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FIN380 Investments

Fin380: Investments

Final Exam Spring 2017 (Form A)

Please read the following before you start answering questions:

  1. Academic Integrity!!!
  1. Time Management: If you get stuck on one question, do the other questions first and then come back to it at the end.
  1. Rounding Errors: Please keep four decimal values when carrying over answers from the previous steps.

Question 1: Multiple Choices (10 points)

  1. The semistrong form of the efficient market hypothesis implies that ____________ generate abnormal returns and ____________ generate abnormal returns. 
     

A. 

technical analysis cannot; fundamental analysis can

B. 

technical analysis can; fundamental analysis can

C. 

technical analysis can; fundamental analysis cannot

D. 

technical analysis cannot; fundamental analysis cannot

  1. Assume that a company announces unexpectedly high earnings in a particular quarter. In an efficient market one might expect _____________. 
     

A. 

an abnormal price change immediately after the announcement

B. 

an abnormal price increase before the announcement

C. 

an abnormal price decrease after the announcement

D. 

no abnormal price change before or after the announcement

  1. The term random walk is used in investments to refer to ______________. 
     

A. 

stock price changes that are random but predictable

B. 

stock prices that respond slowly to both old and new information

C. 

stock price changes that are random and unpredictable

D. 

stock prices changes that follow the pattern of past price changes

  1. According to the semistrong form of the efficient markets hypothesis, ____________. 

A. 

stock prices do not rapidly adjust to new information

B. 

future changes in stock prices cannot be predicted from any information that is publicly available

C. 

corporate insiders should have no better investment performance than other investors even if allowed to trade freely

D. 

arbitrage between futures and cash markets should not produce extraordinary profits *NOTE WE DIDN”T TALK ABOUT THIS, YOU WILL NOT BE RESPONSIBLE FOR KNOWING ABOUT FUTURES AND CASH MARKETS

  1. The weak form of the EMH states that ________ must be reflected in the current stock price. 

A. 

all past information, including security price and volume data

B. 

all publicly available information

C. 

all information, including inside information

D. 

all costless information

  1. If you believe in the __________ form of the EMH, you believe that stock prices reflect all publicly available information but not information that is available only to insiders. 

A. 

semistrong

B. 

strong

C. 

weak

D. perfect

  1. In CAPM, the beta of a security is equal to _________. 

A. 

the covariance between the security and market returns divided by the variance of the market's returns *NOTE WE DIDN’T EMPHASIZE THIS SO I WILL NOT ASK THIS QUESTION ON THE FINAL.

B. 

the covariance between the security and market returns divided by the standard deviation of the market's returns

C. 

the variance of the security's returns divided by the covariance between the security and market returns

D. 

the variance of the security's returns divided by the variance of the market's returns

  1. In a simple CAPM world which of the following statements is (are) correct?

    I. All investors will choose to hold the market portfolio, which includes all risky assets in the world.
    II. Investors' complete portfolio will vary depending on their risk aversion.
    III. The return per unit of risk will be identical for all individual assets.
    IV. The market portfolio will be on the efficient frontier, and it will be the optimal risky portfolio. 

A. 

I, II, and III only

B. 

II, III, and IV only

C. 

I, III, and IV only

D. 

I, II, III, and IV

*Note, III is poorly worded, it should say “per unit of risk (Beta)”

  1. In the context of CAPM, the systematic measure of risk is captured by _________. 

A. 

unique risk

B. 

beta

C. 

the standard deviation of returns

D. 

the variance of returns

  1. According to the CAPM, a security with a _________. 

A. 

negative alpha is considered a good buy

B. 

positive alpha is considered overpriced

C. 

positive alpha is considered underpriced

D. 

zero alpha is considered a good buy

Question 2 (9 points)

  • Consider the CAPM. The risk-free rate is 5%, and the expected return on the market is 15%. What is the beta on a stock with an expected return of 17%? 

.05 + Beta * .10 = .17, beta = 1.2

  • You consider buying a share of stock at a price of $25. The stock is expected to pay a dividend of $1.50 next year, and your advisory service tells you that you can expect to sell the stock in 1 year for $28. The stock's beta is 1.1, rf is 6%, and E[rM] = 16%. What is the stock's abnormal return? (*NOTE THIS SHOULD SAY stock’s “Alpha”)

(28 + 1.5) / 25 = 1.18,   6% + 1.1*10% = 17, alpha is 1%

  • You are a consultant to a large manufacturing corporation that is considering a project.

