Preface and practicalities

Derivatives Trading and Hedging 2019 (FR2211)CourseworkAvailable online: Monday, 4 February 2019, at 15:50Submission deadline: Monday, 18 February 2019, at 15:50This version: Monday, 4 February 2019Preface and practicalitiesThis coursework is about hedging equity portfolios using equity index futures. You will beasked to perform several analyses using real-world data and present your results in a concise report.There is a total of 10 questions in this coursework. The questions carry different weights in the finalmark. The maximum mark attainable is 100%. The choice of software for conducting the analysesis up to you that is, you may use whichever computer program you prefer, whether this is R, Excel,something else, or even a combination. Useful R-code is provided on page 3.This coursework is to be solved strictly within the assigned groups. Questions can be postedon the accompanying Moodle forum. Private conversations about the coursework with anyonebesides i) the members of your coursework group or ii) the lecturer will be regarded as fraud andtreated as such. Any signs of conversations about the coursework across groups or copying of resultsacross groups will result in a total mark of 0% to all members of the involved groups.Please make specific references to the appropriate sections/pages in the modulestextbook and/or the lecture notes (slides) whenever possible and adequate. The same applies to anyother material (other textbooks, academic papers, newspaper articles, etc.) you use in answering thequestions. Rely on dubious/folklore-based sources like Investopedia at your own risk/peril.Some questions will ask you to comment on or interpret your results using no more than aspecified maximum word count. You are welcome to use any number of words up to the maximumin your answer. However, if you use more words than the specified maximum, the mark for theentire question will be reduced by the percentage of words above the maximum allowed. Pleaseindicate the number of words used in your answer to each question with a maximum wordcount adjacent to your answer of the question. Any discrepancies between the stated and the actualnumber of words will be regarded as an error and will result in deduction of marks.Please submit the coursework in a single PDF file. Other file formats (such as Word)will not be accepted. The maximum page count is 10 single-spaced standard pagesusing a font size of 12 or above. Please indicate the group number on your reports frontpage, the names and student numbers of all group members, and (if applicable) the names of anyinactive or non-participating group members. Late submissions will result in a total mark of 0% toall group members.Page 1 of 7 FR2211, 2019Coursework settingIt is now February 2019. You are a group of quantitative analysts working within the assetmanagement unit of a hedge fund. Your responsibilities include monitoring the performance andrisks of the funds positions. You conduct statistical analyses and write reports that ultimately go tothe funds senior management and guide their investment and hedging decisions.Senior management foresees volatile markets for the remainder of 2019 and have asked foran analysis, based on historical data for 2017-2018, on how to best hedge the market exposure ofthe funds positions in 2019. Your group has specifically been assigned two US industry portfolios: The Software industry portfolio, which takes long positions in the stocks (i.e., equitysecurities) of US firms that develop and/or sell (computer) software; and the Gold industry portfolio, which takes long positions in the stocks of US firms thatmine, process, and/or sell (the precious metal) gold.Based on experience, senior management propose the following equity index futures contracts: S&P 500 E-Mini futures. The S&P 500 index is a value-weighted equity index containing500 US firms selected primarily on the basis of being large and representative of the industriesin the US economy. The index is often used as a benchmark for the performance of large USstocks. The S&P 500 Mini futures are the most liquid contracts on the index and have acontract size of $50 times the index. Nasdaq 100 E-Mini futures. The Nasdaq 100 index is a value-weighted equity indexcontaining the largest 100 firms listed on the Nasdaq stock exchange. The index is often used abenchmark for the performance of hi-tech US stocks. The Nasdaq 100 Mini futures are themost liquid contracts on the index and have a contract size of $20 times the index.The overarching question of this coursework is, then: Based on historical data for 2017-2018, how wouldyou recommend senior management to hedge the two industry portfolios market exposure in 2019?To answer this question, senior management instructs you to conduct a statistical analysis forthe performance of each of the industry portfolios in 2017-2018 when hedged using each of theindex futures