CM SampleExam 2

8/10/2019 CM SampleExam 2

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B6302 End-term exam

INSTRUCTIONS: Read these carefully before beginning the exam.

NAME: _____________________________________________

Section: _______________

This exam is taken under the integrity code. The exam is to be done individually. No help can be accepted,

solicited or given during the exam. The exam is open notes, so please use any written material you desire.

You can also use a calculator and/or MS Excel spreadsheets as a calculator but no other computer software.

Any violations of the integrity code will be prosecuted to the fullest extent of the law. This might mean, for

example, that you are given a failing grade in the course for a violation or even expelled from school.

For the multiple choice questions, please circle the correct answer clearly. No partial credit will be given for

multiple choice questions.

For the longer questions, be sure to show all of your work. We will not give credit unless the work is shown,

and you will receive most of the credit if your methodology is correct. Even if you use MS Excel as a

calculator, you still need to show which mathematical formulas you used.

Maintained Assumption: Unless otherwise stated, assume returns are annualized.

The exam has a total of 150 points + 6 bonus points.

Good luck.


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Multiple-choice questions (6 points each; 72 points total + 6 bonus points)

For Questions 1, 2, and 3, use the following assumptions. The risk-free rate is 1%. The expectedmarket premium is E(MktRf) = 5.00%, the size premium is E(SMB) = 3.60%, the value premium isE(HML) = 7.36%, and the momentum premium is E(UMD) = 8.00%. Assume past and future marketvolatility is 20%. All numbers above are annualized.

In addition, suppose that you estimate CAPM and Carhart 4-factor regressions using the dailyexcessreturns of Netflix stock (ticker: NFLX) using the past 1 year of dailyreturn data. The output of theseregressions is provided below.

4-Factor Model: 3 Fama-French factors (MktRf, SMB, HML) and the momentum factor (UMD)

1-Factor Model: Only MktRf

MS Excel gives you the following regression statistics for the two regression models:

Regression Coefficients

Intercept MktRf SMB HML UMD

Std Dev

of Error R

2

4-Factor Model 0.00% 0.40 0.00 0.50 0.80 1.91% 14.3%

1-Factor Model 0.04% 0.40 2.00% 6.0%

All coefficient estimates above, except the SMB coefficient, are statistically significantly different

from zero at the 5% level.

1.

What is NFLXs annualizedexpected return according to the Carhart 4-factor model?

a. 3.00%

b. 2.00%

c. 7.08%

d. 8.08%

2. What was NFLXs CAPM annualizedalpha during the past year?

a. 0.40%

b. 0.04%

c. 2.08%

d. 10.08%

3. What Sharpe ratio could you obtain by combining NFLX with the market?

a. 0.250

b. 0.404

c. 0.567

d. 5.046


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4. Based on its factor exposures alone, which statement below most accurately describes NFLX?

a. It is a large capitalization stock with high past 1-year stock returns

b.

It is a small capitalization stock with low past 1-year stock returns

c. It is a value stock with low past 1-year stock returns

d.

It is a growth stock with low past 1-year stock returns

5. Suppose that XYZ stocka xylophone manufacturerincreases in price by 10% on the day it is

added to the S&P 500. Based on the theory and evidence reviewed in class, which of the following is

likely to mitigate this 10% stock price increase?

a.

There is a large amount of money managed by S&P 500 index funds

b. There is very little money managed by hedge funds employing long-short strategies

c. There are several publicly traded xylophone firms with similar business models to XYZ

d. The loan fee for borrowing XYZ stock is extremely high at 50% per year

6. Which of the following best explains why Barber and Odean (2000) found that certain individual(retail) investors stock portfolios exhibited extremely poor average net returns relative to the stock

market as a whole?

a. Poor stock picking: Certain individuals bought stocks that had very negative alphas

b. Trading costs: Some individuals traded a lot, resulting in costly commissions and price

impact

c. Insufficient diversification: Individuals held only a few stocks, which hurt their average

returns

d. Fear of risky stocks: Individuals avoided stocks with high betas that have higher average

returns

7. Which of the following facts would be predicted by the CAPM?

a. Stocks with high betas and stocks with low betas have similar average returns

b. Value and growth stocks have similar market betas, but value stocks have much higher

returns

c. Call options on stocks have much higher average returns than put options on stocks

d. Market-neutral straddles (puts + calls) have returns that are much lower than the risk-free rate

In Questions #8 and #9, suppose Amazon stock is currently selling at $200 per share; and the 1-year

risk-free rate is 0%. An at-the-money 1-year put on Amazon is selling at $30.

