# The Leverage Space Trading Model

March 29, 2011
By

(This article was first published on Timely Portfolio, and kindly contributed to R-bloggers)

I finally got around to reading Ralph Vince’s latest The Leverage Space Trading Model (for a brief summary see this magazine article in Futures), and I’m happy to say that the book was very helpful in approach and example.  I especially enjoyed the last two chapters which tied his method to the realities of the money management business which do not fit most economic models.

The book’s true value will reveal itself hopefully through my ability to incorporate the material.  As usual with R, some fine folks at http://www.fosstrading.com and http://automated-trading-system.com have already built a package and provided examples on its use.  To extend their examples, I wanted to apply this Leverage Space Model to the EDHEC Hedge Fund Returns provided in the PerformanceAnalytics R package and then use this PerformanceAnalytics package to produce some decent charts illustrating the output.

 From TimelyPortfolio
 From TimelyPortfolio
 From TimelyPortfolio

Since the book uses $amounts instead of percentages, I am not entirely sure I got this correct, but it is certainly close. As always, please let me know if I messed up here or anywhere. After your comments and my own improvements, I hope to extend this to basic systems and show how we can tie multiple managers, systems, or indicies together with the Leverage Space approach. Also, I would like to compare this with other optimization methods to see which are more robust. R code: #Please see au.tra.sy blog http://www.automated-trading-system.com/ #for original code and http://www.fosstrading.com #I take no credit for the majority of this code #I simply changed a couple of things to use edhec data #as another example but this time using xts style returns require(PerformanceAnalytics) # Set Walk-Forward parameters (number of periods) optim<-48 #4 years = 48 monthly returns wf<-6 #walk forward 6 monthly returns # get data series from PerformanceAnalytics edhec dataset data(edhec) rtn<-edhec[,1:13]*100 # Calculate number of WF cycles numCycles = floor((nrow(rtn)-optim)/wf) # Define JPT function jointProbTable <- function(x, n=3, FUN=median, ...) { # Load LSPM if(!require(LSPM,quietly=TRUE)) stop(warnings()) # Function to bin data quantize <- function(x, n, FUN=median, ...) { if(is.character(FUN)) FUN <- get(FUN) bins <- cut(x, n, labels=FALSE) res <- sapply(1:NROW(x), function(i) FUN(x[bins==bins[i]], ...)) } # Allow for different values of 'n' for each system in 'x' if(NROW(n)==1) { n <- rep(n,NCOL(x)) } else if(NROW(n)!=NCOL(x)) stop("invalid 'n'") # Bin data in 'x' qd <- sapply(1:NCOL(x), function(i) quantize(x[,i],n=n[i],FUN=FUN,...)) # Aggregate probabilities probs <- rep(1/NROW(x),NROW(x)) res <- aggregate(probs, by=lapply(1:NCOL(qd), function(i) qd[,i]), sum) # Clean up output, return lsp object colnames(res) <- colnames(x) res <- lsp(res[,1:NCOL(x)],res[,NCOL(res)]) return(res) } for (i in 0:(numCycles-1)) { # Define cycle boundaries start<-1+(i*wf) end<-optim+(i*wf) # Get returns for optimization cycle and create the JPT jpt <- jointProbTable(rtn[start:end],n=rep(10,13)) outcomes<-jpt[[1]] probs<-jpt[[2]] port<-lsp(outcomes,probs) # DEoptim parameters (see ?DEoptim) np=130 # 10 * number of mktsys imax=1000 #maximum number of iterations crossover=0.6 #probability of crossover NR <- NROW(port$f)
DEctrl <- list(NP=np, itermax=imax, CR=crossover, trace=TRUE)
# Optimize f
res <- optimalf(port, control=DEctrl)
# use upper to restrict to a level that you might feel comfortable
#res <- optimalf(port, control=DEctrl, lower=rep(0,13), upper=rep(0.2,13))

# these are other possibilities but I gave up after 24 hours
#res<-maxProbProfit(port, 1e-6, 6, probDrawdown, 0.1, DD=0.2, control=DEctrl)
#res<-optimalf(port,probDrawdown,0.1,DD=0.2,horizon=6,control=DEctrl)

# Save leverage amounts as optimal f
# Examples in the book Ralph Vince Leverage Space Trading Model
# all in dollar terms which confuses me
# until I resolve I changed lev line to show optimal f output
lev<-res\$f[1:13]
levmat<-c(rep(1,wf)) %o% lev #so that we can multiply with the wfrtn
# Get the returns for the next Walk-Forward period
wfrtn <- rtn[(end+1):(end+wf)]/100
wflevrtn <- wfrtn*levmat #apply leverage to the returns
if (i==0) fullrtns<-wflevrtn else fullrtns<-rbind(fullrtns,wflevrtn)
if (i==0) levered<-levmat else levered<-rbind(levered,levmat)
}

#not super familiar with xts, but this add dates to levered from the wflevrtn xts series
levered<-xts(levered,order.by=index(fullrtns) )
chart.StackedBar(levered, cex.legend=0.6)

#just the first six in the series as another example
#I had to fill the window to my screen to avoid a error from R on margins
par(mfrow=c(6,1))
for (i in 1:6) {
chart.TimeSeries(levered[,i],xlab=NULL)
}

charts.PerformanceSummary(fullrtns, main="Performance Summary with Optimal f Applied")