Data on beginning of the month adjusted closing price of stocks on five firms trading on the LSE: British Petroleum, Tesco PLC, Asos PLC, AstraZeneca PLC and Vodafone Group PLC. The data covers the period 01-11-2016 to 01-01-2020
Assume that the risk free rate of return is constant at 0.04% per month throughout the period.
Demonstrate clearly all the methods you are using for these tasks.
Use the price data to find the monthly returns for each firm's stock and then, combine two firms to form a portfolio that will give you the best diversification opportunities. Justify why you choose these two stocks for your portfolio. Explain all the assumptions you have made.
Once you have formed this portfolio, (excludes tables, figures, charts and equations) that covers all the tasks below. Calculate the following and demonstrate all your work, clearly explaining the process. If you are showing summary statistics, please present this in a nice, table. Charts or diagrams need to be properly labelled. Do not include the raw data in your report - I already have this.
a) Find the expected return and the level of risk exhibited by the Global Minimum-Variance Portfolio. What proportions of your wealth are invested in each of the two stocks?
b) Plot the investment opportunity set of the two risky assets. Use increments of 10% over the range 0-100% in the weights (or investment proportions) for w1.
c) Draw and label the Capital Allocation Line (CAL) that is just tangential to the opportunity set. Label this point of tangency P. Explain what P is.
d) Use the solution derived from the maximization problem of the Sharpe Ratio (or slope of the CAL) to find the weights invested in each asset at P. You do not have to show the derivation here - simply use the results from the maximization problem from the textbook or the slides from the lecture.
e) Calculate the expected return and the standard deviation at P. Calculate the Sharpe Ratio for this CAL.
f) If your risk aversion parameter has a value of A = 3, find the composition of the complete portfolio C you would invest in.
Comment on your answer and compare with what you would have earned if you were to invest all your wealth in a single stock.
g) Calculate the standard deviation and the expected return of your complete portfolio C.
h) Explain how your answers to part g) above change when the risk aversion parameter takes on the values 0, 1, 2 and 4 respectively?
Tesco Asos Vodafone 150.825882 190.2379 5047 4725 188.5515 158.657318 BP 343.0327 387.1788 359.2574 344.5938 353.9441 342.302 5266 154.290985 AstraZeneca 3573.957275 3822.01123 3612.2854 3999.869629 4371.300781 4126.596191 4657.381836 177.3852 171.7337 169.1814 167.0393 167.4494 5432 6045 5820 160.284775 165.206848 158.022217 183.783676 172.867798 183.410004 6417 361.0222 348.4016 153.8675 5749 4569.288086 350.762 158.7898 5778 182.914322 350.2507 381.7522 164.8971 170.5943 165.3529 5667 5955 4065.643311 4040.728027 4477.583496 4547.164551 172.504547 408.0662 5697 6060 391.19 177.8338 4316.734375 4627.589844 424.0869 191.7636 6715 178.122543 185.310226 197.816864 189.062424 171.511444 163.489349 7434 7452 4415.684082 4314.926758 4549.662598 4742.503418 6960 406.562 191.5345 385.5078 193.1841 394.7941 188.6936 443.1908 216.1865 474.7413 225.1676 482.67 237.1719 5846 178.119385 Date 01/11/2016 01/12/2016 01/01/2017 01/02/2017 01/03/2017 01/04/2017 01/05/2017 01/06/2017 01/07/2017 01/08/2017 01/09/2017 01/10/2017 