Background
Problem Statement
Aim and Objectives
This was to study the performance of the universal portfolio in the short and long term.
Scope and Limitation of the Study
He suggested that there may be a situation where the portfolio is efficient but with a high expected return and variance or vice versa. He studied portfolio investments by considering borrowing the remaining money to earn interest or borrowing money to buy the portfolio. Cover (1991) researched universal portfolios, updating the portfolio and changing the allocation daily to generate maximum profit.
The portfolio is updated based on the side information, such as whether the stock performed well in previous trading days, so that investors can allocate their assets to the best performing stock each day. The trading period of the portfolio is divided into a number of segments that the portfolio will only rebalance and pay the transaction fee at the beginning of each segment. An incorrect selection of parameters will result in the capital generated by the universal portfolio being lower.
They continuously monitor the daily performance of a finite-order universal portfolio created over a range of parameters. MAMR can implement online learning techniques in portfolio selection and achieve comparable performance as.
Low Order Universal Portfolio
Order 1 Universal Portfolio
Order 2 Universal Portfolio
Order 3 Universal Portfolio
Order 𝛎 Universal Portfolio’s Wealth Function
Low Order Universal Portfolio Generated by Five Special Distributions
Order 1 Universal Portfolio
Order 2 Universal Portfolio
Order 3 Universal Portfolio
Special Distributions
Order 1 Universal Portfolio Generated by Burr Distribution
Order 1 Universal Portfolio Generated by Transformed Gamma Distribution
Wealth Function of Order 1 Universal Portfolio
Expected Work Schedule
Flow Chart
Low Order Universal Portfolio Generated by Selected Distributions
For the Loglogistic distribution, its parameters were randomly generated within [4,103] for 𝛾 and [1,100] for 𝜃 to create a universal portfolio of order 1. A higher order universal portfolio will be created by increasing the range of 𝛾 by 1 while keeping 𝜃 unchanged. For the paralogistic distribution, its parameters were randomly generated within [2,101] for 𝛼 and [1,100] for 𝜃 to generate a universal portfolio of order 1.
The higher-order universal portfolio will be generated by increasing the range of 𝛼 by 1 while leaving 𝜃 unchanged. The higher-order universal portfolio is generated by increasing the range of 𝛾 by 1, while leaving 𝛼 and 𝜃 unchanged. For the transformed gamma distribution, its parameters are randomly generated within [1,100] for 𝛼, [1,100] for 𝜃, and [1, 100] for 𝜏 for generated order 1 universal portfolio.
Based on the result obtained, the lower order universal portfolio takes less time to generate wealth. Furthermore, the result showed that the universal portfolio generated by the Pareto distribution can outperform the universal portfolio generated by the other distribution and CRP. Since the parameters used to generate the wealth of a low-order universal portfolio are randomly generated, 500 trials may not be sufficient to determine the maximum wealth generated by each distribution.
Parameter
Parameter
Parameter
Parameter’s Sensitivity Test
Performance of the universal portfolio of Order 1, which is generated by the Paralogistic distribution with chosen values of 𝛼2 and 𝜃2 for Portfolio C.
Performance of Universal Portfolio in The Short and Long Run To identify how stocks' trading days in a portfolio affect the wealth generated,
Conclusions
This project aimed to generate a universal low order portfolio with five selected distributions: Pareto, Loglogistic, Paralogistic, Burr and Transformed Gamma distribution. For example, three datasets each consist of the share price of three different companies from KLSE and are collected from Yahoo Finance. The wealth generated with BCRP and CRP is used as a benchmark to study the performance of the distribution generated universal portfolio.
After the data has been collected, a mathematical model for the universal portfolio is generated using VBA in Excel. According to the result obtained, the time taken to generate the terminal wealth increases as the order of the universal portfolio increases. Furthermore, it is found that the Pareto distribution was able to generate the highest wealth among all the other selected distributions.
However, most of the distributions are not able to outperform BCRP, but can outperform CRP. This indicates that 500 trials may not be sufficient to determine the best parameter for each distribution to generate maximum wealth for the universal portfolio. According to the result obtained, each portfolio will be affected by different parameters of the chosen distributions.
Then each distribution parameter is assigned a selected parameter value to generate the highest possible wealth of the universal portfolio. In addition, to determine whether a universal portfolio will outperform in the long run, each distribution is measured with selected parameters from the. The result shows that as the range of trading days of the portfolio increases, terminal wealth will increase.
However, for Portfolio B, the terminal wealth of 2000 trading days is reduced as it continues to 2500 trading days. The ultimate goal of this project is to determine the performance of a diversified and non-diversified universal portfolio. Allocation parameters are essential because they are key to creating the most wealth of a universal portfolio, and a universal portfolio will have better performance over the long term.
Limitation and Recommendation
Furthermore, it is found that the Burr and Transformed Gamma distribution cannot generate wealth for the Order 3 A and B portfolios that are comparable to the other distributions, BCRP and CRP. So again it shows that the selected parameter value may not be suitable for Burr and Transformed Gamma distribution. According to the wealth generated by each Pareto-distributed portfolio, diversified universal portfolios can outperform undiversified universal portfolios.
Markowitz (1952) suggested that diversification across different industries in a portfolio should be considered as they have different market characteristics resulting in lower covariances. Chart A-1: Stock performance for Hong Leong Bank Berhad (blue line), Public Banking Berhad (green line), and Malayan Banking Berhad (red line). Chart A-2: Stock performance for Top Glove Corporation Berhad (blue line), Fraser & Neave Holdings Berhad (green line), and Malayan Banking Berhad (red line).
GraphA-3: Development of stocks for Top Glove Corporation Berhad (green line), Malayan Banking Berhad (red line) and Hong Leong Banking Berhad (blue line).
