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School of Economics

ECO-7009A: Financial Econometrics

FORMATIVE ASSESSMENT

2021

· It is recommended you spend a maximum of THREE HOURS completing this formative assessment.

· Answer ALL THREE questions.

· Questions are divided into parts.  There are 25 parts in total.    All parts carry equal marks (i.e. 4% each).

· Write (or type) your answers in the spaces provided.

· Some parts simply require you to insert numerical answers in tables.  Other parts require you to provide interpretation and discussion of results.  In the latter case, you are advised not to exceed 100 words in your answer to any single part.

· Written material MAY be consulted.

· Your answer should be submitted as a single document, on the Blackboard site.

· Your work will NOT be marked.

· When you have submitted your answer, you will receive a document containing the correct answers.  You should use this document in preparing for the Summative Assessment in January.

The data sets required to answer the questions in this test are:

Ø BIKES_2021

Ø BIGMAC_JAN_2021

Ø STOCKS_JAN_2021

QUESTION 1  (40 marks)

The file BIKES_2021 contains data from a developing economy (quarterly; 1998 q4 through to 2019 q3) on the following variables:

year: Year

q: Quarter (1 if JFM; 2 if AMJ; 3 if JAS; 4 if OND)

t: Time trend variable

bikes: Real aggregate expenditure on motorbikes ($million at 2019 prices)

income: Real personal disposable income ($billion at 2019 prices)

pbike: Real price of motorbikes (index)

pcar: Real price of cars (index)

pfuel: Real price of motor fuel (index)

(a) What was real aggregate expenditure on motorbikes in the third quarter of 2012?

(b) Using the command regress bikes income pbike pcar pfuel, estimate a regression model with bikes as the dependent variable, and income, pbike, pcar and pfuel as the explanatory variables.  Report the coefficients and standard errors in the following table (USE 3 DECIMAL PLACES).  Also report the R² and the sample size.

Variable	Coefficient	Standard error
income
pbike
pcar
pfuel
constant
R-squared
Sample size

(c) Interpret the coefficient of income.  How strong is the evidence that motorbikes are a normal good?  [Report the relevant t-statistic and p-value.]

Interpretation of coefficient:

t_income:

p-value:

Interpretation of test result:

(d) Do the coefficients on pbike, pcar and pfuel have the expected signs?  Explain your answers.

(e) Is there evidence to suggest that cars and motorbikes are substitutes?  Carry out an appropriate test.  (Hint: t-test on pcar).

(f) Using the command corr pbike pcar pfuel, find the correlation matrix between these three explanatory variables.  Report the correlations in the table below.

|    pbike     pcar    pfuel

-------------+---------------------------

pbike |

pcar |

pfuel |

Explain why elements of this matrix might be the reason for your conclusion in (e).

(g) Add i.q to the list of explanatory variables in the regress command used in (b).  DO NOT REPORT THE REGRESSION RESULTS.  Conduct an F-test of the significance of season in explaining the demand for motorbikes. Use the F-test formula on the formula sheet, and verify that your answer is correct using the test command in STATA. Interpret the result.

(h) By interpreting the coefficients of the quarterly dummies, provide a ranking of the four quarters according to (ceteris paribus) comparison of motorbike expenditure.  In which quarter is expenditure on motor-cycles highest (ceteris paribus), and in which quarter is it lowest?

(i) Using the command bgodfrey, lags(1 4), test for first-order and fourth-order serial correlation in the model of (g) (the model with the quarterly dummies).  Report the results in the following table.  Do the results tell us that there is a problem with the model?

Lags	Chi2	df	p-value
1
4

Interpretation:

(j) Add the 1-period lag of bikes (L.bikes) to the model of (g) (the model with the quarterly dummies).  DO NOT REPORT THE REGRESSION RESULTS.  Test for serial correlation again.  Is the result different from (i)?  Comment.

Lags	Chi2	df	p-value
1
4

Interpretation and Comment:

QUESTION 2  (20 MARKS)

The file BIGMAC_JAN_2021 contains data on 55 countries in January 2021.  The variables are:

p_local: price of a Big Mac (the McDonald’s hamburger) in local currency in January 2021

p_usa: price of Big Mac in the USA in January 2021 (note: this is the same value in every row)

e:     exchange rate for against the US dollar in January 2021 (that is, e is the number of units of local currency that can be exchanged for one US dollar in January 2021)

gdp_ratio: Ratio of GDP-per-head in country to GDP-per-head in USA (both measured in US$)

(a) From the available data, compute the exchange rate for the Guatemalan Quetzal (GTQ) against the Chinese Yuan (CNY) January 2021 (i.e. find the number of Guatemalan Quetzal that can be exchanged for one Chinese Yuan).

