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.

    # Load the LSPM package
    library(LSPM)

    # Multiple strategy example (data found on pp. 84-87)
    trades <- cbind(
     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
    port <- lsp(trades,probs)

    # 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)

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