Part 1: Multiple Choices (28 points)

Choose one best answer to each question.

1.  (4 points) Which of the following is a reasonable annual riskfree rate in Australia now? (a) -5%                      (b) 1.5%                      (c) 10%                       (d)15%

2.  (4 points) Which one of the following is a good approximation to a riskfree asset in Australia?

Gold

(b) Vanguard small-cap mutual fund

(c) One-month term deposit

ASX200 index fund

3.  (4 points) Suppose that the annualized simple return for a 4-month term deposit is 3%. If you deposit 1000 dollars into this term deposit account, how much can you withdrawn by the end of the 4-month period?

(a) 1010                     (b) 1020                      (c) 1030                      (d)1075

4.  (4 points) Given that the distribution of financial returns exhibits fat tails, which of the following is more likely to represent the pdf of financial returns?

5.  (4 points) Which of the following statement is not true?

(a) If the efficient market hypothesis holds, no asset/fund could have a significantly positive

alpha in a CAPM regression.

(b) The price of value risk (value premium) may change over time.

(c) The risk free rate may change over time.

6.  (4 points) (standard

10

5

0

-5

The following figure is the scatter plot of 4 sets of x and y and the coefficient estimates error is reported in parenthesis) from regression model yt  = b0 + b1 xt + et .

(b)

0

x

(c)

2

0

x

(d)

2

x

Which set of x and y are likely to be independent?                                          (a)                              (b)                              (c)                              (d)

7.  ( 4 points) Suppose that {yt } is a stochastic process. Which of the following is not correct?

(a) Et (yt ) = yt

(b) E3 (2y5 ) = 2E3 (y5 )

(c) E2 (y5 ) = E2 (E3 (y5 ))

(d) E4 (y4 y5 ) = y4 y5

Part II: Short Answers (76 Points)

Question A (24 points)

Suppose that the monthly log price of an asset, pt , follows a random walk with drift,

pt  = 0.01 + pt − 1 + et ,

where e N(0, 1).  The value of pt  in a few selected months are given in the following table. Use the definition of continuously compounded return to answer the following questions.

8.  (4 points) Compute the monthly return T1 , T2 , and T3 . Express the returns in percentages.

9.  (4 points) Compute the quarterly return T3 (3). Express the returns in percentages.

10.  (4 points) Suppose that we are at the end of Mar 2022 (t = 3), what is the best point forecast for pt  in Apr 2022? Justify your answer (write down the correct conditional expectation for the prediction and show the steps).

11.  (4 points) Suppose that we are at the end of Mar 2022 (t = 3), what is the best point forecast for pt  in June 2022? Justify your answer (write down the correct conditional expectation for the prediction and show the steps).

12.  (4 points) Suppose that we are at the end Mar 2022 (t = 3), what is the best point forecast of the monthly return in June 2022?  Justify your answer (write down the correct conditional expectation for the prediction and show the steps).

13.  (4 points) Suppose that we are at the end Mar 2022 (t = 3), what is the best point forecast of the quarterly return from Apr, May, and June 2022?  Justify your answer.  (write down the correct conditional expectation for the prediction and show the steps).

Question B (28 points)

Table 1 and 2 present CAPM and FF 3 factor estimates for a fund ABC and a fund XYZ with 60 yearly observations from 1950 to 2010. Table 3 presents the price of market, size, and value risk, and the riskfree rate, all in percentages. Note that T denotes the return, and z denotes the e北cess return. All returns are continuously compounded.

Table 1: CAPM Estimates

αi

βi           E(zit )

fund ABC     2.3       0.50

S.E.         (1.1)    (0.06)

fund XYZ

S.E.

-2

(0.5)

0.85

(0.07)

NA

NA