EXAMINATION QUESTION PAPER – Course paperComponent of continuous assessmentFIN 36181Financial EconometricsDepartment of Finance Start date:Finish date:21.10.202128.10.2021Time 09.00Time 12.00 Component weight:Total no. of pages:20% of FIN 3618112 incl. front page No. of attachments files toquestion paper: 0To be answered: In groups of 1 – 4 students.Answer paper size: 5 excl. attachmentsMax no. of answer paperattachment files:1Allowed answer paper filetypes:pdfAllowed answer paperattachment file types:pdfIf sources such as the course literature or any external sources are used, they must belisted as references at the end of the solution paper. The list of references does not counttowards the five-page constraint. For a thorough explanation of how to use quotes andreferences, go to https://portal.bi.no/en/examination/assignment-thesis/cite-sources. Forinformation on formal requirements and template paper, seehttps://www.bi.edu/templatepaper.FIN 3618 Financial Econometrics{ Assignment 2 {Autumn 2021Upload your solution paper (as a pdf file) in DigiEx by Thursday, October 28, 12:00 p.m. (atnoon). Your solution paper may have up to five pages plus an appendix which has to be uploaded as aseparate attachment (as a pdf file) and does not count towards the five pages. For your solution paper,please use the standard BI template paper, and stick to the default font style, font size, line spacing,margins, etc. The template paper is available for downloading here. The appendix shall contain all theR code (with clarifying comments) you used to produce your results and the corresponding output. Togenerate the pdf file in RStudio, make sure that the packages rmarkdown and tinytex are installedand loaded. Then, go to the File” menu and click on Compile report…”. Open the pdf file that hasbeen created in your working directory and make sure that long lines of code are not cut off if theyexceed the page width.Read each question carefully and give precise answers. In your calculations, use four positionsafter the decimal point.Please note that I will not respond to any individual emails, messages etc. If you have questionsor want me to clarify something, please post a thread in the discussion forum I have created onitslearning.The student code of conduct applies, i.e., the solution paper must be written and prepared by thecorresponding group members only. Collaboration with classmates or other individuals outside thegroup is not permitted and is considered cheating.All papers are automatically subject to plagiarism control.Students need to include a list of all literature used to answer the assignment.Good luck!2 Total assignment pointsAppendix A contains a list of useful R functions.(100 points) 1. Value and size as trading strategies (20 points)According to the CAPM, differences in average returns on different stocks should be entirely dueto different market betas.1 In this exercise, you want to check whether this is true using stockssorted into the so-called Fama-French portfolios” used in Fama and French (1992, 1993). OpenKenneth French’s homepage and download the monthly returns on the following 6 PortfoliosFormed on Size and Book-to-Market (2 x 3).”2 Among other things, this file contains theaverage (simple) returns on the following six value-weighted portfolios at the monthly returnhorizon on a monthly frequency: Book-to-market ratiolowgrowthmediumneutralhighvalueMarket equitylow small(1)(2)(3)high big(4)(5)(6) Your tasks are as follows: Import the data into R without modifying the files you downloaded. Restrict the data tothe sample period from January 1992 to August 2021. In order to focus on the difference between small and big stocks, calculate the average(simple) return on the small portfolio and on the big portfolio:smallt = 13(small growtht + small neutralt + small valuet)bigt = 13(big growtht + big neutralt + big valuet) :{ Report the mean and the standard deviation of the return on the smalland the big portfolio in your solution paper. Which of the two portfoliosearns higher average returns? After that, construct the so-called size portfolio SMBt (Small Minus Big)” which involvesgoing long in small stocks and going short in big stocks, i.e., buying small stocks and shortselling big stocks.