Investments

Midterm Exam – Fall 2014

Professor Pedro Santa Clara

This exam consists of 22 questions. Each question is worth 1 point.

Some questions are more difficult than others. The exam is long so if you get hopelessly stuck

on some questions move forward and come back to them later if time permits.

This is a closed book exam. You are allowed one-sided page of notes. Calculators are permitted.

Good luck!

____________________________________________________________

Print Name and Number

True or False Questions

1. ___ The Fed is reducing QE gradually.

2. ___ You know you will be receiving the following cash flow stream: 600€ in 0.75

years, 400€ in 1.25 years and finally 800€ in 1.5 years. If the appropriate discount rate

is 4.5%, the present value is 1629.02€.

3. ___ Stock A and Stock B have the same expected return but stock A has a standard

deviation of 15% while stock B has standard deviation of 20%. Stock A must be a better

addition to my portfolio than stock B.

4. ___ Studies found that the asset allocation process has no impact on portfolio

performance.

5. ___ If the expected return of an asset is below the security market line then the

asset is overvalued.

6. ___ If stock A has a standard deviation of 10% and stock B a standard deviation of

15%, under the CAPM stock B has a higher expected return than A.

7. ___ Achieving positive abnormal returns using technical analysis is evidence against

all forms of market efficiency.

8. ___ Under the CAPM, all investors should hold a combination of the market

portfolio and the risk-free asset.

9. ___ Stock returns in the United States are not related to political cycles.

10. ___ The only two limits to arbitrage are the bid-ask spread and short selling

restrictions.

Short Questions (maximum 50 words)

1. State two assumptions of the Markowitz portfolio choice model and comment on them.

2. Criticize the use of the historical mean as an estimator of the market risk premium.

3. Give examples of market tests of (i) weak-form efficiency, (ii) semi-strong efficiency and (iii)

strong-form efficiency.

Problems

Problem 1

On January 1st you buy 1,000 shares of AAPL for €10. On February 1st, AAPL has a stock split

on the ratio of 5:1. On March 1st, AAPL pays a dividend of €0.25 per share. On April 1st, you

sell all AAPL shares for €1.85 each. What was your holding period return?

Problem 2

Consider that you want to retire 40 years from now and expect to live for 20 years after retiring.

If you want to ensure an income of $25,000 on the first year of your retirement and also that

your income grows by 2% per year thereafter, how much will you have to save per year to

achieve your target “retirement income”?

Assume that you start saving exactly one year from now and that the interest rate on your

savings is 5% per year (annual compounding). In addition, assume that you start using your first

“retirement income” exactly one year after retiring.

Problem 3

Imagine that you start with a portfolio of 60% stocks and 40% bonds. The returns on stocks,

bonds, and gold are uncorrelated. Stocks earn a higher expected return than bonds. Bonds and

gold earn the same lower expected return, but gold returns are three times as volatile as bond

returns, as measured by the standard deviation. You want to minimize risk, measured by the

variance of your portfolio return, without changing the expected return on your portfolio. What

should be your portfolio weights of stocks, bonds and gold?

Problem 4

Assume that the CAPM holds and that exposure to the market is the only source of correlation

for stocks. Consider that the market portfolio has an expected return of 10% and a

standard deviation of returns of 20%. The risk-free rate is 3%. What is the covariance between

two stocks that have betas of 0.9 and 1.2?

Problem 5

Stock A has an expected return of 12% and a Beta of 1.2. The risk free rate is 3%. Assuming that

the CAPM holds and Stock A is correctly priced, write down the equation for the security market

line.

Problem 6

You have regressed the WML (momentum) factor on monthly market excess returns from

January 1927 to August 2014. Interpret the results you obtained.

WML

Alpha 0.01

t-stat 5.84

Beta -0.38

t-stat -11.66

Use the information below to answer problems 7 to 9

Stock A and B have following characteristics

A B

E[r] 5% 11%

σ 12% 24%

Corr -0.20

Rf 3%

Problem 7

Compute the Sharpe ratio of the minimum variance portfolio.

Problem 8

Compute the Sharpe ratio of the optimal risky portfolio.

Problem 9

Compute the weights of the optimal portfolio of Stocks A and B and the risk free asset for a risk

aversion coefficient of 4.