calculations. Round your answers to the nearest whole number.)

Variance

Security A

Security B

Security C

b. Now assume that there are an infinite number of assets with return characteristics identical to those of

A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B,

and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not

round intermediate calculations. Round your answers to the nearest whole number. Omit the

"%" sign in your response.)

Mean Variance

Security A %

Security B %

Security C %

Worksheet Difficulty: 2 Intermediate

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