{ Report the mean as well as the standard deviation of this trading strategy in your solution paper. Is there a premium to be earned on the sizeportfolio?1Although the CAPM refers to average excess returns, the above statement is still true because you add the (same)risk-free rate to the excess returns of the different stocks.2Details on the construction of the Fama-French portfolios can be found in Appendix B.3 Next, focus on the difference between stocks with low and high book-to-market ratios.Compute the average (simple) return on the growth portfolio and on the value portfolio:growtht = 12(small growtht + big growtht)valuet = 12(small valuet + big valuet) :{ Report the mean and the standard deviation of the return on the growthand the value portfolio in your solution paper. Which of the two portfoliosearns higher average returns? After that, construct the so-called value portfolio HMLt (High Minus Low)” which involves going long in value stocks (with a high book-to-market ratio) and going short ingrowth stocks (with a low book-to-market ratio), i.e., buying value stocks and short-sellinggrowth stocks.{ Report the mean as well as the standard deviation of this trading strategyin your solution paper. Is there a premium to be earned on the valueportfolio? Since you are curious whether the portfolio returns on value and growth can be explainedby the CAPM, go to Kenneth French’s homepage and download the monthly returns onthe Fama/French 3 Factors.” Among other things, this file contains the (simple) averageexcess return on the market, RM;t e = RM;t-Rf;t. Import the data into R without modifyingthe file you downloaded and run the following regressions:valuet = αvalue + βvalue RM;t e + uvalue;growtht = αgrowth + βgrowth RM;t e + ugrowth:{ Summarize the parameter estimates and their t-statistics of the slope coefficients in a table in your solution paper.{ Based on these results, can the CAPM explain the return difference between value and growth? Explain your answer.42. The Fama-French five factor model (80 points)Follow the steps outlined in Appendix C and download the daily stock return time series of TheWalt Disney Company from WRDS. Next, open Kenneth French’s homepage and downloadthe Fama/French 5 Factors (2×3) [Daily]”. The file contains the daily time series of the fivefactors Fama and French (2015, 2016) propose as an extension of their conventional three-factormodel in which they suggest two new factors: operating profitability and investment. Thus, theyconsider the following five factors: ReM;t (Market Minus Risk-free): the simple average return on the market minus the simpleaverage risk-free rate. SMBt (Small Minus Big): the simple average return on the portfolio containing smallstocks minus the simple average return on the portfolio containing big stocks. HMLt (High Minus Low): the simple average return on the portfolio containing valuestocks minus the simple average return on the portfolio containing growth stocks. RMWt (Robust Minus Weak): the simple average return on the portfolio containing stockswith robust operating profitability minus the simple average return on the portfolio containing stocks with weak operating profitability. CMAt (Conservative Minus Aggressive): the simple average return on the portfolio containing stocks with conservative investment strategies minus the simple average return onthe portfolio containing stocks with aggressive investment strategies.Moreover, the last column contains the daily time series of the simple return on the U.S.-Treasury bill with one month to maturity which we will use as a proxy for the risk-free rate inthis exercise.Your tasks are as follows: Import the data into R without modifying the files you downloaded. Use the five Fama-French factors at time t as the independent variables and the excessreturn of Disney at time t as the dependent variable, i.e., run the following regression:ReD;t = β1 + β2 RM;t e + β3 SMBt + β4 HMLt + β5 RMWt + β6 CMAt + uD;t:{ Summarize the parameter estimates, and their t-statistics in a table inyour solution paper.{ Based on a significance level of 5%, which of the variables are statisticallysignificantly different from zero? Is there a variable you would considerdeleting from the regression? Explain your answer.{ For each variable which is statistically significant, provide an assessmentof its economic significance by looking at the impact of a one-standarddeviation increase in the corresponding independent variable.5 Next, you want to test the following hypotheses:{ H0 : β2 = 0 and β3 = 0 and β4 = 0 and β5 = 0 and β6 = 0 vs.H1 : β2 6= 0 or β3 6= 0 or β4 6= 0 or β5 6= 0 or β6 6= 0∗ Write down the restricted regression and provide an economic interpretation.∗ Explain in detail all the steps underlying the test of the hypothesisgiven above. In your explanations, refer to the unrestricted and therestricted residual sum of squares.∗ Perform the test using a significance level of 5% and report the resultsin your solution paper.∗ After the last step of the test, interpret your results from an economicpoint of view.