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. 
    

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

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

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

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

6. 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. 

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

8. 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. 

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

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

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

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, r_f is 6%, and E[r_M] = 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 r_f = 8% and E(r_M) = 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:

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:

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:

• 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:
R_A= 0.01 + 0.8R_M+ e_A
R_B= 0.02 + 1.2R_M+ e_B
s_M= 20%, s(e_A) = 20%, s (e_B) = 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 9^th, 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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