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Description

Answer the ten questions below to make sure you know exactly what you need to know. The original document of the question is attached.

QUESTION 1 [5 pts]

Suppose you are presented with the following two-pass regression designed to test the empirical

success of the CAPM:

Ri,t − r f ,t = αi + βi[Rm,t − r f ,t ] + εi,t (1)

Ri,t − r f ,t = γ0 + γ1 bβi + γ2σ 2

ε,i + ei,t (2)

where in equation (1), Ri,t is the return to portfolio i in period (month) t, r f ,t is the risk-free rate, Rm,t

is the return on the market portfolio, and εi,t is the residual of the regression; and in equation (2) Ri,t is

the average return to portfolio i over the sample, bβi is the estimated CAPM beta from equation (1) (for

portfolio i), and σ 2

ε,i is the variance of portfolio i′s residuals in equation (1).

(a) What does the CAPM predict should be the values of γ0, γ1, and γ2. Explain your answers.

(b) Suppose that in the sample, the risk premium on the market portfolio is Rm,t − r f ,t = 6.5%, but

the estimate from equation (2) is bγ1 = 4%. Is the empirical Security Market Line (the SML implied by

the data) too steep or too flat compared to what the CAPM predicts? Explain.

QUESTION 2 [5 pts]

Name two empirical facts that suggest the CAPM is not the ”correct” asset pricing model (even

though it is still pretty good!)

QUESTION 3 [5 pts] Suppose asset A has an alpha of αA = 1% and a CAPM beta of βA = 1, and

asset B has an alpha of αB = −0.5% and a CAPM beta of βB = 0.75. Suppose also you put −133.33%

of your wealth in asset B, 100% in asset A, and 33.33% in the risk-free asset.

(a) What is the CAPM beta of this portfolio?

(b) What is the alpha of the portfolio?

(c) Does this constitute an arbitrage? Why or why not?

QUESTION 4 [5 pts]

Suppose you have log-utility u(x) = ln(x). You are faced with the following gamble: a 50% chance

of getting $100 and a 50% chance of getting $200. You have no wealth at the start of the gamble, so

your wealth after the gamble will either be $100 or $200.

What is the certainty equivalent of the gamble?

QUESTION 5 [5 pts]

Imagine you are choosing between two portfolios, and you believe the CAPM is the correct pricing

model. Portfolio A has a market beta of βA = 0.6. Portfolio B has a market beta of βB = 0.9. The average

excess return for A is 6%, while for B the average excess return is 8.5%. The average excess return on

the market is 7%. The standard deviation of A’s return is 12%, and for B is 18%.

(a) Which portfolio, A or B, has a higher alpha?

(b) Which portfolio has a higher Sharpe ratio?

(c) If you could borrow as much as you want at the risk-free rate (say r f = 1%), which portfolio

is better, A or B? (hint: suppose you wanted your investment to have a market beta of βp = 1, which

portfolio would you choose?) Explain.

QUESTION 6 [5 pts]

Consider the following figure:11-1

11.1 Cumulative Abnormal

Takeover Attempts:

Target Companies

The figure shows the cumulative abnormal return plotted against the days to a merger announce-

ment. State whether each of the three forms of the Efficient Market Hypothesis are supported by or can

be rejected by the figure, and explain your answer:

(a) Weak form

(b) Semi-strong form

(c) Strong form

(Notes: (1) abnormal return means the unexpected return, like the difference between the actual

return and the return predicted by the Fama French 3-factor model; (2) it is a common observation that

firms that get acquired (taken over, merged, etc.) are often acquired at a very high premium above their

current market price, so we would expect at the time of a merger/takeover announcement that the return

for the target company would increase significantly)

QUESTION 7 [5 pts]

XYZ stock price and dividend history are as follows:

Year Beginning-of-year-price Dividend Paid at Year End

2015 $ 100 $4

2016 $ 120 $4

2017 $ 90 $4

2018 $ 100 $4

An investment manager buys three shares of XYZ at the beginning of 2015, buys two more shares

at the beginning of 2016, sells one share at the beginning of 2017, and sells all four remaining shares

at the beginning of 2018.

(a) What are the arithmetic and geometric average returns the manager earned with this strategy?

(b) What is the dollar-weighted return?

QUESTION 8 [5 pts]

Consider stocks A and B below, with performance estimated according to the CAPM. The risk-free

rate over the period was 6%, and the market’s average return was 14%.

Stock A Stock B

CAPM regression estimates 1% + 1.2(rm − r f ) 2% + 0.8(rm − r f )

Residual standard deviation, σ (e) 10.3% 19.1%

Standard deviation of excess returns 21.6% 24.9%

Standard deviation of market return 18%

(a) Calculate the following statistics for each stock:

1. Information ratio

2. Sharpe ratio

3. M2 measure

4. Treynor ratio

(b) Which stock is best if it is the only risky asset held by the investor?

(c) Which stock is best if it will be mixed with the rest of the investor’s portfolio, which is currently

composed of holding only the market portfolio?

QUESTION 9 [5 pts] Say whether each is true or false, and explain your answers: The tangency

portfolio has:

(a) the maximum Sharpe ratio

(b) a market beta equal to 0 (if CAPM is true)

(c) the minimum possible variance of all risky portfolios

QUESTION 10 [5 pts]

Suppose we are in a standard APT factor model type world, with two factors F1 and F2. Suppose

a well-diversified portfolio A has expected return of 11%, with betas of 0.4 on the first factor and 0.6

on the second factor. Also assume that two factor portfolios exist (corresponding to the two factors we

have), F1 has an expected return of 7%, and F2 has an expected return of 8%.

(a) Is there arbitrage here? If so, how would you construct the arbitrage portfolio? If not, why not?