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This midterm exam covers everything through Week 5 on Descriptive Statistics. You have 1.5 hours for the exam and only 1 attempt . Read each question carefully.

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

Question 1

Questions 1 - 14 depend on the following information:

Consider a 1-month investment in two assets: the Vanguard S&P 500 index (VFINX) and the Vanguard Emerging Markets Stock Index (VEIEX). Suppose you buy one share of the S&P 500 fund and one share of the emerging markets fund at the end of September, 2010 for $P_{VFINX, t-1} = 105.06$ , $P_{VEIEX, t-1} = 28.64$ , and then sell these shares at the end of October, 2010 for $P_{VFINX, t} = 109.04$ , $P_{VEIEX, t} = 29.49$

(5) What is the simple 1-month return for VFINX?

3.0%

3.8%

4.1%

2.8%

Question 2

(5) What is the simple 1-month return for VEIEX?

3.6%

3.0%

2.7%

1.7%

Question 3

(5) What is the continuously compounded (cc) 1-month return for VFINX?

4.1%

4.0%

3.5%

3.7%

Question 4

(5) What is the continuously compounded (cc) 1-month return for VEIEX?

2.5%

3.1%

2.9%

2.7%

Question 5

(5) Assume that you get the same monthly return for VFINX from Q1 every month for the next year. What is the annualized simple return? (Note: Do not use the rounded answer to compute this.)

62%

43%

39%

56%

Question 6

(5) Assume that you get the same monthly return for VEIEX from Q2 every month for the next year. What is the annualized simple return? (Note: Do not use the rounded answer to compute this.)

22%

53%

37%

42%

Question 7

(5) Assume that you get the same monthly return for VFINX from Q1 every month for the next year. What is the annualized cc return ? (Note: Do not use the rounded answer to compute this.)

45%

42%

48%

49%

Question 8

(5) Assume that you get the same monthly return for VEIEX from Q2 every month for the next year. What is the annualized cc return? (Note: Do not use the rounded answer to compute this.)

35%

30%

32%

37%

Question 9

(5) Assume that you get the same monthly return for VFINX from Q1 every month for the next year. Approximately how much will $10,000 invested in VFINX be worth after 1 year? (Note: Do not use the rounded answer to compute this.)

$16,247

$14,384

$13,908

$15,624

Question 10

(5) Assume that you get the same monthly return for VEIEX from Q2 every month for the next year. How much will $10,000 invested in VEIEX be worth after 1 year? (Note: Do not use the rounded answer to compute this.)

$15,311

$13,827

$12,294

$14,204

Question 11

At the end of September, you have $10,000 to invest in VFINX and VEIEX over the next month. Suppose you purchase $2,000 worth of VFINX and the remainder in VEIEX.

(4) What is the portfolio weight in VFINX?

48%

20%

52%

80%

Question 12

(4) What is the portfolio weight in VEIEX?

20%

80%

48%

52%

Question 13

(5) What is the 1-month simple portfolio return?

2.8%

3.4%

3.2%

3.1%

Question 14

(5) What is the 1-month continuously compounded portfolio return?

3.1%

3.4%

3.2%

2.8%

Question 15

For questions 15 - 20:

Let $r_{VFINX}$ and $r_{VEIEX}$ denote the monthly continuously compounded returns on VFINX and VEIEX and suppose that

r V F I N X \sim iid N (0.001, (0.05) 2),

$r_{VFINX} \sim \text{ iid } N(0.001, (0.05)^2),$

r V E I E X \sim iid N (0.01, (0.09) 2) .

$r_{VEIEX} \sim \text{ iid } N(0.01, (0.09)^2).$

(5) In the following graph, the black dotted line corresponds to the return distribution of which asset?

VFINX

VEIEX

Question 16

(5) Which asset appears more volatile?

VFINX

VEIEX

Question 17

(5) Let

W0=$100,000 $W_0 = \$100,000$ be the initial wealth invested in each asset. Compute the 5% monthly Value-at-Risk for VFINX. (Hint:

qZ0.05=−1.645 $q^Z_{0.05} = -1.645$ )

-7255

-8443

-8125

-7804

Question 18

(5) Let

W0=$100,000 $W_0 = \$100,000$ be the initial wealth invested in each asset. Compute the 5% monthly Value-at-Risk for VEIEX. (Hint:

qZ0.05=−1.645 $q^Z_{0.05} = -1.645$ )

-13805

-13107

-12894

-12782

Question 19

(5) Let

W0 $W_0$ = $100,000 be the initial wealth invested in each asset. Compute the 5% annual Value-at-Risk for VFINX.

-23885

-22455

-31304

-27292

Question 20

(5) Let

W0 $W_0$ = $100,000 be the initial wealth invested in each asset. Compute the 5% annual Value-at-Risk for VEIEX.

-41404

-27556

-32488

-39286

Question 21

(6) Let

{Yt} $\{Y_t\}$ represent a stochastic process. Under which of the following conditions is

{Yt} $\{Y_t\}$ covariance stationary? Check all that apply.

Question 22

(4) Realizations from four stochastic processes are given below. Which processes appear to be covariance stationary?

Process 1

Process 2

Process 3

Process 4

Question 23

The figure below shows some graphical diagnostics of the monthly return distribution for the Vanguard S&P 500 index, VFINX, over the 5-year period September 2005 through September 2010.

(6) Check all that apply:

Question 24

The figure below shows some graphical diagnostics of the monthly return distribution for the Vanguard Emerging Markets index, VEIEX, over the 5-year period September 2005 through September 2010.

(6) Check all that apply:

Question 25

(5) Based on the scatterplot of the returns shown below, does there appear to be any linear dependence between the returns on VFINX and VEIEX?

Unable to tell

Yes

Question 26

For the following questions, consider the AR(1) model:

Y t = 3 + .45 Y t - 1 + ϵ t ϵ t \sim N (0, 1.5 2)

$Y_t = 3 + .45Y_{t-1} +\epsilon_t \\ \epsilon_t \sim N(0, 1.5^2)$

(5) The process is covariance stationary.

True

False

Question 27

(5) What is the mean of the process?

5.45

6.67

Question 28

(5) What is the variance of the process?

2.82

1.5

2.25

Question 29

(5) What is the covariance of

(Yt,Yt−1) $(Y_t, Y_{t-1})$ ?

2.82

0.45

1.27

Question 30

(5) What is the correlation of

(Yt,Yt−1)? $(Y_t, Y_{t-1})?$

1.27

2.25

0.45

In accordance with the Coursera Honor Code, I (Anonymous Student) certify that the answers here are my own work.

You cannot submit your work until you agree to the Honor Code. Thanks!

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