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计算机代写|7SSMM800: Quantitative Techniques Examination 2021/22

计算机代写|7SSMM800: Quantitative Techniques Examination 2021/22




  1. There are 3 questions in total. Answer 1 question only.
  2. If you answer more questions than specified, only the first answers (up to the specified number) will be marked.
  1. Paste any required diagrams and graphs for your answers directly onto the answer sheet using software or uploaded photos.
  1. A template answer sheet has been provided on the KEATS page, you should complete the first page ‘cover sheet’ and then type your answers below. Make sure you clearly indicate the questions you are answering (e.g. Section A, Question 1).
  1. If you have a PAA cover sheet, you should include this in addition to the template answer sheet
  1. Save your work regularly, at least every 15 minutes.


  1. Your answer sheet should be submitted via the Turnitin submission link on the module KEATS page.
  1. Ensure your document is submitted through Turnitin with the title CANDIDATE ID – MODULE CODE- e.g. AC12345-7SSMM800
  1. Once submitted please check you are satisfied with the uploaded document via the submission link.
  1. If you experience technical difficulties uploading your assessment to KEATS please email a copy to with the subject of the email as CANDIDATE ID- MODULE CODE- PERIOD 1 ASSESSMENT. You should attach supporting evidence of technical issues where possible.

Answer only ONE question out of three

Question 1

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?

[25 marks]

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]

Question 2

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]

Question 3

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:

𝑦௜௧ = 𝛼 + 𝛽𝑥௜௧ + 𝜇௜ + 𝜐௜௧ ,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]