程序代写案例-MANG6008W1
时间:2022-05-13
UNIVERSITY OF SOUTHAMPTON MANG6008W1
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SEMESTER 2 EXAMINATIONS 2018-2019
QUANTITATIVE RESEARCH IN FINANCE

DURATION: 120 MINUTES (2 HOURS)
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This paper contains FOUR questions.

Answer ANY TWO questions.

An outline marking scheme is shown in brackets to the right of each
question.

Only University approved calculators may be used.

A foreign language direct ‘Word to Word’ translation dictionary (paper
version) ONLY is permitted provided it contains no notes, additions
or annotations.


Statistical Tables are provided.












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1.

a) What is an estimator? Is the OLS estimator superior to all other estimators?
Explain.
(30 Marks)

b) An analyst tells you that shares in Chris Mining plc have no systematic risk, in
other words that the returns on its shares are completely unrelated to
movements in the market. The value of beta and its standard error are
calculated to be 0.214 and 0.186, respectively. The model is estimated over
thirty-eight quarterly observations. Write down the null and alternative
hypotheses. Test this null hypothesis against a two-sided alternative. Form and
interpret a 95% confidence interval for beta using the figures given. Consider
the critical t-value is ±2.03.
(40 Marks)

c) A researcher estimates the following model for stock market returns, but thinks
that there may be a problem with it. The standard error are given in
parentheses. By calculating the t -ratios and considering their significance and
by examining the value of 2R or otherwise, suggest what the problem might
be. How might you go about solving the perceived problem?


� = 0.638 + 0.4022 − 0.8913 , 2 = 0.96,�2 = 0.89 (0.436) (0.291) (0.763)
(30 Marks)


2.

a) What do you understand by the term “auto correlation” of residuals in CLRM?

(30 Marks)






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b) Assume that you have estimated a regression of the form given below in
order to evaluate the effect of various firm-specific factors on the returns of a
sample of firms. You have run a cross-sectional regression with 200 firms:

iiiiii uBETAPEMBSr +++++= 43210 βββββ

where: ir is the percentage annual return for the stock
iS is the size of firm i measured in terms of sales revenue
iMB is the market to book ratio of the firm
iPE is the price/earnings (P/E) ratio of the firm
iBETA is the stock’s CAPM beta coefficient


You have obtained the following results (with standard errors in parentheses)

)092.0()397.0()130.0()124.0()059.0(
096.0188.0391.0851.0090.0ˆ iiiii BETAPEMBSr −+++=



Calculate the t -ratios. Assume that 97.1=criticalt . What do you conclude about the
effect of each variable on the returns of the security? On the basis of your results,
what variables would you consider deleting from the regression? If a stock’s beta
increased from 1 to 1.2, what would be the expected effect on the stock’s return? Is
the sign on beta as you would have expected? Explain your answers in each case.
(40 Marks)


c) In CLRM, are assumptions made concerning the unobservable error terms
)( tu or about their sample counterparts, the estimated residuals )ˆ( tu ?
Explain your answer.
(30 Marks)



TURN OVER


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MANG6008W1

3.

Consider the following regression model
1 1, 2 2,t t t tY X uXα β β= + ++
(a) Specify the assumptions that must hold, so the least squares estimators of
the Coefficients are BLUE.
(25 marks)

(b) Specify the procedure of testing if β1=0 at significance level of 1% (You will
need to provide the hypotheses and the function of test statistics and explain
how to make the statistical judgement).
(25 marks)

(c) Explain how we can test if we adopt the wrong functional forms of independent
variables?
(10 marks)

(d) If 1,tX can be written as 1, 2,5t tX X= , Can we still use the original function to
perform the regression and why?
(10 marks)

(e) What is the consequence if instead of using the original regression model, you
end up with the following model,

1 1, 2 2, 3 3,t t t t tY XX uXα β β β+ + + +=
where X3,t is irrelevant to Yt but might be correlated with the other
regressors.
(10 marks)

(f) If ˆtu is the fitted value of tu , after estimating the coefficients we find that
1ˆ ˆt t tu u vρ −= + , in which ρ is significantly different from 0. What problem will it
cause for the originally estimated coefficients? Which test can be used to
detect this problem?
(20 marks)


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4.

Consider the following linear regression model for Y and X :
ttt XY εβα ++=
where tε is the stochastic error term. Assume that instead of )iid(0, ~
2σε t
, it is expressed in the following form.
2
110
2
−+= tt εδδσ

(i) With respect to the above processes, discuss why the error term tε is
conditionally normal.
(10 marks)
(ii) What assumptions do we need impose on 0δ and 1δ ? Explain.
(15 marks)

(iii) What type of Kurtosis you associate with the distribution of the tε term.
Explain.
(10 marks)

(iv) Show that a GARCH(1,1) can be represented by an ARCH )(∞ process.
(45 marks)

(v) Assume that the ruling political party in the UK lost election. This ‘news’ might
affect the stock market volatility. To test this hypothesis, a researcher
estimated an asymmetric GARCH model for a stock market return series for
the UK. The results from his estimation are presented in Table 1:








TURN OVER
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MANG6008W1


Table 1: Asymmetric GARCH estimation of UK stock market return

Dependent variable: UK_return
Method: ML-ARCH – Normal distribution
Sample (adjusted): 2008 after adjustments
Convergence speed achieved after 9 iterations
GARCH = C(2)+C(3) RESID(-1)^2 + C(4) RESID(-1)^2*RESID(-1)<0) +
C(5)*GARCH(-1)
Variance eq. Coefficient Std. Error z-statistic Prob
C 0.00244 0.0005 4.880 0.009
RESID(-1)^2 0.03003 0.0042 7.150 0.000
RESID(-
1)^2*RESID(-
1)<0)
-0.0089 0.0031 -2.871 0.009
GARCH(-1) 0.92413 0.0052 177.717 0.000
R-Squared = -0.00098
Adj. R-Squared = -0.0029
Durbin-Watson stat = 1.960


In Table 1, comment on the significance of the each coefficient at 5% levels of
significance. Interpret the sign of the asymmetric term.
(20 marks)


END OF PAPER













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