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Final exam. You have unlimited time for the exam and 2 attempts. Read each question carefully. For questions that rely on answers from previous questions, please use your full precision answer and not the rounded answer.

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:

The graph below shows the efficient frontier computed from three Vanguard mutual funds: Pacific Stock Index (vpacx), US Long Term Bond Index (vbltx), and Emerging Markets Fund (veiex).

Expected return and standard deviation estimates for specific assets are summarized in the table below. These estimates are based on monthly continuously compounded return data over the five year period September 2004 – September 2009. some_text

(5) What is the annualized continuously compounded mean of vpacx?

6.11%

5.28%

5.16%

4.86%

Question 2

(5) What is the annualized standard deviation of vpacx?

18.47%

19.36%

19.92%

20.75%

Question 3

(5) What is the annualized sharpe ratio of vpacx? (Remember, please use full precision from your previous answers)

0.217

0.204

0.229

0.187

Question 4

(5) What is the annualized continuously compounded mean of vbltx?

6.47%

6.22%

6.04%

5.88%

Question 5

(5) What is the annualized standard deviation of vbltx?

10.05%

11.12%

11.67%

9.64%

Question 6

(5) What is the annualized sharpe ratio of vbltx? (Remember, please use full precision from your previous answers)

0.490

0.481

0.466

0.521

Question 7

(5) What is the annualized continuously compounded mean of veiex?

15.36%

13.21%

16.49%

14.88%

Question 8

(5) What is the annualized standard deviation of veiex?

28.21%

27.56%

29.27%

28.78%

Question 9

(5) What is the annualized sharpe ratio of veiex? (Remember, please use full precision from your previous answers)

0.492

0.546

0.328

0.481

Question 10

(10) Find the efficient portfolio of risky assets only (e.g. a portfolio on the Markowitz bullet) that has an expected monthly return equal to 1%. In this portfolio, how much is invested in vpacx, vbltx, and veiex?

vpacx = 33%, vbltx = 33%, veiex = 33%

vpacx = -74%, vbltx = 115%, veiex = 58%

vpacx = -22%, vbltx = 171%, veiex = -49%

vpacx = 45%, vbltx = 28%, veiex = 27%

Question 11

(5) How much should be invested in T-bills and the tangency portfolio to create an efficient portfolio with expected return equal to 1%?

Tangency = 62%, T-bills = 38%

Tangency = 44%, T-bills = 56%

Tangency = 55%, T-bills = 45%

Tangency = 50%, T-bills = 50%

Question 12

(5) What is the standard deviation of the efficient portfolio from the previous question?

4.33%

3.58%

3.21%

4.19%

Question 13

(5) In the efficient portfolio from the previous 2 questions, what are the shares of wealth invested in T-Bills, vpacx, vbltx, and veiex?

T-bills = 38%, vpacx = -122%, vbltx = 94%, veiex = 90%

T-bills = 56%, vpacx = -87%, vbltx = 66%, veiex = 64%

T-bills = 50%, vpacx = -99%, vbltx = 76%, veiex = 73%

T-Bills = 45%, vpacx = -108%,vbltx = 83%, veiex = 79%

Question 14

(100 Assuming an initial $100,000 investment for one month, compute the 5% value-at-risk on the global minimum variance portfolio.

-$4,356

-$4,181

-$5,287

-$2,903

Question 15

The following represents R linear regression output from estimating the single index model for the Vanguard Pacific Stock Index (vpacx) using monthly continuously compounded return data over the 5 year period September 2004 – September 2009. In the regressions, the market index is the Vanguard S&P 500 index (vfinx).

(2) What is the estimated value of

β $\beta$ for vpacx? (Answer must be EXACT based on R output.)

Question 16

(2) What is the estimated standard error of

β $\beta$ for vpacx? (Answer must be EXACT based on R output.)

Question 17

(2) What is the estimate of

σϵ $\sigma_{\epsilon}$ for vpacx? (Answer must be EXACT based on R output.)

Question 18

(2) What is the

R2 $R^2$ for the regression for vpacx? (Answer must be EXACT based on R output.)

Question 19

The following represents R linear regression output from estimating the single index model for the Vanguard long-term bond index (vbltx) using monthly continuously compounded return data over the 5 year period September 2004 – September 2009. In the regressions, the market index is the Vanguard S&P 500 index (vfinx).

(2) What is the estimated value of

β $\beta$ for vbltx? (Answer must be EXACT based on R output.)

Question 20

(2) What is the estimated standard error of

β $\beta$ for vbltx? (Answer must be EXACT based on R output.)

Question 21

(2) What is the estimate of

σϵ $\sigma_{\epsilon}$ for vbltx? (Answer must be EXACT based on R output.)

Question 22

(2) What is the

R2 $R^2$ for the regression for vbltx? (Answer must be EXACT based on R output.)

Question 23

The following represents R linear regression output from estimating the single index model for the Vanguard Emerging Markets Fund (veiex) using monthly continuously compounded return data over the 5 year period September 2004 – September 2009. In the regressions, the market index is the Vanguard S&P 500 index (vfinx).

(2) What is the estimated value of

β $\beta$ for veiex? (Answer must be EXACT based on R output.)

Question 24

(2) What is the estimated standard error of

β $\beta$ for veiex? (Answer must be EXACT based on R output.)

Question 25

(2) What is the estimate of

σϵ $\sigma_{\epsilon}$ for veiex? (Answer must be EXACT based on R output.)

Question 26

(2) What is the

R2 $R^2$ for the regression for veiex? (Answer must be EXACT based on R output.)

Question 27

(5) What is the percentage of total risk not due to the market (diversifiable risk) for vpacx?

28%

67%

72%

33%

Question 28

(5) What is the percentage of total risk not due to the market (diversifiable risk) for vbltx?

36%

93%

64%

Question 29

(5) What is the percentage of total risk not due to the market (diversifiable risk) for veiex?

56%

73%

44%

27%

Question 30

(5) Which asset is riskiest relative to the S&P 500?

vbltx

veiex

vpacx

Question 31

(5) Which asset is most beneficial to hold in terms of diversification?

vpacx

veiex

vbltx

Question 32

(6) For each asset, test the null hypothesis that

β $\beta$ = 1 against the alternative that

β≠1 $\beta \neq 1$ using a 5% significance level. For which assets do you reject the null hypothesis?

vbltx

veiex

vpacx

Question 33

(10) Using the information listed in Question 1, what is the

β $\beta$ of the global minimum variance portfolio?

1.15

1.55

0.22

0.86

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!

Introduction to Computational Finance and Financial Econometrics

Introduction to Computational Finance and Financial Econometricsby Eric Zivot

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Introduction to Computational Finance and Financial Econometrics
by Eric Zivot