Finite order universal portfolio generated by recursive calculation of continuous random variable's moment generating function

Chong, You Chuen (2024) Finite order universal portfolio generated by recursive calculation of continuous random variable's moment generating function. Final Year Project, UTAR.

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Abstract

This project studied the finite order universal portfolio (UP) generated by five different continuous random variables’ (CRV) moment generating functions (MGF), the gamma, lognormal, logistic, Weibull, and generalized Pareto distribution. five machine learning models were adopted to perform stock selection to filter the top-performing companies based on selected dataset, the ridge regression, least absolute shrinkage selection operator, elastic net, boosted regression tree and long-term short-term memory models. All machine learning models formed portfolios based on predicted performance, and all outperformed the KLSE benchmark return. The selected portfolios were used to calculate the universal portfolio by a recursive study of CRV’s MGF on orders 1, 2, and 3. The terminal wealth of all portfolios did not outperform the best constant rebalance portfolio (BCRP) as a benchmark comparison but did outperform Buy and Hold (BH), Cover UP (CUP), and Successive Constant Rebalance Portfolio (SCRP) in all portfolios, and Constant Rebalance Portfolio (CRP) in portfolios B and C. As the universal portfolio will adjust the allocation weight based on past observed performance, a transaction cost of 1% was added into consideration. The Bayesian Optimization technique was used in stock selection and universal portfolio construction processes. In stock selection, each model’s best parameters will be determined, which will minimize the means squared error of prediction. In contrast, in the universal portfolio, each distribution’s best parameters were determined to maximize the terminal wealth generated by the distribution. Parameter sensitivity testing was conducted to study the allocation preferences and relationships between parameter value with the terminal wealth, maximum allocation, and range of allocation. Scenario testing was conducted during the COVID-19 period to study the performance of the universal portfolio during a market downturn. Additionally, scenarios of reducing the trading periods to study the performance of the universal portfolio in the short term were conducted as well. Portfolio A and B outperformed the BCRP benchmark return in all shorter trading periods, while Portfolio C underperformed the BCRP in all periods.

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