Computer Exercises (10 questions) Assignment

Computer Exercises (10 questions)

The numbers in your answers might be slightly different depending on the soft-

ware used. Select the answer that most closely matches your results (a,b,c, ord).

You should only include original (no photocopies) relevant software output in an

appendix if asked in an exercise.

For the period 01/01/2012 – 31/12/2012, download daily data on the DAX

index into a spreadsheet from the following link:

http://uk._nance.yahoo.com/q/hp?s=^GDAXI

also, for the same period, download daily data from ALV.DE, CBK.DE from

the following link:

http://uk._nance.yahoo.com/q/cp?s=^GDAXI

Load the data into your preferred software – R, Matlab, Stata.

Exercise 1 Plot the log prices and includes the plot in the appendix. Which answer most closely summarizes the log price behavior in your plots?

(a) The data appears to be mean reverting for all series

(b) The data appears to be non-stationary

(c) The data appears to be non-stationary but mean reverting for all series

(d) The data appears to be mean reverting for the Dax and stationary for the rest

Exercise 2 In order to verify that the prices are efficient for all the data series, you decide to compute the Dickey-Fuller test statistic for the model

Exercise 3 Consider the t-statistic of the slope parameter???? in

What is the value of this statistic for each series and using it, do you reject the null of???? = 0 at the 5% level of significance?

(a) Statistic for DAX = 1.49 and do not reject, for ALV.DE = 1.61 and do not reject, for CBK.DE= 1.52 and do not reject

(b) Statistic for DAX =-1.49 and do not reject, for ALV.DE =-1.61 and do not reject, for CBK.DE=-1.52 and do not reject

(c) Statistic for DAX =-1.49 and reject, for ALV.DE =-1.61 and reject, for CBK.DE=-1.52 and reject

(d) Statistic for DAX =-4.35 and reject, for ALV.DE =-1.61 and reject, for CBK.DE=-4.80 and reject

Exercise 4 Compute the log returns for each series and then compute the Jarque-Bera statistic for these returns for each series (you can read about the Jarque-Bera statistic in your textbook, or in http://en.wikipedia.org/wiki/Jarque-Bera test). What is the asymptotic distribution of the test statistic, the value of the statistic for each series and can you reject the null hypothesis that the returns are normally dis-

tributed at the 5% level of significance rejected?

(a) the distribution is Chi-Square with 2 degrees of freedom under the null,and the statistic for DAX =18.13 and reject, for ALV.DE =59.23 and reject, for CBK.DE=48.42 and reject

(b) the distribution is Chi-Square with 1 degrees of freedom under the null, and the statistic for DAX =18.13 and reject, for ALV.DE =59.23 and reject, for CBK.DE=48.42 and reject

(c) the distribution is Chi-Square with 3 degrees of freedom under the null, and the statistic for DAX =18.13 and reject, for ALV.DE =59.23 and reject, for CBK.DE=48.42 and reject

(d) the distribution is Chi-Square with 2 degrees of freedom under the null, and the statistic for DAX =18.13 and do no reject, for ALV.DE =59.23 and do no reject, for CBK.DE=48.42 and do not reject.

Exercise 5 Plot the ACF (include graph in the appendix). Consider the Ljung-Box test to test the null of no autocorrelation for the first 5 lags. What is the value of the statistic for each series and is the null of independence rejected at the 5% level of significance?

(a) Statistic for DAX =2.87 and do not reject, for ALV.DE =1.97 and do not reject, for CBK.DE=0.35 and do not reject

(b)Statistic for DAX =9.87 and reject, for ALV.DE =4.97 and reject, for CBK.DE=2.35 and do not reject

(c) Statistic for DAX =9.87 and do not reject, for ALV.DE =4.97 and do not reject, for CBK.DE=2.35 and do not reject

(d) Statistic for DAX =9.87 and reject, for ALV.DE =4.97 and reject, for CBK.DE=2.35 and reject

Exercise 6 Plot the ACF for the square of the returns (include graph in the appendix). Consider the Ljung-Box test to test the null of no autocorrelation for the first 5 lags. What is the value of the statistic for each series and is the null rejected at the 5% level of significance?

(a) Statistic for DAX =4.36 and do not reject, for ALV.DE =3.88 and do not reject, for CBK.DE=21.90 and reject

(b) Statistic for DAX =3.88 and do not reject, for ALV.DE =4.36 and reject, for CBK.DE=21.90 and reject

(c) Statistic for DAX =4.36 and reject, for ALV.DE =3.88 and do not reject, for CBK.DE=21.90 and reject

(d) Statistic for DAX =4.36 and do not reject, for ALV.DE =3.88 and do not reject, for CBK.DE=21.90 and do not reject

Exercise 7 Using your answers to the above, do you think a random walk for log prices could be a good model, and do you see much evidence of GARCH effects?

(a) For all the models, based on the results above, a random walk does not seem reasonable. Some GARCH effects for CBK, hence could model prices as a stationary AR(1) with GARCH errors for CBK.

(b) For all the models, based on the results above, a random walk with GARCH effects seems reasonable.

(c) For all the models, based on the results above, a stationary ARMA(1,1,) for the returns is reasonable. Some GARCH effects for CBK.

(d) For all the models, based on the results above, a random walk seems reasonable. Some GARCH effects for CBK, hence could use a random walk with GARCH errors for CBK, i.e. log returns follow a GARCH(1,1).

Exercise 8 Use OLS to estimate the cointegrating relation between the stock log-prices of ALV, CBK and DAX, assuming one cointegrating relation and ALV as left hand variables. What is the cointegrating vector, and from plotting the residuals, does cointegration seem to hold?

(a) The cointegrating vector is[1,-0.1289]and log prices could be cointegrated.

(b) The cointegrating vector is[1,-1.4184]and log prices could be cointegrated.

(c) The cointegrating vector is[1,-0.1289,-1.4184]and log prices could be cointegrated.

(d) The cointegrating vector is[1,-0.1289,-1.4184], but log prices do not seem to be cointegrated.

Exercise 9Consider the one factor model for the stocks excess returns using the DAX index as factor:

Which null and alternative hypothesis are most suited to test the validity of the CAPM?

Exercise 10 Suppose that the annualized interest rate is 0.75% and that there are 360 days in a year. What is the daily interest rate, and does the CAPM holds at a 5% level of confidence?(You should use arithmetic excess returns for this question.)

(a) the daily interest rate is 0.75%; the CAMP holds for both stocks

(b) the daily interest rate is0.002%; the CAMP holds for ALV but not for CBK

(c) the daily interest rate is 0.002%; CAMP holds for CBK but not for ALV.

(d) the daily interest rate is0.75%; CAMP holds for CBK but not for ALV.

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