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1 UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PGT 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
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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 Glencore (Basc Resources) was followed for a perod of seven months. The percentage monthly return on Glencore stock (Y), and the percentage monthly change n the stock market ndex (X), are presented n the followng table: Month Glencore (Y) Market (X) January 1 February -3 - March -1-1 Aprl 0 May 1 June 1 0 July 4 1 (a) Obtan estmates of α and β n the smple regresson model: Y = α + βx + u t = 1, L, 7 t t t Var u ( ) = σ t Report the beta coeffcent for Glencore stock. [10 marks] (b) (c) Fnd the resduals from the smple regresson performed n (a). Hence fnd an estmate of the parameter σ. Call the estmate ˆ σ. What s the nterpretaton of ˆ σ n ths context? [7 marks] Fnd a 95% confdence nterval for β. Does the confdence nterval ndcate that Glencore s an aggressve stock, a defensve stock, or nether? Is ths what you would expect for Glencore? [8 marks] TURN OVER
4 Page 4 QUESTION [0 marks] We have data on 53 countres n 017. Let p_local be the prce of a Bg Mac (the McDonald s hamburger) n country n local currency n 017. Let e be the exchange rate for country aganst the US dollar n 017 (that s, e s the number of unts of local currency that can be exchanged for one US dollar n 017). (a) Data on three of the 53 countres s shown n the followng table. Country Currency p_local e South Korea Won Egypt Pound Swtzerland Franc 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 017, and whch appears over-valued? [7 marks] The followng regresson model s estmated usng data from all 53 countres n 017 (p_usa s the prce of a Bg Mac n the USA n 017): _ log p local = β + 1 βlog e + u ; = 1, L,53 (1) 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 =.6077 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) = 56.4 Prob > F = test (_b[log_e]=1) ( 1) log_e = 1 F( 1, 51) = Prob > F =
5 Page 5 (b) (c) 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 the LOP. Is t rejected by the 017 Bg Mac data? Whch theory s beng tested by the second test? Is t rejected? [7 marks] Explan the Balassa-Samuelson effect, and explan why you mght expect t to hold. How would you extend the regresson model (1) n order to carry out a test of the Balassa-Samuelson effect? [6 marks] TURN OVER
6 Page 6 QUESTION 3 [5 marks] For the stocks n the FTSE-100 Index, the followng varables are computed usng daly return data for the past two years: beta: beta: beta3: sg: rbar: beta coeffcent (beta coeffcent) squared (beta coeffcent) cubed standard measure of unsystematc rsk mean daly return Consder the followng two models wth mean daly return as the dependent varable: MODEL 1 MODEL rbar = γ + γ beta + γ sg + u 1 3 rbar = γ + γ beta + γ beta + γ beta + γ sg + u The two models are estmated n STATA wth the followng results:. * MODEL 1. regress rbar beta sg Source SS df MS Number of obs = F(, 99) =.5 Model.1034e e-06 Prob > F = Resdual e-07 R-squared = Adj R-squared = Total e-07 Root MSE = rbar Coef. Std. Err. t P> t [95% Conf. Interval] beta sg _cons * MODEL. regress rbar beta beta beta3 sg Source SS df MS Number of obs = F(4, 97) = 5.86 Model e e-06 Prob > F = Resdual e-07 R-squared = Adj R-squared = Total e-07 Root MSE = rbar Coef. Std. Err. t P> t [95% Conf. Interval]
