Balancing small fixed and proportional transaction cost in trading strategies

TL;DR

This paper investigates the combined effects of small fixed and proportional transaction costs on portfolio optimization, revealing how these costs influence the value function and proposing an expansion based on their asymptotic behavior.

Contribution

It provides a heuristic analysis of the interplay between fixed and proportional transaction costs, deriving a new asymptotic expansion for the value function in portfolio optimization.

Findings

Deviation of value function is of order ε^{1/2} with fixed costs

Different from the proportional cost case where deviation is ε^{2/3}

Proposes an expansion of the value function in powers of ε^{1/2}

Abstract

Transaction costs appear in financial markets in more than one form. There are several results in the literature on small proportional transaction cost and not that many on fixed transaction cost. In the present work, we heuristically study the effect of both types of transaction cost by focusing on a portfolio optimization. Here we assume the presence of fixed transaction cost and that there is a balance between fixed and proportional transaction cost, such that none of them dominates the other, asymptotically. We find out that the deviation of value function, when the fixed transaction cost is $\varepsilon$, from the Merton value function, without transaction cost, is of order $\varepsilon^1/2$ which is different from the pure proportional cost of $\varepsilon^2/3$. Based on this, we propose an expansion for the value function in terms of powers of $\varepsilon^1/2$.