AcF 321 INVESTMENTS

QUESTION 1

ANSWER ALL PARTS OF THE QUESTION

a. Explain how the CAPM beta of a stock is estimated. [3 marks]

b. Suppose the index model for stocks A and B is estimated from excess returns with the following results:

𝑅𝐴 = 3% + 0.7𝑅𝑀 + 𝑒𝐴 𝑅𝐵 = −2% + 1.2𝑅𝑀 + 𝑒𝐵 𝜎𝑀 = 20%;

𝑅𝑆𝑞𝑢𝑎𝑟𝑒𝑑𝐴 = 0.20;

𝑅𝑆𝑞𝑢𝑎𝑟𝑒𝑑𝐵 = 0.12

i. What is the standard deviation of each stock? [4 marks]

ii. Break down the variance of each stock into its systematic and idiosyncratic components. [4 marks]

iii. Assuming the residuals of the index models are independent of each other, what are the covariance and the correlation coefficient between the two stocks? [4 marks]

iv. What is the covariance between each stock and the market index? [4 marks]

v. Consider portfolio P with investment propositions of 0.60 in A and 0.40 in B. What is the covariance between portfolio P and the market index? [6 marks]

vi. Now, consider another portfolio Q with investment propositions of 0.50 in A, 0.30 in the market, and the remaining T-Bills. What is the covariance between portfolio Q and the market index? [8 marks]

QUESTION 2

ANSWER ALL PARTS OF THE QUESTION

a. If a substantial body of investors decided to exclude “sin stocks” (e.g. tobacco, armaments) from their portfolios, would both the Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM) continue to hold? Explain. [6 marks]

b. An analyst is interested in testing whether liquidity risk (LIQ) is priced in addition to the market factor (Market) that is considered in CAPM. The analyst has decided to employ the Fama-MacBeth two-stage procedure.

i. Explain the first-stage of the regression analysis the analyst would employ. [6 marks]

ii. What are the dependent and independent variables in the second stage of the analysis? [6 marks]

iii. What would the results be in a CAPM world? [6 marks]

c. Consider the following data for a one-factor economy. All portfolios are well diversified.

Suppose that another portfolio, portfolio E, is well diversified with a beta of 0.6 and expected return of 7%. Would an arbitrage opportunity exist? If so, what would be the arbitrage opportunity? [9 marks]

QUESTION 3

ANSWER ALL PARTS OF THE QUESTION

a. A manager buys three shares of stock today and then sells one of those shares each year for the next three years. His actions and price history are summarized below. The stock pays no dividends.

i. Calculate the time-weighted geometric average return for the manager. [3 marks]

ii. Calculate the time-weighted arithmetic average return for the manager. [3 marks]

iii. Explain if you would expect the dollar-weighted average to be higher or lower than the time-weighted geometric average? (You do not have to calculate the dollar-weighted average). [2 marks]

b. Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of the portfolio allocated to each sector in column 2, the benchmark or neutral sector allocation in column in 3 and the returns of sector indices in column 4.

(i) Comment on the manager’s performance [3 marks]

(ii) What was the contribution of security selection to the manager’s performance? [5 marks]

(iii) Confirm that the sum of selection and allocation contributions equals her total “excess” return. [8 marks]

c. The following figure shows the pattern of cumulative abnormal returns (CARs) for insider sales and purchases around an insider trading event. Explain whether this evidence is consistent with the Grossman-Stiglitz paradox? [9 marks]

QUESTION 4

ANSWER ALL PARTS OF THE QUESTION

a. You observe the following term structure of discrete yields to maturity:

i. If you believe that the term structure next year will be the same as today’s, calculate the return on a1-year zero coupon bond and a 4-year zero coupon bond. [4 marks]

ii. Which zero coupon bond provides the greatest expected 1-year return? [3 marks]

iii. Redo your answers to (i) and (ii) if you believe in the expectations hypothesis [5 marks] b. Clean Prices, coupon rates (assumed paid annually) and maturities of three comparable Treasury bonds, as of May 15, 2021, are listed below:

b. Clean Prices, coupon rates (assumed paid annually) and maturities of three comparable Treasury bonds, as of May 15, 2021, are listed below:

i. Calculate all three spot rates implicit in these prices. [9 Marks]

ii. What is the expected one-year spot rate after one year assuming that the expectations theory of term structure is correct? [3 Marks]

iii. Based on the spot rates you have calculated, is there an arbitrage opportunity if a 12% coupon (paid annually) bond maturing in 3 years is priced at $115? Explain. [5 Marks]

c. Long-term Treasury bonds currently are selling at yields to maturity of nearly 8%. You expect interest rates to rise. The rest of the market thinks that they will remain unchanged over the coming year. In each question, choose the bonds that will provide the higher holding-period return over the next year if you are correct. Briefly explain your answer.

i. A Baa-rated bond with coupon rate 8% and time to maturity 20 years, OR an Aaa-rated bond with coupon rate of 8% and time to maturity 20 years. [2 marks]

ii. An A-rated bond with coupon rate 4% and maturity 20 years, OR an Arated bond with coupon rate 8% and maturity 20 years. [2 marks]

QUESTION 5

ANSWER ALL PARTS OF THE QUESTION

a. The following figure is a plot of serial correlation of a hedge fund’s return (x axis) and its Sharpe ratio (y axis). How do you interpret this graph? [8 marks]

b. Consider a passive mutual fund, an active mutual fund, and a hedge fund. The mutual funds claim to deliver the following gross returns:

The passive fund charges an annual fee of 0.10%. The active mutual fund charges a fee of 1.20% and seeks to beat the same stock market index by about 1% per year after fees. The active mutual fund has a beta of 1 and has a tracking error variance (var(ε )) = 3.5%.

The hedge fund uses the same strategy as the active mutual fund to identify “good” and “bad” stocks (different alphas but the same betas), but implements the strategy as a long-short hedge fund, applying 4 times leverage. The riskfree interest rate is rf=1% and the financing spread is zero (meaning that borrowing and lending rates are equal). Therefore, the hedge fund’s return before fees is

i. What is the hedge fund’s volatility? [3 marks]

ii. What is the hedge fund’s beta? [3 marks]

iii. Based on the mutual fund’s alpha estimate, what is the hedge fund’s alpha before fees? [5 marks]