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Markowitz Mean-Variance Optimization

ANLY 515 Risk Modeling Homework 4 (100 points) Remember to upload your answers by the due date. There will be a penalty of 10 points for each day the homework is late.

• The homework report must include all charts and answers required. • Must upload 2 files

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• Include the questions and the answers in one file, code on a separate file • Upload 2 pdf files (answers, code)

• A file with the R code you developed must be included as an appendix. Please label each section of the code based on the question that you are answering. For example the code to download and create the subsets should be under “Create the data files”.

Students should have a five-year portfolio. The calculations for this homework will be based on the data from the fifth year of your portfolio.

Part A – Markowitz Mean-Variance Optimization

1. Using all securities from your portfolio (from different sectors)

a) Calculate Variance-Covariance (VCOV) Matrix of Returns b) Identify the Minimum Variance Portfolio c) Identify Tangency Portfolio d) Plot the Mean-Variance (MV) Efficient Frontier

Part B – Suitable distributions for returns Identify

1. The global-minimum variance portfolio. 2. The most diversified Portfolio, 3. The equal-risk contributed Portfolio 4. Minimum tail-dependent portfolio

Show the results graphically

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