Tools › Investing › Portfolio and Risk › Position Size and Risk › Example

Sizing a trade: 1 % of a 50,000 account at risk with a 2.50 stop, and what the reward-to-risk ratio implies

ToolPosition Size and Risk
SourceClosed-form arithmetic; the gambler's ruin problem and runs of losses in Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed. John Wiley and Sons, New York; Kelly, J. L. (1956). "A New Interpretation of Information Rate." Bell System Technical Journal, Vol. 35, No. 4, pp. 917–926. The case is illustrative, not a printed example.
LevelUndergraduate

Problem

An account of 50,000 risks 1 % on one trade bought at 40.00 with a stop at 37.50 and a target at 46.00. Find the number of shares, the size of the position beside the account, the reward-to-risk ratio, the win rate at which it breaks even and the expectancy at an assumed win rate of 40 %.

Inputs to Enter

  • Account 50,000; risk per trade 1 %; maximum position 25 % of the account
  • Entry 40.00, stop 37.50, target 46.00; win rate 40 % (an assumption)
Open the Position Size and Risk tool (loaded with this example)

Answers

  • Money at risk 50,000 · 0.01 = 500.00; loss per share 40.00 − 37.50 = 2.50; shares 500 / 2.50 = 200
  • Position value 200 · 40 = 8,000.00, which is 16 % of the account (within the 25 % entered)
  • Gain per share 6.00; reward-to-risk ratio 6.00 / 2.50 = 2.40; break-even win rate 1 / (1 + 2.40) = 29.41 %
  • Expectancy 0.40 · 1,200 − 0.60 · 500 = 180.00 a trade, 0.360 of the money risked
  • Advanced mode (commission 0.005 and slippage 0.02 a share, each way): loss per share 2.55, 196 shares, ratio 2.33, break-even 30.00 %, expectancy 166.60
  • Advanced mode, 100 trades each risking 500: chance of the account falling 10 % below its start 5.58 % ± 0.16 by simulation (20,000 runs, seed 347; exact for the model 5.81 %); longest losing streak averages 7.87 losses; Kelly fraction 14.29 % beside the 1 % entered

Notes

The tool's default inputs are this case; press Submit. The sizing arithmetic, the simulation, the losing-streak distribution and the Kelly fraction are checked against a separately written numpy / scipy reference (test_position_size_risk.php). The win rate is an assumption, not an estimate of any real trade. A calculator for education and analysis, not investment advice.