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IB2B20_A Financial Econometrics

创建日期：2024-07-09 17:13:05

所属分类：金融Finance

标签： IB2B20

Financial Econometrics

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IB2B20_A

Financial Econometrics

Section A

Answer ALL questions in this section

Question 1

Consider the following results, of a linear regression estimated by ordinary least squares (OLS), investigating the determinants of the excess returns of an individual company’s stock:

where ERt is the excess return on a stock, is the excess return on an aggregate stock market index, SMBt is the small minus big and HMLt the high minus low risk factors of Fama and French. The first coefficient is the estimate of the intercept and the coefficients next to the variable names are the estimated respective slope parameters. The numbers in brackets beneath the estimated coefficients are their standard errors.

a) Provide an interpretation of the estimated coefficient on the variable. (2 marks)

b) What is the key assumption for least squares when considering bias of OLS estimators? Explain carefully and use the assumption to show unbiasedness of the coefficients. (5 marks)

c) Describe, providing mathematical expressions, the difference between the adjusted and unadjusted R-squared. Does a low R-squared invalidate a regression? Explain carefully. (3 marks)

Question 2

Consider again the estimation results in equation (1) (from Question 1).

a) If you were to test the null hypothesis that the estimated coefficient on the term is equal to 1, against the one-sided alternative that it is less than 1, would you reject or fail to reject the null at any of the three 1%, 5% and 10% significance levels? Explain clearly how you reached the conclusion. (Hint: the critical values of the t-student distribution tn−k−1 at the 1%, 5% and 10% significance level are equal to 2.327, 1.645, and 1.281, respectively) (3 marks)

b) Do the independent variables in equation (1) help or not help explain ERt? Construct a joint test of this hypothesis and provide mathematical formula where appropriate. (Hint: the critical values of the F-student distribution Fq,n−k−1 with degrees of freedom q=3 and n-k-1 = 120 are 2.13, 2.68 and 3.78 at the 10%, 5% and 1% significance level respectively) (5 marks)

c) State briefly the general principle of the joint hypothesis test using an F-statistic.

Question 3

Consider again the estimation results from equation (1) (from Question 1).

a) Say we have omitted from the regression a risk factor measuring momentum. What are the relevant facts we need to consider when determining if this omission causes the estimated coefficient on the SMBt variable to be biased? What might be direction of the bias of the OLS estimated coefficient for SMBt? (6 marks)

b) Construct the 90% confidence interval for the coefficient on the term HMLt (three decimals are enough). State in one sentence how you interpret this confidence interval. Provide mathematical formula where appropriate. (Hint: the 90th critical value c of the t-student distribution tn−k−1 is equal to 1.64. (4 marks)

Question 4

We want to estimate the following linear regression model by OLS:

We are concerned about the potential problem of heteroscedasticity in the regression error.

a) What happens to OLS estimators and their variances if we introduce heteroscedasticity but retain all other assumptions of the classical linear regression model? (2 marks)

b) Suppose we test for the presence of heteroscedasticity in the model’s residuals, where the p-value from the White test is 0.03. How would you interpret this result? State carefully the null and alternative hypothesis of the test. How would you address the issue of heteroscedasticity if it were present? Provide mathematical expressions where appropriate. Write down any regression equations you would need to estimate. (4 marks)

c) Describe and define the concept of a weakly dependent time-series. Give an example and explain why this property is important for time-series regression analysis. Explain carefully and provide mathematical expressions where appropriate. (4 marks)

Section B

Answer ANY TWO questions

Question 5

a) Consider the following AR (1) process:

Write down the set of equations for the one-step, two-step, and three-step ahead forecasts of yt. Provide a detailed description and use mathematical formulas where appropriate. (7 marks)

b) Outline how you would evaluate the relative forecast performance of two models (for example an AR(1) as in part a) and an AR(2)) using a “pseudo out-of-sample” forecasting exercise. Provide a detailed description of each stage and use mathematical formula where appropriate. (10 marks)

c) IGNORE THIS QUESTION – NOT COVERED IN 2024 COURSE. Consider the following GARCH (1,1) process:

Write down a set of equations in and and their lagged values, which could be employed to produce one-step, two-step and three-step ahead forecasts for the conditional variance of yt. How would you evaluate the performance of the forecasts of the conditional variance? Provide a detailed description and use mathematical formula where appropriate. (13 marks)

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CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 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