A stop loss serves as a risk management tool, helping investors limit potential losses by automatically triggering the sale of a security when its price reaches a predetermined level. This level is set below the purchase price for long positions and above the purchase price for short positions. By implementing stop-loss orders, investors can protect their capital and minimize losses in case the market moves against their positions.
Reference [1] investigates the effectiveness of stop losses by formulating a market model based on fractional Brownian motion to simulate asset price evolution, rather than using the conventional Geometric Brownian motion. Using this new model, the authors analyze the efficacy of stop losses and explore the optimal stop loss threshold. They pointed out,
Existing research shows that a stop-loss strategy adds value to the trading of risky assets if their prices evolve according to autoregressive or regime-switching processes. We extend the analysis of stop-loss strategy to a market environment in which fractal behaviors of financial asset prices such as long-range dependence are explicitly modeled by fBMs. Both theoretical analysis and simulation studies demonstrate that stop-loss rules improve investment performance of the buy-and-hold strategy when return-generating processes are assumed to follow fGBMs. fBM-based asset price models lead to more accurate assessment of the efficacy of stoploss policies. Specifically, simulation studies find that the Hurst parameter, expected return, and volatility of fGBM influence the efficacy of stop-loss rules. To achieve the best performances of stop-loss strategies, stopping threshold shall be optimized with respect to these variables. A polynomial regression method is developed to approximate the relationship between the optimal stopping threshold and these variables.
In short, the paper formulated a market model based on fractional Brownian motion. Using this model, we can formally study the effectiveness of stop losses. It showed that stop losses enhance the risk-adjusted returns of the buy-and-hold investment strategy when the asset price is trending.
We note, however, that when the underlying asset is in the mean-reverting regime, stop losses decrease the risk-adjusted returns.
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References
[1] Yun Xiang and Shijie Deng, Optimal stop-loss rules in markets with long-range dependence, Quantitative Finance, Feb 2024
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