Analyzing Optimal Portfolios of Eleven Assets under Different Constraints

Faculty of Art and Science, Queens University, Kingston, Canada

^* Corresponding author: 21xl92@queensu.ca

Abstract

Portfolios, which allocate investor capital to different investments, are a common risk management strategy. It aims to spread investment risk using diversification. The purpose of this paper is to allocate assets to stocks in the technology sector, consumer sector, and pharmaceutical sector. Stocks of SPX500 and ten companies are selected, and the Yahoo Finance database in Python is utilized to export the historical data, and the knowledge of statistics is applied to calculate the basic values of the stocks. For example, data such as annualized average return, annualized standard deviation, and alpha. These data are utilized to obtain the correlation coefficients between eleven assets and to plot the Capital Allocation Line (hereinafter referred to as CAL), efficient frontier and inefficient frontier images under different constraints. The results show that PG’s asset share is the highest among the five different constraints, both in the minimum variance case and in the maximum Sharpe ratio case. After imposing constraints, the portfolio’s return at the same risk decreases.