{ H0 : β3 = 0 and β4 = 0 and β5 = 0 and β6 = 0 vs.H1 : β3 6= 0 or β4 6= 0 or β5 6= 0 or β6 6= 0∗ Write down the restricted regression, and provide an economic interpretation.∗ Perform the test using a significance level of 5% and report its resultsin your solution paper.{ H0 : β5 = 0 and β6 = 0 vs.H1 : β5 6= 0 or β6 6= 0∗ Write down the restricted regression, and provide an economic interpretation.∗ Perform the test using a significance level of 5% and report its resultsin your solution paper. You read online that there can be substantial differences between the returns on a specificdays of the week. Hence, you decide to study this for Disney. Therefore, you define thefollowing dummy variables, one for each day of the week:DMon,t = 1 if day 0 otherwise t is a Monday…DFri,t = 1 if day 0 otherwise t is a FridayFor instance, the Monday dummy variable at day t will be equal to one (DMon,t = 1) ifand only if t is a Monday. If this is not the case, the dummy variable will be equal to zero(DMon,t = 0).Use the five Fama-French factors as well as the five dummy variables as independentvariables and the excess return of Disney as the dependent variable, i.e., run the followingregression:ReCP;t = β2 RM;t e + β3 SMBt + β4 HMLt + β5 RMWt + β6 CMAt + β7 DMon,t+ β8 DTue,t + β9 DWed,t + β10 DThu,t + β11 DFri,t + uCP;t:The missing intercept is captured through the dummy variables altogether.{ Summarize the parameter estimates and their t-statistics in a table in yoursolution paper.{ What do your results tell you about return differences on weekdays?6ReferencesFama, E., and K. French. 1992. The Cross-Section of Expected Stock Returns. Journal of Finance47:427{465. doi:10.1111/j.1540-6261.1992.tb04398.x.Fama, E., and K. French. 1993. Common risk factors in the returns on stocks and bonds. Journalof Financial Economics 33:3{56. doi:10.1016/0304-405X(93)90023-5.Fama, E., and K. French. 2015. A five-factor asset pricing model. Journal of Financial Economics116:1{22. doi:10.1016/j.jfineco.2014.10.010.Fama, E., and K. French. 2016. Dissecting anomalies with a five-factor model. Review of FinancialStudies 29:69{103. doi:10.1093/rfs/hhv043.7AppendixA Useful R functionsOf course, there are a thousand different ways to solve the tasks in this assignment which might alllead to the same (correct) results. To provide some kind of guidance, you can find here a list of Rfunctions that might come in handy: as.numeric which is part of the base package> x as.numeric(x)[1] 1 2 3 as.character which is part of the base package> x as.Date(x, format = ‘%Y%m%d’)[1] “2021-10-13” paste which is part of the base package > year month day paste(year, month, day, sep=”-“)[1] “2021-12-01”> as.Date(paste(year, month, day, sep=”-“), format = “%Y-%m-%d”)[1] “2021-12-01”> str(as.Date(paste(year, month, day, sep=”-“), format = “%Y-%m-%d”))Date, format: “2021-12-01” days in month which is part of the lubridate package> date days in month(date)31 format which is part of the base package> date format(date, “%Y”)[1] “2021”> format(date, “%m”)[1] “12”> format(date, “%d”)[1] “01”> format(date, “%A”)[1] “Wednesday”8 merge which is part of the base package> data1 data1month x11 1 52 2 13 3 44 4 95 5 16 6 2> data2 data2month y11 4 32 5 33 6 44 7 15 8 26 9 9> merge(data1, data2, by = “month”, all=TRUE)month x1 y11 1 5 NA2 2 1 NA3 3 4 NA4 4 9 35 5 1 36 6 2 47 7 NA 18 8 NA 29 9 NA 9 logical indexing> x test test[1] TRUE FALSE FALSE FALSE FALSE> as.integer(test)[1] 1 0 0 0 0> x[1] “A” “B” “C” “D” “E”> x[as.integer(test)][1] “A”9B Fama-French PortfoliosThe starting point of Fama and French (1992, 1993) are all the firms in the CRSP database (i.e., allcommon stocks traded at the NYSE, AMEX, and NASDAQ). For each firm, the authors calculate: its market equity (also known as market capitalization), i.e., stock price × number of sharesoutstanding; its book-to-market ratio, i.e., market equity book equity .Then Fama and French sort all the firms (independently) according to each of these quantities, fromthe lowest to the highest. Firms sorted with respect to market equity are divided into two portfolios. Stocks which havea market equity. . .{ smaller than the median market equity of all NYSE traded stocks are considered as small;{ larger or equal to the median market equity of all NYSE traded stocks are considered asbig. Firms sorted with respect to the book-to-market ratio are divided into three portfolios. Stockswhich have a book-to-market ratio . . .