Question

I am trying to see how “winning percentage” affects returns for a trading strategy.

I download the prices of S&P and calculating the daily returns. Then, I randomly select x% of these returns and say I correctly predicted it’s direction so the return is positive. For the remainder 1-x%, I say I am wrong and the return is negative. I replicate this process say 1000 times and collect the annualised geometric return.

I vary x from 0.5 to 0.6 at 0.01 increment intervals.

Here is my code:

library(quantmod)
library(multicore)

getSymbols("^GSPC", from = "1950-1-1")
ret <- ROC(GSPC)[-1,4]

set.seed(123)

winpct <- seq(0.5, 0.6, 0.01)
ret <- coredata(ret)

system.time(res <- simplify2array(mclapply(winpct, function(x) replicate(1000, drawsample(ret, x)))))

drawsample <- function(ret, winpct){
  len = length(ret)
  ret = abs(ret)

  win = sample(1:len, round(winpct * len))
  a = c(ret[win], -ret[-win])
  return(prod(1 + a) ^ (252 / length(a)) - 1)
}

Time taken:

   user  system elapsed 
 18.904   0.842   5.580 

Are there any further optimisations I can do to speed things up?

Answer 1

I made the following two tweaks:

1/ use exp(sum(a)) rather than prod(1+a). I think you want this anyways, as you have created a log returns series with ROC(GSPC)[-1,6]. According to rbenchmark this got me a speedup of about 7%.

2/ sample from c(-1,-1) for the length of the ret series, and then multiply with the ret series, to obtain the signed series of returns. This got me another 30%.

Note that in my code, i’ve re-named your a as bin.

drawsample2 <- function(ret, winpct){
  len = length(ret)
  win = sample(c(-1,1), len, replace=TRUE, prob = c((1-winpct), winpct))
  ret <- abs(ret)
  bin <- ret*win
  return(exp(sum(bin))^(252/length(ret)) - 1)
}

Benchmarking against your drawsample() i get ~37% speedup.

bb <- benchmark(simplify2array(mclapply(winpct, function(x) replicate(1000, drawsample(ret, x)))), 
          simplify2array(mclapply(winpct, function(x) replicate(1000, drawsample2(ret, x)))),
          columns =c('test', 'elapsed', 'relative'),
          replications = 10,
          order = 'elapsed')

On my MBP, here are the benchmarks:

> bb

  elapsed relative
2  17.254    1.000
1  27.734    1.607