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Kelly Formula

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Introduction

Construction

PercentW = winning percentage W = average size of winning trade L = average size of losing trade

OptimumRiskPercent = PercentW - [ (1-PercentW) / (W/L) ]

Example

Say we win 60% of the time, PercentW = 0.6. The win is W = 8 and the loss is L = 4.

Then OptimumRiskPercent = 0.6 - [0.4 / 8/4] = 0.6 - 0.2 = 0.4

Therefore the percentage of equity that would provide max rate of return is 40%.

Example

PercentW = 0.1 W = 6 L = 4

Then OptimumRiskPercent = 0.1 - [0.9 / 6/4] = 0.1 - [0.9/1.5] = -0.5

Therefore we would always lose using this system.

Signals

Strength

Notes

  • We should ensure that OptimumRiskPercent > 0.1.
  • Say W/L = R
    • 0.1 <= s - [(l-s)/(w/l)]
    • 0.1 <= s - l(l-s)/w
    • 0.1 <= s - l/w + ls/w
    • 0.1 <= (sw -l + ls) / w
  • Sometimes a trading system can have a string of losses, unless your drawdown < x% then do not risk > x% of your equity


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