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QUANTITATIVE METHODS FOR FINANCE
QUESTION 1
Consider the following data
N Y X1 X2
1 2 3 8
2 6 2 2
3 3 1 3
4 7 9 2
5 7 3 5
6 9 6 3
7 9 5 2
8 4 2 1
9 11 7 1
10 8 4 2
1.1 Estimate the parameter coefficients of the model
using OLS and clearly state the assumptions you are making about the error term.

1.2 Test the statistical significance of each parameter coefficient.
1.3 Test the overall significance of your model using F-test and R2.

1.4 Derive the implicit restriction on the parameters involved if you rewrite model [1] above as model [2] below:
[2]
where, and .
1.5 Test the linear restriction ß1+ß2=1 in model [1] and in model [2] using t-test.

1.6 What are the diagnostic tests that need to be conducted in order to ensure that your model is correctly specified and satisfies all the classical assumptions you stated in 1a above? (word limit 250)

End of question 1!
QUESTION 2
Using the Annual data for the US manufacturing sector for 1899 to 1922, the following regression results were obtained:
, [1]
, [2]
Requirement:
2.1. Justify the functional form for model [1] and explain the logic behind estimating model
2.2. Do you suspect that there is multi-collinearity in model [1]? Does model [2] specification reduce multicollinearity? Explain your answer.
2.3. Explain one method of eliminating the multicollinearity problem and what problems are associated with your method?
The analyst believes that heteroskedasticity might be a problem in the following model. He therefore wishes to conduct Goldfeld-Quandt test to investigate if the model exhibits heteroskedasticity. He estimates two regressions with the following results.


Requirement:
2.4. Describe the Goldfeld-Quandt (QF) test procedure.
2.5. Conduct the QF test-statistic using the above RSS1 and RSS2 for heteroskedasticity.
2.6. Explain the limitations of the QF test and suggest one alternative test for heteroskedasticity that could be used instead.



QUESTION 3
A hedge is when you make an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract. For example, if you owned a stock, then sold a futures contract setting the price at which you will sell the stock will prevent the loss of adverse price changes occurring.
You are to investigate whether gold price is an adequate hedge against inflation or NYSE is a better hedge against inflation using the data from Gujarati and Porter (2009), Table 3.7. This dataset can be downloaded from Gretl Sample data as Table 3.7 from Gujarati
Dataset is for the United States from 1977 to1991 on:
PRICE = Price of Gold at New York, $ Per Troy Ounce
CPI = Consumer Price Index, 1982-1984=100
NYSE = New York Stock Exchange Index, December 31, 1965=100. It includes most of the stocks listed on the NYSE
Source: CPI and NYSE from Economic Report of the President, 1993, Tables B-59 and B-91. Gold price from U.S. Department of Commerce, Bureau of Economic Analysis, “Business Statistics, 1963-1991″, p. 68
You should consult relevant literature and conduct your own research on the topic. Lecture and seminar materials alone are not sufficient to answer this question.
Requirement
3.1 Based on theory explain why gold price may be a good hedge against inflation. How would you test this empirically using the above data? You should explore both informal methods such as scatterplot and correlation matrix as well as formal methods such as restriction testing for model [1]
[1]
3.2 Based on theory explain why NYSE may be a good hedge against inflation. How would you test this empirically using the above data? You should explore both informal methods such as scatterplot and correlation matrix as well as formal methods such as restriction testing for model [2]
[2]
3.3 Analyse and compare the results from 3.1 with 3.2 in light of the relevant literature stating which measure provides a better hedge and why?
3.4 Test for the violation of any of the classical assumption, such as non-constant variance of error term? Is this an adequate model or does it need re-specification in terms of functional form, change of variables? [15 marks]
3.5 Re-estimate your model correcting for any breakdown of the classical assumptions. Compare the original and the modified models and explain which is better and why?

QUANTITATIVE METHODS FOR FINANCE

QUESTION 1
Consider the following data
N Y X1 X2
1 2 3 8
2 6 2 2
3 3 1 3
4 7 9 2
5 7 3 5
6 9 6 3
7 9 5 2
8 4 2 1
9 11 7 1
10 8 4 2
1.1 Estimate the parameter coefficients of the model
using OLS and clearly state the assumptions you are making about the error term.
1.2 Test the statistical significance of each parameter coefficient.
1.3 Test the overall significance of your model using F-test and R2.
1.4 Derive the implicit restriction on the parameters involved if you rewrite model [1] above as model [2] below:
[2]
where, and .
1.5 Test the linear restriction ß1+ß2=1 in model [1] and in model [2] using t-test.
1.6 What are the diagnostic tests that need to be conducted in order to ensure that your model is correctly specified and satisfies all the classical assumptions you stated in 1a above? (word limit 250)
End of question 1!
QUESTION 2
Using the Annual data for the US manufacturing sector for 1899 to 1922, the following regression results were obtained:
, [1]
, [2]
Requirement:
2.1. Justify the functional form for model [1] and explain the logic behind estimating model
2.2. Do you suspect that there is multi-collinearity in model [1]? Does model [2] specification reduce multicollinearity? Explain your answer.
2.3. Explain one method of eliminating the multicollinearity problem and what problems are associated with your method?
The analyst believes that heteroskedasticity might be a problem in the following model. He therefore wishes to conduct Goldfeld-Quandt test to investigate if the model exhibits heteroskedasticity. He estimates two regressions with the following results.
Requirement:
2.4. Describe the Goldfeld-Quandt (QF) test procedure.
2.5. Conduct the QF test-statistic using the above RSS1 and RSS2 for heteroskedasticity.
2.6. Explain the limitations of the QF test and suggest one alternative test for heteroskedasticity that could be used instead.
QUESTION 3
A hedge is when you make an investment to reduce the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting position in a related security, such as a futures contract. For example, if you owned a stock, then sold a futures contract setting the price at which you will sell the stock will prevent the loss of adverse price changes occurring.
You are to investigate whether gold price is an adequate hedge against inflation or NYSE is a better hedge against inflation using the data from Gujarati and Porter (2009), Table 3.7. This dataset can be downloaded from Gretl Sample data as Table 3.7 from Gujarati
Dataset is for the United States from 1977 to1991 on:
PRICE = Price of Gold at New York, $ Per Troy Ounce
CPI = Consumer Price Index, 1982-1984=100
NYSE = New York Stock Exchange Index, December 31, 1965=100. It includes most of the stocks listed on the NYSE
Source: CPI and NYSE from Economic Report of the President, 1993, Tables B-59 and B-91. Gold price from U.S. Department of Commerce, Bureau of Economic Analysis, “Business Statistics, 1963-1991″, p. 68
You should consult relevant literature and conduct your own research on the topic. Lecture and seminar materials alone are not sufficient to answer this question.
Requirement
3.1 Based on theory explain why gold price may be a good hedge against inflation. How would you test this empirically using the above data? You should explore both informal methods such as scatterplot and correlation matrix as well as formal methods such as restriction testing for model [1]
[1]
3.2 Based on theory explain why NYSE may be a good hedge against inflation. How would you test this empirically using the above data? You should explore both informal methods such as scatterplot and correlation matrix as well as formal methods such as restriction testing for model [2]
[2]
3.3 Analyse and compare the results from 3.1 with 3.2 in light of the relevant literature stating which measure provides a better hedge and why?
3.4 Test for the violation of any of the classical assumption, such as non-constant variance of error term? Is this an adequate model or does it need re-specification in terms of functional form, change of variables? [15 marks]
3.5 Re-estimate your model correcting for any breakdown of the classical assumptions. Compare the original and the modified models and explain which is better and why?

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