Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

TL;DR

This paper introduces a threshold rebalanced portfolio algorithm for optimal investment in markets with transaction costs, maximizing expected wealth by selectively trading only when thresholds are breached, and demonstrates significant wealth improvements over existing methods.

Contribution

It presents a novel threshold rebalanced portfolio approach tailored for markets with transaction costs, optimizing wealth in two-asset Black-Scholes models and extendable to multiple assets.

Findings

Maximized expected wealth using threshold rebalancing in two-asset markets.

Significant wealth improvement over existing portfolio algorithms.

Method applicable to markets with more than two stocks.

Abstract

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.