The project’s beta is 1.8. Assuming that rf = 8% and E(rM) = 16%, what is the required rate of return (cost of capital) based on CAPM? Suppose that you estimate that the internal rate of return (IRR) of the project is 20%. Should you recommend investing in the project?

.08 + 1.8*(.16-.08) = 22.4.  No you should not invest.

Question 3 (9 points)

  • Two investment advisers are comparing performance. Adviser A averaged a 20% return with a portfolio beta of 1.5, and adviser B averaged a 15% return with a portfolio beta of 1.2. If the T-bill rate was 5% and the market return during the period was 13%, which adviser was the better stock picker? 

20 – .05 – 1.5*(.13-.05) = .03

15 - .05 – 1.2*(.13-.05) = .004

Adviser 1 was a better stock picker

  • Consider the following SML based on the CAPM:

What is the expected return for a portfolio with a beta of 0.5?

.05 + .5*(.5) = .075%

  • A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year? Assuming that the risk-free rate is 6% and the expected rate of return on the market is 16%.

E[R] = 6% + 1.2*.1 = 18%

= (X + 6) /50  -  1, X = 53

Question 4 (10 points)

  • Consider the following data for a one-factor economy:

Portfolio

E(r)

Beta

A

15%

1.5

F

6%

0.0

Suppose that another portfolio E is well diversified with a beta of 0.5 and expected return of 8%. Construct an arbitrage strategy by investing $1 in the long position and $1 in the short position. What is the profit for the arbitrage strategy?

A portfolio of 1/3 A and 2/3 F has a beta of 0.5 and an expected return of (1/3*(1.5) + 2/3*(.06)) =.09

Go long this portfolio $1 and short $1 of Portfolio E. Make 1.09 – 1.08 = .01

  • Consider the multifactor APT. There are two independent economic factors, F1and F2. The risk-free rate of return is 6%. The following information is available about two well-diversified portfolios:

Portfolio

β on F1

β on F2

Expected Return

A

0.5

2.0

19%

B

2.0

0.5

12%

Assuming no arbitrage opportunities exist, what is the risk premium on the factor F2 portfolio?

.19 - = .06 + .5 RP1 + 2 RP2

.12 = .06 + 2 RP1 + 0.5 RP2

Multiply first equation by 2, divide second by 2 to get

.26 =  RP1 +4 RP2

.03  =  RP1 + 0.25 RP2

Subtract equation 2 from equation 1 to get .23 = 3.75 RP2, RP2 = .06133

Question 5 (10 points)

  • Consider the multifactor APT with two factors: Industrial Production (IP) and Interest Rates (INT). A stock has a beta of .5 on IP and a beta of 1.25 on INT. The risk premiums on IP and INT are 1% and 7%, respectively. The risk-free rate of return is 7%. What is the expected return on the stock if no arbitrage opportunities exist?

.07 + .5*.01 + 1.25*.07 = 16.25%

  • Continue from (1). Suppose that the expected rate of change for IP is 3% and the expected rate of change for INT is 5%. If it turns out that the actual rates of change are 4% for IP and 3% for INT respectively, what is your best guess for the rate of return on the stock?

.1625 + .5*(.01) + 1.25*(-.02) = .1425

  • An index model regression applied to a company’s stock returns produces the following estimates: r = 0.2% + 1.5 r(M). Suppose that the company has been involved in a closely contested lawsuit and the jury came back today with the ruling. The rate of return on the company was r=5% for the day. Suppose that the market return r(M) today was 4%. Did the company win or lose the lawsuit? Why?

Expected return on this day was 0.2% + 1.5 (4%), 6.2%. Company likely lost the lawsuit.

Question 6. (15 points)

An investor can design a risky portfolio based on one stock fund (S) and one bond fund (B). The Stock fund has an expected return of 21% and a standard deviation of return of 39%. The bond fund has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of two funds is 0.4. The risk-free rate of return is 5%.  ***NOTE*** THIS QUESTION WHERE YOU HAVE TO SOLVE FOR THE OPTIMAL SHARPE RATIO WILL NOT BE ASKED (THE FORMULA IS COMPLICATED) REFER TO THE QUESTION ON THE MIDTERM FOR THE TYPE OF QUESTION I MIGHT ASK INVOLVING ALLOCATING TO TWO RISKY ASSETS.