{ smaller than the 30th percentile of the book-to-market ratio of all NYSE traded stocksare considered as growth stocks;{ smaller than the 30th percentile and larger or equal to the 70th percentile of the bookto-market ratio of all NYSE traded stocks are considered as neutral stocks;{ larger or equal to the 70th percentile of the book-to-market ratio of all NYSE tradedstocks are considered as value stocks.In the next step, Fama and French perform a double sort.” This means they sort, e.g., small stocksinto small-growth, small-neutral, and small-value portfolios. Afterward, they end up with the followingsix portfolios: Book-to-market ratiolowgrowthmediumneutralhighvalueMarket equitylow small(1)(2)(3)high big(4)(5)(6) Note that the number of firms in each portfolio can be different and the portfolios are updated everyyear.The next step of Fama and French is then to compute the (simple) return on each of the six portfolios.To calculate this, you need the stock returns of the firms contained in that portfolio and the portfolioweight of each stock. Fama and French (1992) compute portfolio returns using portfolio weights whichreflect a stock’s market cap relative to the market cap of the portfolio. These so-called value-weightedportfolio returns are reported in the 6 Portfolios Formed on Size and Book-to-Market (2 x 3)” thatis available on Kenneth French’s homepage.10 To get a rough idea how value-weighted portfolio returns are calculated, consider the followingexample. Suppose there are n = 2 stocks in a portfolio. The first stock has a return of 0.06 and amarket capitalization of 70$, whereas the second stock yields a return of 0.18 and has a marketcap of 30$. Consequently, the total market cap of the portfolio is 70$ + 30$ = 100$. Thus theportfolio weights for the two stocks are 100$ 70$ = 10 7 and 100$ 30$ = 10 3 . Therefore, the value-weightedportfolio return is 10 7 · 0:06 + 10 3 · 0:18 = 0:0960. An alternative we are not considering in this assignment would be equal-weighted portfolio returns. In this case, all n stocks which enter a portfolio have the same weight, n1. In the exampleabove, the equal-weighted portfolio return is 1 2 · 0:06 + 1 2 · 0:18 = 0:1200.To capture the difference between small and big stocks, Fama and French construct the so-calledsize portfolio SMB (Small Minus Big).” Therefore, they calculate the average (simple) return onthe small portfolio and the big portfolio:small = 13(small growth + small neutral + small value)big = 13(big growth + big neutral + big value) :The Fama-French factor Small Minus Big (SMB) (also known as the size factor”) is the result of atrading strategy that involves going long in the small portfolio (containing stocks with low marketcapitalization) and going short in the big portfolio (containing stocks with high market capitalization).Put differently, this trading strategy involves buying small stocks and short-selling big stocks.Fama and French also focus on the difference between stocks with low and high book-to-market ratios.Hence, they compute the average (simple) return on the growth portfolio and the value portfolio:growth = 12(small growth + big growth)value = 12(small value + big value) :The Fama-French factor High Minus Low (HML) (also known as the value factor”) is the result ofa trading strategy that involves going long in the value portfolio (containing stocks with high bookto-market ratios) and going short in the growth portfolio (containing stocks with low book-to-marketratios). Put differently, this trading strategy involves buying value stocks and short-selling growthstocks.11C Returns on Disney(1) Open the this homepage and log into WRDS.3(2) Click on CRSP”, and choose Stock / Security Files”.(3) Select Daily Stock File” and fill out the query form.(a) Step one is to specify that you want to download data for the longest possible time span,i.e., from 1958-01-01″ to 2020-12-31″.(b) Under step two, select the identifier for the stock you wish to download. Choose PERMNO”and type in as company code 26403″.(c) In step three, you have to select the variables you want to download. Select Holding PeriodReturn” which is defined asRi;t = pi;t + di;tpi;t-1– 1;where pi;t denotes the price of firm i at time t, dt its dividend, and Ri;t firm i’s simple netreturn.(d) The fourth step involves determining the output format. Pick Excel spreadsheet (*.xlsx)”,scroll further down, and hit the Submit Query” button.(4) A the top of the homepage, a green message will pop up that your query was successfullysubmitted. Click on the query number.(5) In the Results” row, you find the output files” of your query. Click on the resulting .xlsx fileto download it.(6) Use WRDS Disney daily” as filename.3You can find the username and password in the Wharton Research Data Services (WRDS)” note in the folder2 – Introduction and dealing with data” on itslearning.12

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