Do not turn over until you are told to do so by the Invigilator.

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1 UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton FINANCIAL ECONOMETRICS ECO-7009A Tme allowed: HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 5%; queston carres 0%; queston 3 carres 5%; and queston 4 carres 30%. Marks awarded for ndvdual parts are shown n square brackets. A formula sheet, t-tables, and F-tables are attached at the end of the exam paper. Notes are not permtted n ths examnaton. Do not turn over untl you are told to do so by the Invglator. ECO-7009A Module Contact: Prof. Peter Moffatt, ECO Copyrght of the Unversty of East Angla Verson 1

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3 Page 3 QUESTION 1 [5 Marks] ALL WORKING MUST BE SHOWN IN YOUR ANSWER TO THIS QUESTION The share prce of Natonal Grd (Utltes) was followed for a perod of seven months. The percentage monthly return on Natonal Grd stock (Y), and the percentage monthly change n the stock market ndex (X), are presented n the followng table: Month Natonal Grd (Y) Market (X) January 1 February - -3 March -1-1 Aprl 0 May 1 June 0 1 July 1 4 (a) Obtan estmates of and n the smple regresson model: Y X u t 1,,7 t t t Var u t Report the beta coeffcent for Natonal Grd stock. [10] (b) (c) Fnd the resduals from the smple regresson performed n (a). Hence fnd an estmate of the parameter. Call the estmate ˆ. What s the nterpretaton of ˆ n ths context? [7] Fnd a 95% confdence nterval for. Does the confdence nterval ndcate that Natonal Grd s an aggressve stock, a defensve stock, or nether? Is ths what you would expect for Natonal Grd? [8] TURN OVER

4 Page 4 QUESTION [0 marks] We have data on 53 countres n 016. Let p_local be the prce of a Bg Mac (the McDonald s hamburger) n country n local currency n 016. Let e be the exchange rate for country aganst the US dollar n 016 (that s, e s the number of unts of local currency that can be exchanged for one US dollar n 016). (a) Data on three of the 53 countres s shown n the followng table. Country Currency p_local e South Afrca Rand Norway Kroner Japan Yen Compute the prce of a Bg Mac n each of the three countres n US dollars. On ths bass, whch of the three currences appears under-valued n 016, and whch appears over-valued? [7] The followng regresson model s estmated usng data from all 53 countres n 016 (p_usa s the prce of a Bg Mac n the USA n 016): _ log p local 1 log e u ; 1,,53 p_ usa Followng the regresson, two tests are performed. The results are as follows:. regress log_p_rato log_e Source SS df MS Number of obs = F(1, 51) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = log_p_rato Coef. Std. Err. t P> t [95% Conf. Interval] log_e _cons test (_b[_cons]=0) (_b[log_e]=1) ( 1) _cons = 0 ( ) log_e = 1 F(, 51) = Prob > F = test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = 15. Prob > F =

5 Page 5 (b) Consder the two tests performed followng the regresson above. The frst test s a test of the Law of One Prce (LOP). Explan the concept of LOP. Is t rejected by the 016 Bg Mac data? Whch theory s beng tested by the second test? Is t rejected? [7] A further varable, gdp_rato, s generated, defned as GDP per head n the local country n US dollars dvded by GDP per head n the USA. Ths varable s added to the regresson, wth the results:. regress log_p_rato log_e gdp_rato Source SS df MS Number of obs = F(, 50) = Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE =.8059 log_p_rato Coef. Std. Err. t P> t [95% Conf. Interval] log_e gdp_rato _cons (c) Does gdp_rato have a sgnfcant effect on log_p_rato? What s the name of the theory that s beng confrmed by ths test? Does the test result provde an explanaton for the results of the tests carred out n (b)? Explan your answer. [6] TURN OVER

6 Page 6 QUESTION 3 [5 marks] For the 50 stocks n the FTSE-50 Index, and also the precous metal GOLD, the followng varables are computed usng daly return data from an unspecfed perod: beta: beta: sg: rbar: beta coeffcent (beta coeffcent) squared standard measure of unsystematc rsk mean daly return Mean return s plotted aganst beta, and aganst sg, wth lowess smoothers supermposed n each case. The plots are shown below. (a) (b) One of the beta coeffcents seen n the left-hand graph s negatve. Ths s the beta coeffcent for the commodty GOLD. Explan why Gold s usually found to have a negatve beta coeffcent. [5] Are ether of both of the two plots shown above consstent wth the Captal Asset Prcng Model (CAPM)? Explan your answers n detal. [8] TURN OVER

