# Maximum Probability of Profit

To continue with the LSPM examples, this post shows how to optimize a Leverage Space Portfolio for the maximum probability of profit. The data and example are again taken from The Leverage Space Trading Model by Ralph Vince.

These optimizations take a very long time. 100 iterations on a 10-core Amazon EC2 cluster took 21 hours. Again, the results will not necessarily match the book because of differences between DEoptim and Ralph’s genetic algorithm and because there are multiple possible paths one can take through leverage space that will achieve similar results.

The results from the EC2 run were:

iteration: 100 best member: 0.0275 0 0.0315 -0.928 -1 best value: -0.9999

The book results (on p. 173) were:

iteration: 100 best member: 0.085 0.015 0.129 -0.76 -0.992 best value: -0.9999

Specifying an initial population can give DEoptim an initial set of parameters that are within the constraint. This guarantees a starting point but it can slow optimization if the f (and/or z) values are too low. Therefore, experiment with the initial population to find a set of f (and/or z) values that produce a result within, but not far from, the constraint.

```
# Load the LSPM and snow packages
library(LSPM)
library(snow)
# Multiple strategy example (data found on pp. 84-87, 169)
trades <- cbind(
c(-150,-45.333,-45.333,13,13,13,13,13,79.667,79.667,79.667,136),
c(253,-1000,-64.429,-64.429,-64.429,253,253,448,-64.429,-64.429,-64.429,253),
c(533,220.143,220.143,-500,533,220.143,799,220.143,-325,220.143,533,220.143))
probs <- c(0.076923076923,0.076923076923,0.153846153846,0.076923076923,
0.076923076923,0.076923076923,0.076923076923,0.076923076923,
0.076923076923,0.076923076923,0.076923076923,0.076923076923)
# Create a Leverage Space Portfolio object
port <- lsp(trades,probs)
# Number of population members
np <- 30
# Initial population
initpop <- cbind(runif(np,0,0.01),runif(np,0,0.01),runif(np,0,0.01),
runif(np,-1,-0.8),runif(np,-1,-0.8))
# DEoptim parameters (see ?deoptim)
DEctrl <- list(NP=np, itermax=11, refresh=1, digits=6, initial=initpop)
# Create a socket cluster with snow to use both cores
# on a dual-core processor
cl <- makeSOCKcluster(2)
# Drawdown-constrained maximum probability of profit (results on p. 173)
res <- maxProbProfit(port, 1e-6, 12, probDrawdown, 0.1,
DD=0.2, calc.max=4, snow=cl, control=DEctrl)
```