(b) By dividing p_local by e, compute the price of a Big Mac in each country in US dollars (do NOT report the complete results).  On this basis, which of the 55 currencies appears the most under-valued in January 2021, and which the most over-valued?

Generate the required variables, and estimate the following regression model:

(1)

Do not report the results.

(c) In Model (1), perform a test of the null hypothesis .  Interpret the result of the test.  Which theory is being tested?

Next, generate the additional required variable, estimate the following regression model:

(2)

Do not report the results.

(d) In Model (2), test the significance of the effect of the added variable, log(gdp_ratio).  That is, report the result of the t-test of .  Interpret the result of the test.  What is the name given to this effect?

t_{log(gdp_ratio)} =

p-value =

Interpretation:

Name of effect:

(e) In Model (2), perform a test of the null hypothesis .  Do you get a different answer from (c)?  Can you explain this difference?

QUESTION 3  (40 MARKS)

The file STOCKS_JAN_2021 contains daily data (Tuesday 12 January 2016 – Tuesday 12 January 2021) on the following variables:

date: Calendar date

t: time trend (1 for first observation; 2 for second; and so on)

x1: Price of GOLD (Precious metal)

x2: Share price of UNILEVER (Food and Beverages)

x3: Share price of GLENCORE (Basic Resources)

xm: FTSE-100 index

r1: Daily return on GOLD

r2: Daily return on UNILEVER

r3: Daily return on GLENCORE

rm: Daily return on FTSE-100 index

(a) On 23 July 2020, what day of the week was it, and what were the prices of Gold, Unilever, and Glencore, and the value of the FTSE-100 index?  Insert your answers below.

Day of week on 23 July 2020: ______________________

Stock	Price on 23 July 2020
GOLD
UNILEVER
GLENCORE
FTSE-100 INDEX

(b) Using the daily-return variables, carry out the regressions and other tasks that are necessary to find the beta coefficients, the unsystematic risk (sigma), and the mean return (rbar) for each of Gold, Unilever, and Glencore.  Insert the results in the following table (USE 4 DECIMAL PLACES):

Stock	Sector	beta	sigma	rbar
GOLD	Prec. metal
UNILEVER	Food&Bev.
GLENCORE	Basic Res.

(c) Of Unilever and Glencore, which is “aggressive”, and which is “defensive”?  Explain your answer.  Is this what you would expect, in the view of the sectors these stocks are in?

(d) Comment on your estimate for the beta coefficient of Gold.  Provide an explanation for value of this beta coefficient.

The remainder of the question focuses on the FTSE100 index (named xm in the data set).  Let R_t represent the daily return on FTSE100 index.

(e) Use the command regress rm L.rm L2.rm L3.rm L4.rm L5.rm in order to estimate the following model (you may need to use the command tsset t first):

Report coefficients only, in the following table (USE 4 DECIMAL PLACES):

Parameter	Variable	Coefficient
b1	Rt-1
b2	Rt-2
b3	Rt-3
b4	Rt-4
b5	Rt-5
b0	Constant

(f) For the model of (e), use an F-test to test the joint hypothesis:

H₀: b₁ = 0

b₂ = 0

b₃ = 0

b₄ = 0

b₅ = 0

Report the F-statistic and the p-value.  Is the result consistent with EMH?  Briefly explain your answer.

(g) Assume that the Covid_19 crisis commenced on 16 March 2020 (t=1090).  Using the command gen covid=t >= 1090, generate a dummy variable taking the value 1 during the crisis, and zero otherwise.

Consider the following model of the FTSE 100 Return:

Note that this is a GARCH(1,1) model in which the variable covid appears in both the return equation and the conditional-variance equation.

Using the arch command with appropriate options, estimate the above model.  Report coefficients and p-values in the following table (USE 4 DECIMAL PLACES):

	Coeff.	p-value
(covid)
(constant)
(covid)
(constant)
(ARCH)
(GARCH)

Based on these results, what effect has the Covid_19 crisis had on FTSE 100 Returns?

(h) In order to value an option written on the FTSE100 Index, a measure of the annual volatility (σ) of the FTSE100 Index is required.  One way of obtaining such a measure is to apply the formula:

where R is the daily return on the FTSE100 Index.

Apply this formula to the available data, and report your measure of annual volatility.

(i) Consider four European call options written on the FTSE100 Index, traded on 12 January 2021 (the last day of the sample), with 70 days (0.1918 years) to expiry, and with the strike prices given in the table below.  The risk-free rate is 0.001.  For the volatility, use your answer to (h).  Using the “option pricing calculator”, find the values of these four call options, and insert the answers in the table below. (Remember that you first need to find out the “current price” from last row of the data.)