AY Term 2 Mock Examination

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AY 206-7 Term 2 Mock Examiatio Date / Start Time Course Group Istructor 24 March 207 / 2 PM to 3:00 PM QF302 Ivestmet ad Fiacial Data Aalysis G Christopher Tig INSTRUCTIONS TO STUDENTS.

1 AY Term 2 Mock Examiatio Date / Start Time Course Group Istructor 24 March 207 / 2 PM to 3:00 PM QF302 Ivestmet ad Fiacial Data Aalysis G Christopher Tig INSTRUCTIONS TO STUDENTS. This mock examiatio paper cotais a total of 34 questios ad comprises 8 pages icludig this istructio sheet. 2. For this mock exam oly, you are allowed to refer to your otes ad usig your computer. 3. For each MCQ, choose the best aswer, either A or B or C or D. 4. For each short questio, give you aswer accordig to the specified decimal place or percetags. 5. All the aswers are to be etered ito the attached excel spreadsheet Aswer_Sheet.xlsx ad submit it to elear s dropbox before 3:00 PM.

2 . Deote the variace of a radom variable Y by σy 2. A sample of size is take. The variace of the sample average Y is A. σ 2 Y B. σ 2 Y C. σ 2 Y D. σ 2 Y 2. For a sample of past 30 mothly stock returs o a compay, the mea retur is 4% ad the sample stadard deviatio is 20%. The stadard error of the sample is estimated to be = 3.65%. What is the 95% cofidece iterval for the mea mothly retur? A. [ 3.464%,.464%] B. [ 3.453%,.453%] C. [ 2.20%, 0.20%] D. [ 2.94%, 0.94%] 3. Based o 2 daily returs o a asset, a risk maager estimates the stadard deviatio of the asset s daily returs to be 2%. Assumig that returs are ormally distributed ad that there are 260 tradig days i a year, what is the earest χ 2 test statistic if the risk maager wats to test the ull hypothesis that the true aual volatility is 25% at the 5% sigificace level? A B C D The coefficiet of determiatio for a simple liear regressio of a stock retur o a market portfolio retur is 77%. What is the correlatio betwee the depedet variable ad the idepedet variable? Your aswer must be i the format of xx.xx%, for example, 2.34%. 5. The liear model obtaied from the regressio of Questio 4 is kow as A. the capital market lie B. the capital asset pricig model C. the market model D. the security market lie 6. The explaied sum of squares for the regressio i Questio 4 is 4. The umber of observatios is 22. What is the ubiased volatility of the stock retur? Your aswer must be i the format of xx.xx%, for example, 2.34%. 7. Give the iformatio i Questios 4 ad 6, what is the adjusted R 2 of the regressio? Your aswer must be i the format of xx.xx%, for example, 2.34%. c Christopher Tig Page 2 of 8

3 8. Which of the followig four statemets o models for estimatig volatility is least accurate? A. I the EWMA model, some positive weight is assiged to the log-ru average variace. B. I the EWMA model, the weights assiged to observatios decrease expoetially as the observatios become older. C. I the GARCH(,) model, a positive weight is estimated for the log-ru average variace. D. I the GARCH(,) model, the weights estimated for observatios decrease expoetially as the observatios become older. 9. A quatitative aalyst uses OLS liear regressio i her aalysis. She fids that the residuals exhibit serial correlatios as show i the graphs below. A. The idepedet variable is a AR(2) process. B. The residual is a AR(2) process. C. Both the depedet variable ad the residual are ARMA(,) process. D. Oly the residual is ARMA(,) process. 0. For Questio 9, despite the evidece of serial correlatios, A. the least squares estimators are still BLUE. B. the least squares estimators are still statistically sigificat. C. the least squares estimators are still ubiased. D. the variace of the itercept estimate is still ubiased.. Suppose ɛ t is i.i.d. oise ad ɛ t N(0, ). Which of the followig time series X t is o-statioary? A. X t = 0.7X t + 0.5ɛ t B. X t = X t + 0.5ɛ t C. X t = 0.5ɛ t D. X t =.0ɛ t + 2.0ɛ t. c Christopher Tig Page 3 of 8

4 2. A quatitative tradig strategy either makes a profit or a loss, with probability p ad p, respectively. A trader executes trades. If is sufficietly large, the the distributio of a biomial variable X, which is the umber of wis i every trades, is well approximated by a ormal distributio with mea p ad variace p( p). What is the variace of Y = X p? p( p) A. p( p) C. 0 B. p( p) D. 3. A quatitative aalyst tests the structural stability i the followig regressio model: y t = β + β 2 x 2,t + β 3 x 3,t + u t. The total sample of 200 observatios is split exactly i half for the sub-sample regressios. Which of the followig is the urestricted Residual Sum of Squares (RSS)? A. The RSS for the whole sample B. The RSS for the first sub-sample C. The RSS for the secod sub-sample D. The RSS for the first sub-sample plus the RSS for the secod sub-sample 4. Suppose the residual sum of squares for the three regressios correspodig to the Chow test described i questio 3 are, respectively, 56.4, 76.2, ad 6.9. What is the value of the F statistic for this Chow s test closest to? A B C D Which of the followig may be the cosequeces of oe or more of the Classical Liear Regressio Model assumptios beig violated? (i) The coefficiet estimates are biased. (ii) The stadard error estimates are biased. (iii) The distributios assumed for the test statistics are iappropriate. (iv) Coclusios regardig the stregth of relatioships betwee the depedet ad idepedet variables may be ivalid. A. (i) ad (iii) oly B. (ii) ad (iv) oly C. (i), (ii), ad (iii) oly D. (i), (ii), (iii), ad (iv) c Christopher Tig Page 4 of 8

