In the previous article1 we’ve defined money management as a part of a trading strategy that defines the risk that should be taken at opening a position and the size of the position to be maintained at a given moment relative to the capital. In the present article some of the popular money management methods are going to be reviewed.
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A dictionary of money management Money Management Mathematical expectation of profit – the sum of profit probabilities multiplied by the size of those profits minus the sum of loss probabilities multiplied by the size of those lossesΕ = S The mathematical expectation may be roughly estimated as the profit probability (%Win/100), multiplied by average profit (AvgWin), minus loss probability (%Loss/100), multiplied by the average loss (AvgLoss). – the sum we are ready to lose before exiting an unprofitable trade per one share (contract). The difference between the entry point an the exit at a loss point.【交易知识www.irich.com.cn § macd.org.cn 收集整理】
Initial risk Current (open) risk Martingale – Antimartingale – Volatility – the measure of the extent of price changes per a given period of time.increasing the position size as the capital increases.– the difference between the current price and the exit point. increasing the position size as the capital decreases.i(Probability of profiti * Profiti ) - S j(Probability of lossj * Lossj )– part of a trading strategy that defines the risk that should be taken at opening a position and the size of the position to be maintained at a given moment relative to the capital. |
Evidently, if we put too little at the stake, we won’t cover our expenditures of time, energy and beer, too. It is much less evident, yet so, that if we start betting too much, sooner or later we are going to lose the entire capital. Economical theories and common sense both keep telling us that the higher the risk, the more the profit. This statement is untrue: the dependece between risk and profit is non-linear.
Let us imagine there are only two outcomes in our treading: losing the bet wit ha probability 100 - PctWin, or winning WinToLoss * bet size with a probability PctWin. In this case the mathematical expectation will be:
Expectancy = PctWin * 0.01 * WinToLoss - (1 - PctWin * 0.01)
Suppose that the PctWin and WinToLoss parameters are set and we can only control the bet size. Let us then review the dependence between profit and bet size after 100 trades with different PctWin and WinToLoss values using Monte Carlo modeling. To do this we repeat over and over 100-trade series for every combination of the bet size, PctWin, WinToLoss parameters. The exact outcome (profit or loss) will be determined by a random number generator.
Here is an example of implementing Monte Carlo methods in TradeStation (the code for the corresponding TradeStation signal is shown in Appendix 1). Copy it to PowerEditor, create in StrategyBuilder a strategy with this signal, apply it to any plot and launch parameter optimization in TradeStation as shown below.
Ill.1
This strategy will save to a file the profit for all combinations of parameters and random trade outcomes. One should keep in mind that the number of bars multiplied by the number of combinations mustn’t exceed 65536 (the maximal number of lines in an Excel file). The Random(100) function will generate an uniformly distributed random value between 1 and 100. Then the PctWin-Random will define with a PctWin probability whether the given trade brings profit or loss, and the profit size will be equal to WinToLoss.
Then we can plot in Excel the plots indicating the profit for the given parameters. For example, let us recall the game played by scientists from the previous article, where the bet won in 60% of cases and lost in 40%. To plot the dependence between average profit and bet size in that game, we must:
- Launch in TradeStation an optimization of a strategy by the PctRisk parameter = 5, 10, …, 90 with constant PctWin = 60%, WinToLoss = 1;
- Open in Excel the file D:\TS_Export\MTrading_MMII.csv;
- Enter the values of the parameters to be optimized in column F and the following formulas in column G:
=SUMIF (A$1:A$20860,"=5",E$1:E$20860)/COUNTIF (A$1:A$20860,"=5")
=SUMIF (A$1:A$20860,"=10",E$1:E$20860)/COUNTIF (A$1:A$20860,"=10")
etc.
