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BE312 Quantitative Foundations Of Finance

tag 0 Download 4 Pages / 778 Words tag 29-06-2021
  • Course Code: BE312
  • University: University Of Essex
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  • Country: United Kingdom


You are given the daily prices for the calendar year 2016, for 20 stocks randomly selected from the Financial Times Stock Exchange 100 (FTSE100). Evaluate the weights of that portfolio which will minimise your portfolio’s variance, which means you should compute the weights of the minimum variance portfolio (MVP).You need to find the weights for the MVP, under two different restrictions:
1. Short Sales are NOT allowed, which means weights CANNOT be negative, so that only long positions are allowed.
2. Short Sales are allowed, which means weights can be negative, so that short positions are also allowed.

The daily prices of the necessary stocks from the FTSE100 are in an Excel file, sent to each of you. This file includes the ID Numbers of your unique portfolio of 20 firms. Using the allocated firms, compose the portfolio of YOUR twenty firms and solve the variance minimisation problem for your portfolio.

Prepare an investment analyst report, describing the steps you took to find the minimum variance portfolio (MVP) in each of the two cases (1) and (2). You are required to help determine the optimum weights across the 20 stocks that will minimise the risk of the portfolio. The investment in the portfolio is £10 million. In an APPENDIX, you should include all the partial differential equations (21 of them) that were solved and explain the steps taken to solve it.

A copy of an investment analyst report has also been included, to help you organise the writing of your report. Your report will of course need to be tailored to the needs of this client. You will need to write a short report, that includes the weights neatly laid on out in table format and with not more than 2 decimal places, on the firms that you have computed for your client. Do not write more than 3 pages.

The share price data are in the Excel file. You need them to compute the daily returns of your 20 firms from the daily share prices of YOUR companies. The ID numbers of the 20 firms of your personal portfolio are also in that Excel file, in the sheet named “ID Nos of Firms and Class List”. In this sheet, you will see against your name,a row of 20 ID numbers, which identify your 20 firms. The ID Nos and the associated prices for the firms are on the sheet named “FTSE100 2016 Daily”. You need to copy the price data for your portfolio of 20 firms and use them to compute the returns. An example, for a few firms, is shown on the sheet named ‘Practice Run Values Only’.
The returns have beencomputed in the cells shaded light green. The standard deviation has been computed in the column shaded red. The correlation matrix has been computed in the cells shaded blue. While this is only an example with a few firms, it demonstrates the steps you will need to follow for your 20 stock portfolio. So, for example, in the case of your 20 stock portfolio, the correlation matrix should be 20 x 20 in size.

You will need to copy and paste the correlation matrix and standard deviation vector to the Maple worksheet for computing of the optimal portfolio weights. A short piece of Maple code is also attached. You will only be able to run the Maple software program in the University labs. You will need to paste your correlation matrix after the equal sign, at the point in the Maple program where it says CorrM := Similarly, you will need to paste your standard deviation vector after the equal sign, at the point in the Maple program where it says TotRisk := After pasting the relevant data sets, you should run the Maple program. This is done by clicking on the button with the three exclamation marks !!! in the top bar of the Maple program.
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