Double Linear Trading Policies Under Transaction Costs

Summary

This paper introduces a class of asset-trading rules called double linear policies and studies their robustness when transactions incur costs. It uses consistently positive expected trading gain across market directions as a robustness criterion. The central theoretical finding is that transaction costs can eliminate the positive expected gain that a policy might otherwise be expected to maintain. The authors then identify conditions under which that positivity can be preserved.

The description reports two forms of evaluation: extensive Monte Carlo simulations for an asset modeled with geometric Brownian motion and jumps, and a historical-data backtest involving Bitcoin-USD. These analyses are offered as checks on the theoretical results, with the historical example providing a cryptocurrency application. However, the supplied text does not state the conditions required for positive gains, the size of costs, backtest design, or numerical performance. It therefore introduces a useful way to frame robustness under trading costs but does not provide enough detail to assess real-world profitability or reproduce the reported results.

Key ideas

• The paper proposes double linear policies for trading assets with transaction costs.
• It defines robustness in terms of positive expected gain across market directions.
• Transaction costs may remove the positive expected gain sought by a trading rule.
• The authors derive conditions under which positive expected gain can be retained.
• Monte Carlo simulations and a Bitcoin-USD historical backtest are used to examine the theory.

Tags

# On Robustness of Double Linear Trading with Transaction Costs


# On Robustness of Double Linear Trading with Transaction Costs









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.

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