01/11/2017 01/12/2017 01/01/2018 01/02/2018 01/03/2018 01/04/2018 01/05/2018 01/06/2018 01/07/2018 01/08/2018 01/09/2018 01/10/2018 01/11/2018 01/12/2018 01/01/2019 01/02/2019 01/03/2019 01/04/2019 01/05/2019 01/06/2019 01/07/2019 01/08/2019 01/09/2019 01/10/2019 01/11/2019 01/12/2019 01/01/2020 5079.859863 6622 6102 161.469101 154.734894 478.4968 240.498 6070 6114 4881.907715 5450.672852 5385.618164 5605.773438 5631.155762 164.162659 154.701248 145.186859 456.7963 235.2316 498.7082 221.5575 480.0902 197.0735 440.0615 183.9425 425.9895 177.0056 5762 5456 130.465195 4958 5750.547852 149.105591 139.212173 2277 5521.165039 446.7327 207.7326 3300 5200.592773 126.174118 3196 3200 5771.229492 5905.448242 122.259041 127.284889 3921 5511.751465 129.287949 459.0156 210.4328 486.5464 216.1126 486.982 232.5934 470.5169 210.8052 485.1916 214.6966 482.6268 211.4767 3440 2550 5614.747559 6197.11084 117.834122 117.74308 2606 6796.799805 207.5937 7044.183594 442.3858 463.8408 2380 2476 141.053192 145.902832 152.256241 147.932907 228.2395 7060.59668 7293.973145 440.0102 222.7466 3530 144.13591 431.827 430.648 219.8164 244.5386 3201 3373 7252.159668 7397.047363 141.913239 144.369354 417.0419 236.5853 3073 7219.098145 Tesco Asos Vodafone 150.825882 190.2379 5047 4725 188.5515 158.657318 BP 343.0327 387.1788 359.2574 344.5938 353.9441 342.302 5266 154.290985 AstraZeneca 3573.957275 3822.01123 3612.2854 3999.869629 4371.300781 4126.596191 4657.381836 177.3852 171.7337 169.1814 167.0393 167.4494 5432 6045 5820 160.284775 165.206848 158.022217 183.783676 172.867798 183.410004 6417 361.0222 348.4016 153.8675 5749 4569.288086 350.762 158.7898 5778 182.914322 350.2507 381.7522 164.8971 170.5943 165.3529 5667 5955 4065.643311 4040.728027 4477.583496 4547.164551 172.504547 408.0662 5697 6060 391.19 177.8338 4316.734375 4627.589844 424.0869 191.7636 6715 178.122543 185.310226 197.816864 189.062424 171.511444 163.489349 7434 7452 4415.684082 4314.926758 4549.662598 4742.503418 6960 406.562 191.5345 385.5078 193.1841 394.7941 188.6936 443.1908 216.1865 474.7413 225.1676 482.67 237.1719 5846 178.119385 Date 01/11/2016 01/12/2016 01/01/2017 01/02/2017 01/03/2017 01/04/2017 01/05/2017 01/06/2017 01/07/2017 01/08/2017 01/09/2017 01/10/2017 01/11/2017 01/12/2017 01/01/2018 01/02/2018 01/03/2018 01/04/2018 01/05/2018 01/06/2018 01/07/2018 01/08/2018 01/09/2018 01/10/2018 01/11/2018 01/12/2018 01/01/2019 01/02/2019 01/03/2019 01/04/2019 01/05/2019 01/06/2019 01/07/2019 01/08/2019 01/09/2019 01/10/2019 01/11/2019 01/12/2019 01/01/2020 5079.859863 6622 6102 161.469101 154.734894 478.4968 240.498 6070 6114 4881.907715 5450.672852 5385.618164 5605.773438 5631.155762 164.162659 154.701248 145.186859 456.7963 235.2316 498.7082 221.5575 480.0902 197.0735 440.0615 183.9425 425.9895 177.0056 5762 5456 130.465195 4958 5750.547852 149.105591 139.212173 2277 5521.165039 446.7327 207.7326 3300 5200.592773 126.174118 3196 3200 5771.229492 5905.448242 122.259041 127.284889 3921 5511.751465 129.287949 459.0156 210.4328 486.5464 216.1126 486.982 232.5934 470.5169 210.8052 485.1916 214.6966 482.6268 211.4767 3440 2550 5614.747559 6197.11084 117.834122 117.74308 2606 6796.799805 207.5937 7044.183594 442.3858 463.8408 2380 2476 141.053192 145.902832 152.256241 147.932907 228.2395 7060.59668 7293.973145 440.0102 222.7466 3530 144.13591 431.827 430.648 219.8164 244.5386 3201 3373 7252.159668 7397.047363 141.913239 144.369354 417.0419 236.5853 3073 7219.098145
