APS Computational Project #2

Instructions: This is an individual assignment. For the mean-variance optimization (MVO) you need to (1) formulate the model by hand (typed is better) with all variables de…ned and the model objective and constraints fully written out and (2) print out the MATLAB …le that contains the data (e.g. through the vectors/matrices) and call to quadprog used to compute the model in MATLAB and the output from calling quadprog that shows the optimal values for the variables and objective function value.

Do not just dump the MATLAB …le, comment it and highlight the optimal values. You must use MATLAB quadprog function but you can call the func-tion from python in which case you must print out your python code. Your project should be contained in a single pdf …le (DO NOT MAKE THIS FILE TOO LARGE i.e. less than 10MB) and when you send me the …le via e-mail (rkwon@mie.utoronto.ca) MAKE THE SUBJECT OF YOUR E-MAIL exactly as APS 502 Computational Project 2. (I will not accept an e-mail that contains a link to your assignment, you must send me the as-signment directly). Write your full legal name and student number on your assignment. Due Dec.9 by 5:00PM (EST). Late assignments will incur penalty.

PART 1

You will use the following three ETFs (exchange-traded funds) to form a portfolio of these three assets. An ETF operates just like a stock, but these assets represent market indices or broad set of securities (stocks or bonds). For example, the purchase of one share of SPY (see below for description) represents an investment into the 500 stocks in the S&P 500.

    (1) SPDR S&P 500 ETF (SPY), this is a fund that mimics the perfor-mance of the S&P 500 which is a well known market index consisting of 500 large capitalization stocks from the U.S.

    (2) iShares Core US Treasury Bond (GOVT), this is a fund that mimics the performance of a wide set of U.S Treasury bonds.

    (3) iShares MSCI Emerging Markets Mini Vol (EEMV), this is fund that mimics the performance of emerging market stocks but with lower volatility compared to other emerging market funds.

Tasks

    (a) Use yahoo (e.g. yahoo.com or yahoo.ca) …nance to get the monthly adjusted closing prices of SPY, GOVT, and EEMV from Jan 2014 to end of Feb 2020 and compute the expected returns of the three assets, the standard deviations of the three assets as well as the co-variances between all assets over this time period. Show these parameters in your report but you don’t have to show the monthly prices or the computations that you did to get the parameters.

    (b) Use the mean-variance optimization model to generate an e¢ cient fron-tier of the three assets. Create a table where for each expected return goal R show the optimal weights of the assets as well as the portfolio variance value.


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Also, plot the e¢ cient frontier. Note: the range of R can be the smallest positive expected return among the three assets to the largest expected return among the assets. You are free to choose the points in the range to use for the optimizations but they should be at least 10 return points equally spaced out.

    (c) Take the minimum variance portfolio from (b) (this is the portfolio in the e¢ cient frontier with the lowest variance). Using monthly returns from only March 2020 compare the minimum variance portfolio with the equal weighted portfolio and a portfolio that has 60% in SPY, 30% in GOVT, and 10% in EEMV. Rank the 3 portfolios in terns of returns. Explain the relative perfor-mance of the portfolios.

Note: A formula sheet will be posted on the blackboard that you can use to get the parameters for PART 1 from the monthly adjusted closing prices. To compute a historical monthly return, use the closing price for the …rst trading day of a month and the closing price of the last trading day of the month.

PART 2

Repeat (b) of PART 1 using the stocks SPY, GOV, EEMV as well as the stocks below (so portfolios will have 8 assets now) that have heavy involvement and connection to development or use of blockchain technology (some people think that these stocks are going to do well in the future)

    (4) CME Group (CME)

    (5) Broadridge Financial Solutions (BR)

    (6) Cboe Global Markets (CBOE)

    (7) Intercontinental Exchange (ICE)

    (8) Accenture (ACN)

Compare the e¢ cient frontiers from PART 1 and PART 2. Does including the stocks in PART 2 lead to better portfolios? Discuss.






















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