8. What is the no-arbitrage price of an at-the-money 1-year call option on Amazon?

a. $0

b. $30

c. $170

d. $230


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9. Assuming Amazon stocks volatility is constant at the level expected by investors, how many

shares of stock would you need to buy to replicate the 1-year put?

a.

0.575

b. 0.425

c.

0.500d. 0.575

For Questions #10, #11, and #12, consider three 3-month American call options with strike prices of$75, $80, and $85 and market prices of $8.99, $6.37, and $4.37, respectively. The stock underlyingthese options is priced at $80 and pays no dividends. Suppose the risk-free rate is 0%.

10. Based on the options implied volatilities in the Black-Scholes model, investors seem to expect:

a. The stock price will be lognormally distributed in 3 months

b.

There is a greater than lognormal probability of extremely good news

c. There is a greater than lognormal probability of extremely bad news

d. There is a greater than lognormal probability of extreme good and bad news

11. If the stocks market beta is 1.0, which call option has the highest market beta?

a. The call with a strike price of $85

b. The call with a strike price of $80

c. The call with a strike price of $75

d. All three call options have the same beta

12. If the stocks alpha is 2% per year, what is the alpha of the call option with a strike price of $75?

a. 1.07%

b.

1.07%

c. 11.81%

d. 15.36%

13. Bonus: A 1-year exotic option on a risky 1-year bond pays off $1 if the bond defaults and $0

otherwise. Suppose the underlying bonds 1-year return is either 20% or 60%, where the latter

return corresponds to the default scenario. Suppose a risk-free 1-year T-Bill yields 0%. [Aside: This

exotic option is similar to a credit default swap (CDS).] What is the no-arbitrage price of the option?

a. $0.20

b. $0.25

c. $0.45

d. $0.75


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Longer Questions

14. (46 points) Suppose that Saks Inc (ticker: SKS) stock is initially priced (i.e., today) at $10 and

will either increase by 25% or decrease by 20% in eachof two 3-month periods. The stock pays no

dividends. Consider an exotic European option based on SKS stock that expires in six months. If

exercised at expiration, the option has a payoff equal to SKSs stock price squared. For example, ifthe option is exercised when SKS is priced at $10, its payoff is 102= $100. Assume the six-month T-

Bill rate is 0%.

a. (24 points) Using whichever method you prefer, compute the values of the exotic SKS option

under both possible stock price scenarios that might occur 3 months from now.


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b. (6 points) Using whichever method you prefer, value the exotic SKS option today.

c. (10 points) Compute the delta of the SKS option today.

d. (6 points) If the market beta of SKS stock is 3.0, what is the beta of the exotic option today?


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Extra Space for Longer Question #14


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15. (32 points) You are managing a large portfolio of investments and plan to rebalance soon. You

ask your trusted research assistant, Todd, to value and analyze several individual stocks. You instruct

him to use the CAPM to evaluate their alphas, betas, and idiosyncratic volatilities; and assume that

the individual stocks idiosyncratic returns are uncorrelated. But, before he could finish the job, Todd

unexpectedly was offered a promotion elsewhere in the firm. He left you with the following

information about the stocks and the market:

Security E(r) a b ()

Market 5% 20%

Risk-free 0%ABT 6% 0.4 32%

DDS 2% 2.0 40%

a. (18 points) Fill in all of the missing information in the table (11 cells in total). Show one exampleof each type of equation that you use to solve for the quantities above.


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b. (9 points) Compute the CAPM alpha, market beta, and information ratio of a portfolio that assigns

weights of 125% and 25% to ABT and DDS, respectively.

c. (5 points) What is the maximum Sharpe ratio that can be obtained by combining your portfolio in

part (b) with the market?


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Extra Space for Long Answer Question #15

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CM SampleExam 2