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.
The globalised minimum variance portfolio has been set for the mean variance which involves the problem solving with the variance covariance. The setup is through the QP solver with the minimisation of the objective functions with returning half of the variance portfolio. The implementation is based on the rate of return and the dispersion return with a particular financial risk. (Clarke et al., 2011). Hence, the information could be set to minimise the portfolio with the standard deviation that also needs to work on more risks with the trade-off set for a better expected return.
The work includes the analysis of the stocks with the FTSE100 for th stock exchange, where the computation of the weights could not be negative. Hence, the short sales are also allowed with the mean weights that can be set to negative standards with short positions as well. The optimum weights are based on the tailoring of the needs of the client along with setting the daily returns for the 20 firms. The portfolio methods are set with the utility maximisation where the functions and formulations are for the minimised net cost of transaction and finance. This will lead to the development and improvement in the risks limits, with assets, sectors and the region. (Kempf et al., 2003).
The approach is about how the measures could be set with the optimisation of weight assets to hold and classify the same asset classes. The equities and the bonds have been set with systematic risks where there has been separate class to hold the portfolio for the different standards and diversification procurement. One of the approaches is the von Neumann Morgenstern utility function that has been defined over the wealth of portfolio where the value has been set to determine the maximisation of the utility function. The reflections are also on the higher returns with increased wealth function, and reflection on the risk aversion.
The optimisation of the constraints could easily be through certain regulatory constraints which lack the liquid market which could lead to applied optimisation process. With this, the taxes, and the cost of transaction with management could be delivering the under-diversified portfolios. (Markowitz, 1952). The investors could completely be forbidden from the law to hold the assets and so there are certain unconstrained portfolio which leads to the short selling of particular assets.
With this, the transaction cost is based on re-optimisation with the setup of the trade-offs to handle the tracking errors and the stock proportions that will have deviation over the time with benchmarks. For the improvement in the portfolio optimisation process, the investor tends to work on the risks with the exhibition of differences to forecast all the values with correlation mainly to the stock pricing movements. The optimisation framework has also been set for the accuracy estimation with the Monte Carlo Simulation process. the marginal distributions are also effective with volatility which allows the empirical standards to match with the stock returns.
Hence, the additional focus is on the tail risk with the values set around averse investors. The financial cries could easily be correlated with the stock price movement and so their diversification is affected mainly by the changing large portfolio patterns. With this, the minimisation is also for the tail risks, where the forecasting is of the asset returns through the use of Monte Carlo simulation which also allow the tail dependency in the larger asset portfolios. (Clarke et al., 2011).
The diversifications also includes the allocations in a manner that will completely lead to the particular asset or the risks based on the change in the price with the variance that is lesser than that of the weighted average value. The return on investment with a diversified portfolio will work on not only related to the lowering of the highest return. Hence, the focus is on handling the loss with the chance that have a single asset which tends to be out with a particular range.
With the change in financial risk, the variance is set to handle the diversification with the portfolio return that is below the level of investment. The asset returns are completely uncorrelated with the setup to lead to a greater diversification of the benefits with the number of assets. The additional forms are involving the subdivision of all the smaller investments as well which adapt to the risks of security and the exposure to the index movement.
Clarke, R., De Silva, H., & Thorley, S. (2011). Minimum-variance portfolio composition. The Journal of Portfolio Management, 37(2), 31-45.
Kempf, A., & Memmel, C. (2003). On the estimation of the global minimum variance portfolio.
Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.