On Robustness of Double Linear Trading with Transaction Costs

TL;DR

This paper introduces a new class of trading policies called double linear policies, analyzes their robustness in the presence of transaction costs, and validates findings through simulations and real cryptocurrency data.

Contribution

It proposes the double linear policy, examines conditions for robustness with transaction costs, and validates results via simulations and Bitcoin-USD data.

Findings

Robust positive expected gain may vanish with transaction costs.

Conditions identified for maintaining positive expected gain.

Monte-Carlo simulations and Bitcoin data validate theoretical insights.

Abstract

A trading system is said to be {robust} if it generates a robust return regardless of market direction. To this end, a consistently positive expected trading gain is often used as a robustness metric for a trading system. In this paper, we propose a new class of trading policies called the {double linear policy} in an asset trading scenario when the transaction costs are involved. Unlike many existing papers, we first show that the desired robust positive expected gain may disappear when transaction costs are involved. Then we quantify under what conditions the desired positivity can still be preserved. In addition, we conduct heavy Monte-Carlo simulations for an underlying asset whose prices are governed by a geometric Brownian motion with jumps to validate our theory. A more realistic backtesting example involving historical data for cryptocurrency Bitcoin-USD is also studied.