Question set

1. Consider the Capital Asset Pricing Model that relates the excess return of a security to the market portfolio. The relevant data set (CAPM.xls) contains prices of different US stocks, S&P 500 index and the series of the US Treasury bills.

a) Estimate CAPM betas for each of the stock. [10 marks]

b) Examine the sizes and signs of the parameters in the regressions. Do these make sense? [10 marks]

c) Explain which of the stocks would you classify as defensive stocks and which as aggressive? [10 marks]

d) Do you agree that the CAPM provides some reasonable explanation of the variability of the returns to each of the stock? [10 marks]

e) Check if the CAMP model for FORD suffers from heteroscedasticity. Use a formal test to check that. [10 marks]

f) Can you use the standard errors in this regression if residuals are heteroscedastic? [10 marks]

g) For the model estimated in part e) formally test if the residuals are correlated? [10 marks]

h) How would you solve the problem of autocorrelation? [10 marks]

i) Suppose you want to regress GE log returns on FORD and S&P log returns. Would you expect to have multi-collinearity? Check it. [20 marks]

2. Select two of the stock series from the CAPM.xls, construct a set of continuously compounded returns, and perform a time series analysis of these returns using EViews which includes

a) An examination of the ACFs and PACFs. [25 marks]

b) An estimation of the information criteria for each ARMA model order from (0,0) to (2,2). [25 marks]

c) An estimation of the model that you feel more appropriate given the results from the previous two parts. [25 marks]

d) The construction of a forecasting framework to compare the forecasting accuracy of

i) Your chosen ARMA model [5 marks]

ii) An arbitrary ARMA(1,1) [10 marks]

iii) A random walk with drift in the log price levels (hint: this is equivalent to an ARMA(0,0) – a simple model with a constant). [10 marks]

[Total: 200 marks]

1. Consider the Capital Asset Pricing Model that relates the excess return of a security to the market portfolio. The relevant data set (CAPM.xls) contains prices of different US stocks, S&P 500 index and the series of the US Treasury bills.

a) Estimate CAPM betas for each of the stock. [10 marks]

b) Examine the sizes and signs of the parameters in the regressions. Do these make sense? [10 marks]

c) Explain which of the stocks would you classify as defensive stocks and which as aggressive? [10 marks]

d) Do you agree that the CAPM provides some reasonable explanation of the variability of the returns to each of the stock? [10 marks]

e) Check if the CAMP model for FORD suffers from heteroscedasticity. Use a formal test to check that. [10 marks]

f) Can you use the standard errors in this regression if residuals are heteroscedastic? [10 marks]

g) For the model estimated in part e) formally test if the residuals are correlated? [10 marks]

h) How would you solve the problem of autocorrelation? [10 marks]

i) Suppose you want to regress GE log returns on FORD and S&P log returns. Would you expect to have multi-collinearity? Check it. [20 marks]

2. Select two of the stock series from the CAPM.xls, construct a set of continuously compounded returns, and perform a time series analysis of these returns using EViews which includes

a) An examination of the ACFs and PACFs. [25 marks]

b) An estimation of the information criteria for each ARMA model order from (0,0) to (2,2). [25 marks]

c) An estimation of the model that you feel more appropriate given the results from the previous two parts. [25 marks]

d) The construction of a forecasting framework to compare the forecasting accuracy of

i) Your chosen ARMA model [5 marks]

ii) An arbitrary ARMA(1,1) [10 marks]

iii) A random walk with drift in the log price levels (hint: this is equivalent to an ARMA(0,0) – a simple model with a constant). [10 marks]

[Total: 200 marks]

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