7 Page 7 Consder the followng model wth mean daly return as the dependent varable: rbar beta beta sg u (1) Model (1) s estmated n STATA wth the followng results:. regress rbar beta beta sg, robust Lnear regresson Number of obs = 51 F(3, 47) = Prob > F = R-squared = Root MSE = 7.4e-05 Robust rbar Coef. Std. Err. t P> t [95% Conf. Interval] beta beta sg _cons.47e (c) (d) Usng the STATA results gven above, carry out two dfferent tests of CAPM. Report all relevant test statstcs and p-values. If you reject CAPM, what s the precse nature of the volaton? Is your answer consstent wth your answer to (b)? [7] Explan why the robust opton has been used wth the regress command. Why do you thnk t s mportant to do ths? [5] TURN OVER

8 Page 8 QUESTION 4 [30 marks] Fve years of daly data on the share prce of TRAVIS PERKINS (Industral Goods and Servces) are used to estmate two models (MODEL 1 and MODEL ). The varable r s the daly return on TRAVIS PERKINS stock. Results from estmaton of the two models are as follows. * MODEL 1. regress r l.r Source SS df MS Number of obs = 1, F(1, 130) = 6.5 Model Prob > F = Resdual , R-squared = Adj R-squared = Total , Root MSE =.017 r Coef. Std. Err. t P> t [95% Conf. Interval] r L _cons durbna Durbn's alternatve test for autocorrelaton lags(p) ch df Prob > ch H0: no seral correlaton * MODEL. regress r l.r l.r l3.r l4.r l5.r Source SS df MS Number of obs = 1, F(5, 194) = 5.60 Model Prob > F = Resdual , R-squared = Adj R-squared = Total , Root MSE = r Coef. Std. Err. t P> t [95% Conf. Interval] r L L L L L _cons

9 Page 9. durbna Durbn's alternatve test for autocorrelaton lags(p) ch df Prob > ch H0: no seral correlaton (a) Frst consder MODEL. Explan why the F-statstc for overall sgnfcance n MODEL amounts to a test of weak-form EMH. Report the F-statstc and the assocated p-value. How strong s the evdence aganst EMH? [5] (b) Test for seral correlaton n both MODEL 1 and MODEL. Report relevant p- values. If you have seral correlaton n one model but not n the other, can you explan ths? [5] A set of day-of-week dummes (day1=monday; day=tuesday; etc.) s added to MODEL. Ths leads to MODEL 3. The results are: * MODEL 3. regress r l.r l.r l3.r l4.r l5.r day-day5 Source SS df MS Number of obs = 1, F(9, 190) = 3.5 Model Prob > F = Resdual , R-squared = Adj R-squared = Total , Root MSE =.0171 r Coef. Std. Err. t P> t [95% Conf. Interval] r L L L L L day day day day _cons (c) (d) Why have only four day-of-week dummes been ncluded n MODEL 3? What problem would arse f all fve were ncluded? [5] Usng an F-test, test the jont sgnfcance of the four day-of-week dummes. Note that ths requres a test of MODEL as a restrcted verson of MODEL 3. Interpret your result. Do you have (further) evdence aganst EMH? [5] TURN OVER

10 Page 10 You are consderng purchasng a call opton wrtten on the TRAVIS PERKINS stock prce. In order to value the opton, you need to obtan a measure of the annual volatlty of the stock prce. Descrptve statstcs for the daly returns are obtaned as follows:. summ r Varable Obs Mean Std. Dev. Mn Max r 1, (e) (f) From the measure of daly volatlty obtaned above, deduce a measure of annual volatlty. [5] Suppose that you then nput your measure of annual volatlty nto the Black- Scholes formula, and you obtan an opton value that s consderably hgher than the market prce of the opton. What would you conclude about the opton? Would you purchase t? Explan your answer. [5] END OF PAPER

11 Page 11 Fnancal Econometrcs Formula Sheet The smple regresson model Consder the model: Y X u 1,..., n. The ordnary least squares estmators of and are: ˆ ( X X ) Y ( X X) ˆ Y ˆ X The ftted values of Y are gven by: Yˆ ˆ ˆ X The resduals are: u Y Yˆ ˆ The standard error of the regresson s gven by: uˆ ˆ n The estmated standard errors of ˆ and ˆ are gven by: se( ˆ ) ˆ 1 ( X X) se( ˆ ) ˆ 1 X n ( X X) Testng jont restrctons n the multple regresson model F RU RR / r 1 RU / n k ~ F r, nk

12 Page 1 Table 1: Crtcal values of the t-dstrbuton df = 0.10 = 0.05 = 0.05 = 0.01 =

13 Page 13 Table : Crtcal values of the F-dstrbuton (=0.05) df 1= df = END OF MATERIALS