  • What is the proportion of the optimal risky portfolio that should be invested in the stock fund?
  • What are the expected return and standard deviation of the optimal risky portfolio?
  • What is the slope of the best feasible CAL?
  • Suppose that the investor prefers to invest in a complete portfolio with an expected return of 12%.What are the proportions of the complete portfolio that should be invested in the risk-free asset, the stock fund, and the bond fund?

Question 7 (8 points)

Investors expect the market rate of return in the coming year to be 13%. The risk-free rate is 3%. QQAG has a beta of 1.7. The market value of its outstanding equity is $200 million.

  • What is your best guess currently as to the expected rate of return on QQAG’s stock if you believe that the stock is fairly priced?

.03 + 1.7*.10 = 20%

  • If the market return in the coming year actually turns out to be 10%, what is your best guess as to the rate of return that will be earned on QQAG’s stock?

Market disappoints by 3%, so 20% + 1.7*(-.03) = 14.9%

  • Continue from (2) and suppose now that QQAG loses a surprising lawsuit during the year. QQAG’s stock return during the year turns out to be 10%. What is your best guess as to the settlement amount paid by QQAG?

The stock disappoints by 4.9%, 4.9% * 200 Million = 9.8 Million

Question 8 (9 points)

Consider the following excel output from a Fama-French three-factor model regression for a stock:

Coefficients

Standard Error

T-stat

P-value

Intercept

0.685

0.993

0.690

0.493

Market

1.578

0.224

7.056

0.000

SMB

-0.209

0.446

-0.468

0.642

HML

1.383

0.378

3.657

0.001

  • What is the estimated alpha for this stock? Is it statistically significant? Explain.

0.685 (no T-stat is less than 2)

  • Are the estimated betas statistically significant from zero? Explain each beta estimate separately.

Market Beta and HML are both positively significant (t-stats of 7 and 3.65). SMB beta is not statistically significant

  • Given the beta estimates, describe the risk characteristics of this stock. Is the stock cyclical? Is it a large or small stock? Is it a value or growth stock? Explain.

The stock is highly cyclical (its beta  is 2.5 SE greater than 1) , and is likely a value stock (it loads on the value factor). We can not tell if it  is large or small (it does not load on SMB).

Question 9 (12 points)

The index model has been estimated for stocks A and B with the following results:
RA= 0.01 + 0.8RM+ eA
RB= 0.02 + 1.2RM+ eB
sM= 20%, s(eA) = 20%, s (eB) = 10%

  • What are the standard deviations for stocks A and B?

Sqrt( .8^2*.2^2 + .2^2) = 0.256

Sqrt(1.2^2*.2^2 + .1^2) = 0.26

  • What are the covariance and correlation coefficient between stocks A and B?

Covariance is .8*1.2*.2*.2 = .0384.  .0384 / .256/.26 = .58 (correlation)

  • What is the total standard deviation of a portfolio with 50% invested in stock A and 50% invested in stock B? What are the systematic standard deviation and the non-systematic standard deviation?

Total variance is  .5^2*.256^2 + .5^2*.26^2 + 2 .5*.5* .0384  = .0525, STDEV = .229

Beta is 1 of this portfolio, so systematic standard deviation is 20%

Non-systematic variance is 0.5^2*.2^2  + .05^2*.1^2 = .0125, sqrt(.0125) = 11.1%

Question 10: Short discussions (8 points)

On April 9th, 2017, United Airlines forcibly removed passenger David Dao from United Express Flight 3411 due to overbooking. Video of the incident recorded by passengers went viral on social media, resulting in outrage over the violent incident. Design an event study (using daily stock returns) to examine the price impact of this incident on United Airlines stock over the one week period following the incident. Please be specific about each step, clearly define the notation, and provide interpretation for all estimations.

Step 1)  Calculate the beta of UA stock with respect to relative indexes. (Probably an airline industry index, could also include the market), using data prior to the law suit.

This gets us an expected return to the UA on a given day of

Alpha + Beta_A *ReturnAirlineIndex + Beta_M ReturnMarket

Step 2) Calculate the return to the airline index and market return over the week of the event, as well as the return to UA

The abnormal return to UA is

Return_UA – alpha – Beta_A * ReturnAirlineIndex – Beta_M Return Market

If this return is significantly negative then it appears that the incident may have negatively impacted UA.

Step 3) To get a sense for the value impact, could multiple this abnormal return times the value of UA at the beginning of the week.

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