Trading Design: Entry/Exit Bands, Spread Dynamics, and Stop-Loss Rules

Knowing the spread is stationary is not enough — you also need to know when to enter and when to exit. Enter too early (small deviation) and transaction costs eat the profit. Enter too late (large deviation) and you miss most of the convergence. The band design problem asks: at what deviation $\Delta$ from equilibrium should a position be opened to maximise expected profit per unit of time?

Vidyamurthy derives the answer for the simplest case — a white noise spread — and then discusses the richer spread dynamics encountered in practice: AR processes, ARMA processes, and the Ornstein-Uhlenbeck model. The chapter closes with a nonparametric approach that avoids distributional assumptions entirely. This note follows that progression and adds the stop-loss design problem, which the Vidyamurthy discussion implicitly motivates but does not formalise.

• set up the profit-per-unit-time objective for a symmetric $\Delta$-band rule on a white noise spread;
• derive the first-order condition and identify the optimal threshold $\Delta^* \approx 0.75\sigma$;
• classify spread dynamics into white noise, AR, and OU families and explain their implications for band design;
• apply the Bollinger-band normalisation to convert a spread into a standardised signal;
• design a stop-loss rule and articulate the trade-off between loss tolerance and trade frequency.

1. 1. The band design problem
2. 1. Optimal threshold for a white noise spread
3. 1. Spread dynamics taxonomy
4. 1. The Bollinger-band normalisation
5. 1. Stop-loss design