contracts. They further instruct you to assume that the position in each portfolio is$10,000,000; that each hedge is a buy-and-hold position; and that the hedges are implemented from1 December 2017 to 30 November 2018.The first part of the coursework (Questions 1 and 2) studies the portfolios in the year beforethe hedges are implemented. Accompanying this part of the coursework is a dataset called CWdata, 2016-12-01 to 2017-11-30. The dataset contains the daily returns in % for the two portfolios(Softw_Ret and Gold_Ret), the broad US stock market portfolio (MKT_Ret), and the two indices(SP500_Ret and Nasdaq1000_Ret). In addition, it includes the daily US risk-free rate in % (RF).The second part of the coursework (Questions 3 to 10) studies the portfolios during thehedging period. Accompanying this part of the coursework is a dataset called CW data, 2017-12-01to 2018-11-30. The dataset contains the same variables as above as well as the daily settlementprices in $ for the two futures contracts with delivery on 21 December 2018 (SP500_FutDec18 andNasdaq100_FutDec18), the daily levels in $ for the two indices (SP500_Idx, Nasdaq1000_Idx), and thedaily values in $ for the two portfolios (Softw_Val, Gold_Val).Page 2 of 7 FR2211, 2019Useful R-codeIf you are interested in learning to program and do statistical analysis in R, then thiscoursework is an excellent opportunity to do so. Below is a very short introduction with usefulfunction that are relevant to the coursework and beyond.Importing csv-files in R can be done using the function read.csv. To import a csv-file and storeit as a data.frame with the name D, use the command D < read.csv(_path_) where _path_ is thepath of the csv-file on your computer. You can obtain the path of any file by dragging the file intothe R-console. To access the variable (or column) X within the data.frame D, use the commandD$X. To access the first entry for the variable X within the data.frame D, use the command D$X[1].To access the last entry for the variable X within the data.frame D, use the command D$X[nrow(D)].To access all but the first entry for the variable X within the data.frame D, use the commandD$X[-1]. Finally, to specify the variable X within the data.frame D as a date-variable, use thecommand D$X <- as.Date(D$X).R has numerous built-in functions for computing standard statistics and manipulatingvariables like mean, var, sd, cor, length, nrow, and so on. All of these functions have arguments toexclude missing (or NA = not available) values, typically in the form of na.rm=T (i.e. setting thefunctions remove NA-argument to TRUE). For instance, to calculate the mean of X fromdata.frame D while removing its missing values simply type mean(D$X, na.rm=T). To define a newvariable M as the mean of X from the data.frame D, while removing the missing values in X beforecalculating its mean, use the command M <- mean(D$X, na.rm=T).Univariate (and multivariate) linear regressions can be done using the function lm. Gettingdetailed output for linear regressions (i.e., t-statistics for the intercept as well as slope-coefficients,residual standard error, R-squared values, etc.) can be prompted by using the function summary inconjunction with the function lm. For instance, to get detailed output for a linear regression of thevariable Y from the data.frame D onto the variable X also from the data.frame D, usesummary(lm(D$Y ~ D$X)). One way to perform the linear regression of the difference variable Y-Zonto the difference variable X-Z, where all of X, Y, and Z are from the data.frame D, is by using thecommand lm(I(D$Y-D$Z) ~ I(D$X-D$Z)). The I-function in e.g. I(D$Y-D$Z) is for identity, andmakes sure that its argument is evaluated before the regression is performed.You can read more about the R-functions read.csv, mean, sd, and lm, as well as see examples ofhow to use them, by prompting their help-page using the commands ?read.csv, ?mean, and ?lm. Thesame applies to all R-functions, which all have an accompanying help page with examples.Furthermore, there are many web forums and blogs specifically targeting R-users where you canfind code examples and clever solutions to common problems. The easiest way to find these is to doa Google search for the task you are trying to accomplish or the problem you are experiencinginitiated with by R: as in R: adding a line to a plot or R: doing a for-loop.Page 3 of 7 FR2211, 2019QuestionsQuestion 1 (10%)a) Calculate and report the mean and the standard deviation of the daily excess return (i.e., thedaily return in excess of the risk-free rate) in % for each of the Software and Gold industryportfolios.b) Recall that the empirical version of the capital asset pricing model (CAPM) says that aportfolios excess return at time t can be described by the linear regression where rt is the portfolio return, rFt is the risk-free rate, rIt is the return on an index, and

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