Position Sizing with Linear, Exponential, and Hyperbolic Growth Models

Summary

The article compares position-sizing rules derived from linear, exponential, and hyperbolic balance-growth models. It first argues that money management presupposes a strategy with stop-loss and take-profit levels and positive expected value; where results are uncertain or expectation is non-positive, it recommends keeping size minimal. Linear sizing uses a fixed or incrementally adjusted volume, with a risk parameter controlling deviation from the model. Exponential sizing relates volume to compounded growth and discusses fixed-percentage sizing, Kelly criterion, and optimal f. Hyperbolic sizing accelerates as the process advances and requires a numerical search for an appropriate lot size.

The author illustrates the models with simulated growth and an expert-advisor test based on moving-average crossovers, reporting net profit and other performance measures for several methods and risk settings. These results are specific to the test setup and do not show that the sizing rules improve a strategy out of sample. The article notes that margin limits, trade direction asymmetry, and the possibility of large losses must be considered; its equations and assumptions warrant independent validation before use.

Key ideas

• Position sizing is presented as an overlay on a trading strategy, which the article says should have positive expected value and defined exits.
• Linear growth methods use fixed or adjusted trade size, with a risk parameter affecting the chosen volume.
• Exponential growth methods compound returns and include fixed-percentage approaches related to Kelly sizing.
• Hyperbolic sizing can accelerate sharply and the article proposes numerical search to select volume.
• The reported crossover test is strategy-specific, and margin constraints and high-loss risk limit the conclusions.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.