Portfolio Management: Allowing Short Selling Using the Lagrange Multiplier Method in R

In this study, an inquest was carried out into the portfolio theory using historical prices of three stocks Astrazeneca Limited (AZN.L), British Telecommunications (BT-A.L) and United Utilities (UU.L) from the dates 2nd of January, 2018 to 31st of December, 2018. The data set was combined and edited leaving only the trading dates (Volume>0) in chronological order. The price of each stock was plotted against the trading days, the daily net returns for each stock and estimates of the mean, standard deviation and correlation between stocks were obtained. A graph of the efficient frontier and minimum variance portfolio was plotted after which the lagrange multiplier method was employed allowing short selling to decide how to invest in these assets to achieve a reasonable target return. Correlations between stocks were obtained and it was observed that stock prices of the Telecommunications and Water companies are more correlated, probably due to the fact that their products are consumed more regularly. The bold part of the efficient frontier plot indicates the efficient frontier, while the leftmost part of the curve is the Minimum Variance Portfolio (MVP) obtained with the help of the Lagrange multiplier method. Finally, Astra stocks was short and monies re- invested in BT and United Utilities.