Portfolio Re-Balancing and Optimization Using Directional Changes and Genetic Algorithms

Dynamic portfolio optimization is a crucial but complex task due to financial market dynamics and the difficulty of disentangling noise from substantial changes in stock prices. In most existing methods, portfolios are re-optimized, hence re-balanced, at pre-specified time periods, return properties of each asset are dynamically computed, and portfolio weights are optimized according to an objective function. We propose a novel algorithm for dynamic portfolio optimization with a two-step signaling mechanism for re-balancing the portfolio including the optimization of re-balancing points and portfolio weights. The first step signals portfolio re-balancing only if there is a substantial price change in one or more of the portfolio constituents. These substantial price changes are defined according to directional change (DC) methods. DC methods create an intrinsic time series for each asset according to whether or not the change in the asset price exceeds a threshold level, hence removing part of the noise in asset prices. The second signaling mechanism uses genetic algorithms (GA) to assess if re-balancing is indeed profitable at each point indicated by the first signaling mechanism. The genetic algorithm is set up such that it simultaneously optimizes the weights of the re-balanced portfolio. For GA, we input the asset price summaries retrieved from DC methods to ensure that the GA can learn from the relatively less noisy data compared to observed asset prices. We show that the GA fit function can be set up to include several conventional trading strategies. As a first step, we apply the proposed method to a portfolio of 30 assets including 29 Exchange Traded Funds (ETF) and one risk-free asset where daily prices are observed during the period between 2 January 2018 and 30 December 2021. Second, we apply the method to 100 individual stocks for the same time period. We compare the obtained portfolio results with benchmarks, such as the simple buy and hold strategy of the S&P 500 index, the naive
$1/N$
portfolio, and a minimum variance portfolio in terms of standard portfolio evaluation methods including the Sharpe ratio.