## Saturday, January 2, 2010

### LSPM Examples

I have received several requests for additional LSPM documentation over the past couple days and a couple months ago I promised an introduction to LSPM.

In this long-overdue post, I will show how to optimize a Leverage Space Portfolio with the LSPM package.  Please use the comments to let me know what you would like to see next.

Some copious notes before we get to the code:

These examples are based on revision 26 31 from r-forge and will not work under earlier revisions (and may not work with later revisions). LSPM is still in very alpha status.  Expect things to change, perhaps significantly.

These examples were run using DEoptim_1.3-3 (and LSPM revision 26 depends on that version) code from DEoptim_1.3-3 that has been bundled inside LSPM.  We are working with the DEoptim authors to address issues with more recent versions of DEoptim.  LSPM will un-bundle and use the most recent version of DEoptim as soon as the issues are resolved.

The first two examples are taken from Vince, Ralph (2009). The Leverage Space Trading Model. New York: John Wiley & Sons, Inc. The results will not match the book because of differences between optimization via DEoptim and Ralph's genetic algorithm implementation.  Ralph believes his genetic algorithm is getting hung up on a local maximum, whereas DEoptim is closer to the global solution.

library(LSPM)

# Multiple strategy example (data found on pp. 84-87)
c(-150,-45.33,-45.33,rep(13,5),rep(79.67,3),136),
c(253,-1000,rep(-64.43,3),253,253,448,rep(-64.43,3),253),
c(533,220.14,220.14,-500,533,220.14,799,220.14,-325,220.14,533,220.14) )
probs
<- c(rep(0.076923077,2),0.153846154,rep(0.076923077,9))

# Create a Leverage Space Portfolio object

# DEoptim parameters (see ?DEoptim)
# NP=30        (10 * number of strategies)
# itermax=100  (maximum number of iterations)
DEctrl
<- list(NP=30,itermax=100)

# Unconstrainted Optimal f (results on p. 87)
res
<- optimalf(port,control=DEctrl)

# Drawdown-constrained Optimal f (results on p. 137)
# Since horizon=12, this optimization will take about an hour
res
<- optimalf(port,probDrawdown,0.1,DD=0.2,horizon=12,calc.max=4,control=DEctrl)

# Ruin-constrained Optimal f
res
<- optimalf(port,probRuin,0.1,DD=0.2,horizon=4,control=DEctrl)

# Drawdown-constrained Optimal f
res
<- optimalf(port,probDrawdown,0.1,DD=0.2,horizon=4,control=DEctrl)

Chris said...

Hi Josh

I am trying to replicate the results on page 87 (as mentioned in your post above) of the LSPM book. I do the following:
> data(port)
> DEctrl <- list(NP=30, itermax=100)
> res <- optimalf(port, control=DEctrl)

The result is :

Iteration: 100 bestvalit: -1.293917 bestmemit: 1.000000 0.000000 0.857813

MktSysA 0.307
MktSysB 0
MktSysC 0.693

Joshua Ulrich said...

Hi Chris,

I mention that in the post; in the last paragraph of text before the code. In short, the optimization algorithms are different and the algorithm in my post is able to find a set of f values that produce a higher GHPR.

Josh,

I am looking to accomplish two things with your R implementation of LSPM:

1. The ability to pickup the f values from a previous search and then continue the search with those values.

2. The ability to stop a search that is in process yet retain the current f values for use.

I have managed to accomplish the former with some rather inefficient code (coding is not my strong point) yet am at a loss as to how one could accomplish the latter:

I accomplish the former by writing the f values to file at the end of a run:

write.csv(results\$f, file="OUTPUT [f].csv")

and then pick them up again prior to the next run by repopulating the initialpop with the following (here N=47):

initialpop=cbind(rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),
rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),
rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),
rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),
rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP),rep(f\$x,NP))

However would you know how I could accomplish stoping a process that is running yet retain the f values so that they could be used or the process can be restarted again at a latter time if required?

Grant

I created a more elegant solution to (1):