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Answer only ONE question out of three
You estimate the following model:
𝐸𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛௧ = 𝛼 + 𝛽𝑒𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛_𝑚௧ + 𝜀௧ ,where 𝑒𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛௧ is the difference between return on Asset A and the risk-free rate, 𝑒𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛_𝑚௧ is the difference between return on the market portfolio and the risk-free rate, and 𝜀௧ is a random error term. Data are for 174 months. You estimate the model via OLS; results are reported below.
OLS estimates using 174 observations Dependent variable: excess return on Asset A
a)What theory can be associated to the model to be estimated? Discuss.[25 marks]
b) How would you test the hypothesis that the market is in equilibrium?
Perform the test at the 5% s.l. and present the logic of the test. Test the hypothesis that the stock is riskier than the market at the 5% s.l. Would you buy the stock if you aim at reducing risk in your portfolio? What issues can you see with this approach?
c) Consider the following augmented CAPM model
𝐸𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛௧ = 𝛼 + 𝛽𝑒𝑥𝑐𝑒𝑠𝑠_𝑟𝑒𝑡𝑢𝑟𝑛_𝑚௧ + 𝛾𝐷𝑒𝑏𝑡௧ + 𝜀௧ ,where 𝐷𝑒𝑏𝑡௧ is the firm’s debt at time t. What is the sign you expect for this variable? Discuss. A regression on 300 observations gives you the value -0.022179 for the estimated parameter for the firm’s debt, and 0.011739 for its standard deviation. Is the variable statistically significant at the 10% s.l.? Are you going to adopt a passive or an active investment strategy based on your result? If your decision builds upon the OLS approach, is there a possibility that you could go for the wrong choice? Discuss.[25 marks]
d) Is the model statistically adequate? What type of analysis would you perform to check whether this is the case? Discuss.[25 marks]
Consider the following model:
𝐲 = 𝐗𝛃 + 𝛆,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, 𝛃 is the vector of parameters to be estimated and 𝛆 is the error term.
a) List and discuss the assumptions you need for the Ordinary Least Squares (OLS) to be a Best Linear Unbiased Estimator (BLUE).[25 marks]
b) Derive the OLS estimator and variance and discuss where each assumption is needed for the derivation of the two parameters.[25 marks]
c) Discuss the properties of linearity, unbiasedness, and efficiency, and what assumption you need for each of these properties to hold and show where each assumption is needed for the derivation.[25 marks]
d) Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.[25 marks]
a) What are the advantages of estimating the panel data models, if one is available? Would it be reasonable to estimate it using the OLS approach?Discuss.[25 marks]
b) Consider the following fixed effects model:
𝑦௧ = 𝛼 + 𝛽𝑥௧ + 𝜇 + 𝜐௧ ,where 𝜇 is taken as a fixed effect. What approach can you adopt to estimate the parameters of interest? Discuss.[25 marks]
c) Describe the random effects model and discuss how this model captures the cross-sectional individual heterogeneity.[25 marks]
d) How do you choose between the fixed effects and random effects panel models? Discuss.[25 marks]