7 Page beta beta beta sg _cons γ = aganst H0: γ 3 > 0 (a) Consder MODEL 1. Explan why a test of H0: 3 0 amounts to a test of the Captal Asset Prcng Model (CAPM). Report the t- statstc and p-value for ths test. Is CAPM rejected? [6 marks] (b) Consder MODEL. Report t-tests and p-values for tests of the hypotheses H0: γ = and H0: γ 4 = 0. Are the effects of beta and/or beta 3 ndvdually 3 0 sgnfcant? On ths bass, s CAPM rejected? [6 marks] H : γ = 0; γ = 0. (c) Agan consder MODEL. Test the jont null hypothess That s, use an F-test to test MODEL 1 as a restrcted verson of MODEL. Is CAPM rejected? Is the concluson dfferent n any way from that of (b)? [7 marks] (d) The correlaton matrx for the four explanatory varables appearng n MODEL s found to be:. corr beta beta beta3 sg (obs=10) beta beta beta3 sg beta beta beta sg Do any of the numbers n the correlaton matrx suggest that near multcollnearty mght be causng problems n the estmaton of MODEL? Could ths explan any contradcton between the conclusons of (b) and (c) above? [6 marks] TURN OVER
8 Page 8 QUESTION 4 [30 marks] Two years of daly data on the FTSE100 Index are used to estmate two models (MODEL 1 and MODEL ). The varable r s the daly return on the FTSE100 Index. Results from estmaton of the two models are as follows.. * MODEL 1. regress r l.r Source SS df MS Number of obs = F(1, 50) =.43 Model Prob > F = Resdual R-squared = Adj R-squared = Total Root MSE = 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 = F(5, 51) = 4.73 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 durbna
9 Page 9 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 the weak-form of the Effcent Markets Hypothess (EMH). Report the F-statstc and the assocated p-value. How strong s the evdence aganst EMH? [5 marks] (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 marks] The daly return on the Dow-Jones Index s also avalable for the same perod, and s named r_dow. The followng analyss s carred out of the two return seres:. varsoc r r_dow, maxlag(10) Selecton-order crtera Sample: 1-54 Number of obs = lag LL LR df p FPE AIC HQIC SBIC e e * e e * e-09* * * e e e e e e Endogenous: r r_dow Exogenous: _cons. var r r_dow, lags(1/4) : :. vargranger Granger causalty Wald tests Equaton Excluded ch df Prob > ch r r_dow r ALL r_dow r r_dow ALL TURN OVER
10 Page 10 (c) (d) The varsoc command results are dsplayed n a table above. Explan how the nformaton n ths table s useful n specfyng a VAR model. What does t tell us n ths case? [5 marks] What s the name of the test performed as a result of the vargranger command? What s the result of the test? Explan why ths test can be nterpreted as a test of the sem-strong form of EMH. Is the sem-strong form of EMH rejected n ths case? [5 marks] You are consderng purchasng a call opton wrtten on the FTSE100 Index. In order to value the opton, you need to obtan a measure of the annual volatlty of the Index. Descrptve statstcs for the daly returns of the FTSE100 Index are obtaned as follows:. summ r Varable Obs Mean Std. Dev. Mn Max r (e) (f) From the measure of daly volatlty obtaned above, deduce a measure of annual volatlty. [5 marks] Suppose that you then nput your measure of annual volatlty nto the Black- Scholes formula, and you obtan an opton value that s consderably lower than the market prce of the opton. What would you conclude about the opton? Would you purchase t? Explan your answer. [5 marks] END OF PAPER
11 Page 11 Fnancal Econometrcs Formula Sheet The smple regresson model Consder the model: α β Y = + X + u = 1,..., n. The ordnary least squares estmators of β and α are: ˆ β = ( X XY ) ( X X) ˆ α = Y ˆ βx The ftted values of Y are gven by: Yˆ = ˆ α + ˆ βx The resduals are: u = Y Yˆ ˆ The standard error of the regresson s gven by: ˆ σ = uˆ n The estmated standard errors of βˆ and αˆ are gven by: se( ˆ β) = ˆ σ 1 ( X X) 1 X se( ˆ α) = ˆ σ + n ( X X) Testng jont restrctons n the multple regresson model F = ( RU RR) / r ( 1 RU ) /( n k) ~ F rn, k TURN OVER
12 Page 1 Table 1: Crtcal values of the t-dstrbuton df α = 0.10 α = 0.05 α = 0.05 α = 0.01 α =
13 Page 13 Table : Crtcal values of the F-dstrbuton (α=0.05) df 1= df = END OF MATERIALS
Module Contact: Dr Susan Long, ECO Copyright of the University of East Anglia Version 1
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