Homework 1file:///C:/Users/Administrator/Documents/WeChat%20Files/littlecharmingprince/Files/HW1.html 1/3Homework 1MAFS6010R- Portfolio Optimization with RMSc in Financial MathematicsFall 2018-19, HKUST, Hong KongProf. Daniel P. PalomarHong Kong University of Science and Technology (HKUST)Shrinkage estimator for \(\boldsymbol{\mu}\)After Week 5 on shrinkage and the Black-Litterman model, you have learned how to improve the naiveestimation of \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}\) (i.e., the sample mean and sample covariancematrix, respectively). In particular, we have seen that the estimation error in \(\boldsymbol{\mu}\) is muchmore signicativethan that of \(\boldsymbol{\Sigma}\).The purpose of this homework is to explore the possible improvements on the estimation of \(\boldsymbol{\mu}\).OutlineStep 1: Load market data (you can also start with synthetic data, but eventually you need to try with realmarket data).Step 2: Compute the sample mean estimator for \(\boldsymbol{\mu}\) and evaluate its performance bycomputing the estimation error compared to the real parameter (in case of synthetic data) or the sampleestimation from the test data (in case of real data).Step 3: Design the Markowitz mean-variance portfolio based on the sample mean estimator for \(\boldsymbol{\mu}\) and the sample covariance matrix estimator for \(\boldsymbol{\Sigma}\). Evaluate it andplot its performance.Step 4: Consider some way to improve the estimation of \(\boldsymbol{\mu}\). For example, you could try theJames-Stein estimator (but have some imagination for the target) or the Black-Litterman model (but havesome imagination for the views).Step 5: Evaluate its performance by computing the estimation error compared to the real parameter (in caseof synthetic data) or the sample estimation from the test data (in case of real data). Compare with theestimation error in Step 2.Step 6: Design the Markowitz mean-variance portfolio based on your estimator for\(\boldsymbol{\mu}\) andthe sample covariance matrix estimator for \(\boldsymbol{\Sigma}\). Evaluate it and plot its performance.Compare with the performance in Step 3.Step 7: Try more ideas. You will get additional points if you can clarify some different methods from class.10/16/2018 Homework 1file:///C:/Users/AdministratoMAFS6010R留学生作业代写、代写R编程设计作业、Portfolio Optimization作业代做、代做R课程设r/Documents/WeChat%20Files/littlecharmingprince/Files/HW1.html 2/3Hint: There are tons of R packages improving estimation for mean and covariance matrix. Figure out whatthey are doing by tracking their references. Some prior knowledge like sector information (partially availablevia function getSectorInfo() in package covFactorModel ) could be helpful. Clarify your method even if it isheuristic because we will count if you can make it reasonable.Format for homeworks in R MarkdownUse the R Markdown (http://rmarkdown.rstudio.com/index.html) format (with leextension .Rmd) to prepareyour homework. It is an extremely versatile format that allows the combination of formattable text,mathematics based on Latex codes, R code (or any other language), and then automatic inclusion of theresults from the execution of the code (plots or just other type of output). This type of format also exists forPython and they are generally referred to as Notebooks and have recently become key in the context ofreproducible research (because anybody can execute the source .Rmd leand reproduce all the plots andoutput). This document that you are now reading is an example of an R Markdown script.R Markdown lescan be directly created or opened from within RStudio. To compile the source .Rmd le,justclick the button called Knit and an html will be automatically generated after executing all the chunks of code(other formats can also be generated like pdf).The following is a simple template that can be used to prepare the homework and projects in this course:10/16/2018 Homework 1file:///C:/Users/Administrator/Documents/WeChat%20Files/littlecharmingprince/Files/HW1.html 3/3---title: Titlesubtitle: Subtitleauthor: Authordate: 2018-10-09output: html_document---Summary of this document here.# First header## First subheader# Second header* bullet list* bullet list - more - moreThis is a link: [R MArkdown tutorial](http://rmarkdown.rstudio.com)```r# here some R code```For more information on the R Markdown formatting:R Markdown tutorial (http://rmarkdown.rstudio.com)R Markdown Cheat Sheet (https://www.rstudio.org/links/r_markdown_cheat_sheet)R Markdown Reference Guide (https://www.rstudio.com/wp-content/uploads/2015/03/rmarkdownreference.pdf)转自：http://ass.3daixie.com/2018101920717431.html