5 6. Which of the followig is most likely ot preset i the stock prices for which the radom walk hypothesis caot be rejected? A. irregular compoet B. seasoal compoet C. o-zero drift D. icreasig variace 7. Which of the followig is a GARCH (,) process? A. V ( u t ) = α0 + α u 2 t + γv ( u t ) B. V ( ) u t = α0 + α u t + γv ( ) u t C. V ( ) u t = α0 + α u 2 t + γv( u 2 ) t D. V ( ) u t = α0 + α u 2 t + γv( ) u t 8. Usig the coefficiet otatios of Questio 7, a GARCH(,) model has α 0 = , α = 0.25, ad γ = The log-term variace is closest to A B C. 0.0 D A ivestor from the Eurozoe bought 500 shares of Microsoft a year ago for $38.3 per share. The exchage rate was $.359 per euro the. Today, Microsoft is traded at $47.74 ad the exchage rate is $ What is the retur i euros (2 decimals i percet, e.g.,.22%)? 20. The followig table presets the result of a variace test o the log retur of a stock. The variace ratio of q-daily returs is deoted by VR(q). q Number of Observatios VR(q) Which of the VR(q) most likely caot reject the ull hypothesis at the 5% sigificace level? A. q = 2 B. q = 3 C. q = 4 D. q = 5 c Christopher Tig Page 5 of 8

6 2. Cosider the followig multi-factor model of a stock s excess retur: r st r ft = β 0 + β MKT t + β 2 SMB t + β 3 HML t + β 4 UMD + β 5 LMI + ɛ t. It comprises, respectively, the market factor, the size factor, the value factor, the mometum factor, ad the liquidity factor. This model is writte i the vector-matrix form as r = Xβ + ɛ. The sample period is from Jauary 990 to December All the returs are mothly. The residual sum of squares for this regressio is.34. Moreover, X X = ad X r = The ull hypothesis for each of the beta parameter is zero. What is the dimesio (rows colums) of the oise ɛ? 22. What is the estimate for β 5 i Questio 2 (4 decimals, e.g., )? 23. What is the t statistic for ˆβ i Questio 2 (2 decimals, e.g.,.78)? 24. Oe of the followig steps is ot required as a step to test for the ull hypothesis: A. compute the stadard error of the estimate B. test for the errors to be ormally distributed C. compute the t-statistic D. compute the p value 25. You have to worry about perfect multicolliearity i the multiple regressio model because A. may ecoomic variables are perfectly correlated. B. the OLS estimator is o loger BLUE. C. the OLS estimator caot be computed i this situatio. D. i real life, ecoomic variables chage together all the time. c Christopher Tig Page 6 of 8

7 26. You are a geeral maager of 4 fud maagers ad oe of them is to be promoted. All of them beat the market with more or less the same mothly average retur µ ad same mothly volatility σ. You cosider the skewess γ ad excess kurtosis κ := κ 3 of their mothly time series of returs. Which oe do you wat to promote? A. Maager A: γ = 0.5 ad κ = 0.5 B. Maager B: γ = 0.0 ad κ = 0.0 C. Maager C: γ = 0.5 ad κ = 0.5 D. Maager D: γ = 0.5 ad κ = Which of the followig is a cosistet but biased estimator of a sample mea for which the populatio mea is µ? A. B. t= x t x t + x 7 t= C. D. t= t= x t + (x 7 µ) x t + + (x 7 µ) 28. Which of the followig statemets about samplig ad the cetral limit theorem is least likely correct? A. The variace of the distributio of sample meas is σ 2 /. B. The cetral limit theorem may be used for large sample sizes for skewed distributios. C. The mea of the populatio ad the mea of all possible sample meas are always equal. D. The stadard deviatio of the mea of may observatios is more tha the stadard deviatio of a sigle observatio. 29. A ivestmet advisor is aalyzig the rage of potetial expected returs of a ew fud desiged to replicate the directioal moves of the BSE Sesex Idex but with twice the volatility of the idex. Sesex s average aual retur is 2.3% ad volatility of 9.0%. Assumig the correlatio betwee the fud?s returs ad that of the idex is 0.95, what is the value of the coefficiet of determiat closes to? A B C D Assume 252 tradig years per year. Give the same iformatio i Questio 29, what is the z score closest to for the ull hypothesis of Sesex Idex s retur if the umber of daily observatios is 00 (2 decimals, e.g..23)? c Christopher Tig Page 7 of 8

8 3. Dowload the Dow Joes Idustrial Average Idex data by clickig Based o the MLE demo excel spreadsheet discussed i Week 0 (Maximum likelihodd estimatio of EWMA, GARCH, ad Variace Targetig), perform the estimatio of EWMA s λ parameter. What is the estimated value (4 decimal places, e.g., 0.234)? 32. Usig the same data i Questio 3, what is the estimate for β i the GARCH (,) model (4 decimal places, e.g., 0.234)? 33. Usig th same data i Questio 3, what is the estimate for GARCH(,) s α parameter usig the variace targetig approach (2 decimals i the format of, e.g., )? 34. Dowload the S&P 500 Idex optios by clickig What is the 60-day model-free volatility (2 decimals i percet, e.g. 7.77%) by liear iterpolatio? c Christopher Tig Page 8 of 8

SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME

All Right Reserved No. of Pages - 10 No of Questios - 08 SCHOOL OF ACCOUNTING AND BUSINESS BSc. (APPLIED ACCOUNTING) GENERAL / SPECIAL DEGREE PROGRAMME YEAR I SEMESTER I (Group B) END SEMESTER EXAMINATION