ECMT2130 R语言分析

ECMT2130 - 2022 semester 2, assignment 1
Your answers need to be submitted using the Canvas quiz forassignment 1. The R script and Microsoft Excelspreadsheet produced in doing this assignment must be uploaded using this Canvas quiz. These documents
must be your own work.

1. Portfolio optimisation

Use the data allocated to you to answer the following questions.
Throughout this assignment, all rates of return are simple monthly rates of return (not annualised),expressed as a decimal rather than a percentage. Thus, for example, a rate of return of 5% would be
expressed in the data set as 0.05.Unless otherwise stated: the investor can invest in all of the managed funds but cannot invest in therisk-free asset; and the investor is fully invested.Use the most recent value of the simple monthly risk-free rate of return as the “current risk-free rate ofreturn” when analysing the following portfolio optimisation problems.Compute the excess rates of return for each fund, in each available time period. Add the current risk-freerate of return to these excess rates of return for each fund to produce simple monthly rates of returnthat do not incorporate risk-free rate of return variation as a source of risk.Compute mean simple monthly rates of return on a fund using these adjusted simple monthly rates ofreturn (average over the entire available sample). If this is not clear, ask for clarification on Ed!Also use these adjusted simple monthly rates of return to estimate the variance-covariance matrix forthe funds’ rates of return. Again use the entire available sample.
(a) (2 points) Estimate the mean and the standard deviation of the simple monthly rate of return forthe Global Minimum VariancePortfolio (GMVP). Report the standard deviation as a percentage,to 2 decimal places.
(b) (2 points) Estimate the mean and the standard deviation of the simple monthly rate of return forthe portfolio with minimum variance when shorting is allowed but no fund is allowed to have aweight with an absolute value greater than 20%.
(c) (2 points) Estimate the mean and the standard deviation of the simple monthly rate of return forthe portfolio with minimum variance when no shorting is allowed and no fund can have a weightabove 20%.
(d) (2 points) Estimate the standard deviation of the simple monthly rate of return for the minimumvariance portfolio that has an expected simple monthly rate of return that is double that of theGMVP.
(e) (2 points) Estimate the slope of the optimal Capital Allocation Line when the investor can investin the risk-free asset and faces no portfolio weight restrictions (other than thefullinvestmentrequirement). Use the current risk-free rate of return when solving this problem.
(f) (2 points) Estimate the mean and the standard deviation of the rate of return for the optimalportfolio for an investor with expected utility described by the following equation:E(U) = E(rp)? 2σ2p (1)
Assume that the investor can invest in all of the risky funds and in the risk-free asset and assumethat there are no constraints on their asset weights (aside from the full-investment requirement).
(g) (2 points) Using the asset weights for the optimal portfolio of the investor with expected utilityshown in equation 1, estimate the excess kurtosis of the portfolio’s simple monthly rate of return.
Use all of the available historical data to produce this estimate.
(h) (6 points) Critique the optimal portfolio weights found for the investor in part F, in terms of theirportfolio optimisation methodology. This part must be answered in no more than 300 words.

2 Assessment data

Each dataset is a numbered file that ends with the “.RData” suffix. Each file is an RData file, containingthe name and value for a number of R variables. You need to write an R script to load the variables fromthe right dataset file and analyse the data stored in these variables.All of the RData files are contained in the same ZIP file that is available on Canvas. Download that ZIPfile, extract its contents and then analyse the data in the RData file that is allocated to you. The number ofthe data file that you have been allocated is listed beside your name in the assignment page on Canvas.Download the zip file containing all of the possible data files and the starting point R script for theassignment and extract the contents of the zip file into the folder where you want to do your work.Your dataset contains 3 eXtensible Time Series (XTS) variables: fundTotalReturnIndicesriskFreeRateOfReturnmarkexTotalReturnIndexEach of these variables contains monthly data relating to rates of return from the beginning of 2000, tothe end of 2021.The total return index for the portfolio managed by each of different fund managers iscontained in thevariable named fundTotalReturnIndices. The totalreturn index for the fund manager “i” has column name:v_i
The data for the monthly risk-free simple rate of return is stored in the riskFreeRateOfReturn variableand its column name is:r_i
The monthly data for the market total return index is stored in the markexTotalReturnIndex variableand its column name is:v_m

You can load the variables from your RData file by running the R function:

load("Assignment 1 dataset X.RData")
replacing “X” with the number of the data set that has been allocated to you.Make sure that folder containing your data file and your R script is your working directory in R Studio.Page 2
Evidence of workWrite an R script that uses the provided data to compute the data you want to export to Microsoft Excelfor portfolio optimisation. Note that you can make your own choiceshere. Use R or Excel, for example, toestimate the relevant means, variances and covariances that you need to use to solve the portfolio optimisation
problems.You can save data to a CSV file using the R command:
write.csv(variableName, "nameOfCSVFile.csv", sep=",")The grid of data in the variable called “variableName” will be written out to the named CSV file withcommas separating each item in each row.
Load the data from the CSV file or files that you exported from R into an Excel workbook and thensolve each portfolio optimisation problem on a separate worksheet in that workbook. The use of a separateworksheet for each problem is required so that markers can review the solver configurations for each problem.If any solver configurations cannot be reviewed, you are unlikely to receive full marks for the associated

optimisation problem.

Upload your final R script and your Excel workbook along with your other answers to the Canvas quizquestions for Assignment 1. Your assignment will be marked based upon those quiz answers and your final Rscript and Excel workbook. The R script needs to include the code and comments necessary to demonstratehow your reached your conclusions.Your marks will be determined by teaching staff based upon their review of your answers. The built-inCanvas quiz answers are the same for everyone and only serve to check that your answers are within a verywide range of values. Do not interpret Canvas automarks as your final marks for the assignment.If you do not upload your R script or Excel workbook, your assessment score will be zero.
Make sure your uploaded documents are your own work. Markers use a wide range of automated methods
to detect plagiarism.
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