Q1. [15 points total] Consider the table below with expected returns, volatilities, and correlations

(1a) Construct a risk-free portfolio and show the weights of stocks in the portfolio, expected return of that portfolio, and the Sharpe Ratio of the portfolio.

(1b) If the risk-free interest rate is 10%, explain what would happen over time to the returns of the stocks in the table.

(1c) What are the expected return and volatility of a portfolio that consists of a long position of $500 in TD Bank, a long position of $500 in shoppers, and a short position of $1,000 in Rogers?

Q2. [10 points total] In the lecture we discussed the Capital Asset Pricing Model (CAPM). (2a) What is the interpretation of beta in the CAPM in words? Use one sentence.

(2b) Mention one similarity between CAPM and Arbitrage Pricing Theory (APT).

(2c) Mention two differences between CAPM and APT.

Q3. [15 points total] Two investment advisers are comparing performance. Investor A has a rate of return of 15% on average, and his portfolio has a beta of 1.25. Investor B has an average 12% rate of return, and her portfolio has a beta of 0.75.

(3a) Can you tell which investor was a better selector of individual stocks? Explain.

(3b) Which investor has a more aggressive style of investing, and which one has a more defensive style of investing? Explain your answer in two sentences at most.

(3c) If the risk-free rate was 3.5%, and the market return during the period was 12%, which investor is the better selector of individual stocks?

Q4. [10 points total] One can write the variance of a portfolio P with n different securities as (where each security has the same weight in the portfolio):

GP(2)  = +#o#

with    being the average variance of all securities, and $o$ is the average of the covariances between the securities.

(4a) Use the formula to explain the principle of diversification.

(4b) What is the portfolio variance if n=75,  = 0.0025, and "=0.081?

Q5.  [20  points total]  Consider the following  information for Amazon with average  monthly returns for four well-diversified portfolios. The monthly risk-free rate is 0.1%. The last column gives the estimates of the factor betas for IBM.

(5a) Explain what the HML portfolio is, and why the portfolio empirically poses a challenge for the CAPM-model.

(5b) Interpret the numbers in the table for the PR1YR portfolio.

(5c) Calculate the expected annualized return (APR) for Amazon based on the  Fama-French- Carhart Factor specification. Show your calculations.

(5d) Amazon has just paid an annual dividend payment of $2.75 and expects dividends to grow by 2% per year indefinitely. Based on this information and your previous answers, what is your estimate of Amazon’s stock price?

Q6. [15 points total] You purchase a “collar”: you buy 1,000 shares currently selling at $155 per share. In addition, you purchase a 1,000 put options with an exercise price of $120, and you write

a 1,000 call options with an exercise price of $175. All options have the same expiration date. (6a) Complete the following table with payoffs :

(6b) Assuming price stays at $155 per share, what are your profits if the premium for a put option is $5.5, and $7.5 for a call option?

(6c) What would be a reason for an investor to use this particular option strategy?

Q7. [15 points total] You have the following information on a stock (no dividends):

12 months

35%

$85

$75

4%

(7a) Use the Black-Scholes formula to find the value of a call option. If needed, use the value in the statistical table that is closest.

(7b) What is the value of a put option on the same stock? If needed, use the value in the statistical table that is closest.

(7c) How will the values of the put and the call option change if the risk-free rate increases? Explain your answer in words.