[R] Do I need to transform backtest returns before using pbo (probability of backtest overfitting) package functions?

[Eric Berger]

Hi Joe,
The centering and re-scaling is done for the purposes of his example, and
also to be consistent with his definition of the sharpe function.
In particular, note that the sharpe function has the rf (riskfree)
parameter with a default value of .03/252 i.e. an ANNUAL 3% rate converted
to a DAILY rate, expressed in decimal.
That means that the other argument to this function, x, should be DAILY
returns, expressed in decimal.

Suppose he wanted to create random data from a distribution of returns with
ANNUAL mean MU_A and ANNUAL std deviation SIGMA_A, both stated in decimal.
The equivalent DAILY

Then he does two steps: (1) generate a matrix of random values from the
N(0,1) distribution. (2) convert them to DAILY
After initializing the matrix with random values (from N(0,1)), he now
wants to create a series of DAILY
sr_base <- 0
mu_base <- sr_base/(252.0)
sigma_base <- 1.00/(252.0)**0.5
for ( i in 1:n ) {
  m[,i] = m[,i] * sigma_base / sd(m[,i]) # re-scale
  m[,i] = m[,i] + mu_base - mean(m[,i]) # re-center}

On Tue, Nov 21, 2017 at 2:10 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:

> Wrong list.
>
> Post on r-sig-finance instead.
>
> Cheers,
> Bert
>
>
>
> On Nov 20, 2017 11:25 PM, "Joe O" <joerodonnell at gmail.com> wrote:
>
> Hello,
>
> I'm trying to understand how to use the pbo package by looking at a
> vignette. I'm curious about a part of the vignette that creates simulated
> returns data. The package author transforms his simulated returns in a way
> that I'm unfamiliar with, and that I haven't been able to find an
> explanation for after searching around. I'm curious if I need to replicate
> the transformation with real returns. For context, here is the vignette
> (cleaned up a bit to make it reproducible):
>
> (Full vignette:
> https://cran.r-project.org/web/packages/pbo/vignettes/pbo.html)
>
> library(pbo)
> #First, we assemble the trials into an NxT matrix where each column
> #represents a trial and each trial has the same length T. This example
> #is random data so the backtest should be overfit.`
>
> set.seed(765)
> n <- 100
> t <- 2400
> m <- data.frame(matrix(rnorm(n*t),nrow=t,ncol=n,
>                        dimnames=list(1:t,1:n)), check.names=FALSE)
>
> sr_base <- 0
> mu_base <- sr_base/(252.0)
> sigma_base <- 1.00/(252.0)**0.5
> for ( i in 1:n ) {
>   m[,i] = m[,i] * sigma_base / sd(m[,i]) # re-scale
>   m[,i] = m[,i] + mu_base - mean(m[,i]) # re-center}
> #We can use any performance evaluation function that can work with the
> #reassembled sub-matrices during the cross validation iterations.
> #Following the original paper we can use the Sharpe ratio as
>
> sharpe <- function(x,rf=0.03/252) {
>   sr <- apply(x,2,function(col) {
>     er = col - rf
>     return(mean(er)/sd(er))
>   })
>   return(sr)}
> #Now that we have the trials matrix we can pass it to the pbo function
>  #for analysis.
>
> my_pbo <- pbo(m,s=8,f=sharpe,threshold=0)
>
> summary(my_pbo)
>
> Here's the portion i'm curious about:
>
> sr_base <- 0
> mu_base <- sr_base/(252.0)
> sigma_base <- 1.00/(252.0)**0.5
> for ( i in 1:n ) {
>   m[,i] = m[,i] * sigma_base / sd(m[,i]) # re-scale
>   m[,i] = m[,i] + mu_base - mean(m[,i]) # re-center}
>
> Why is the data transformed within the for loop, and does this kind of
> re-scaling and re-centering need to be done with real returns? Or is this
> just something the author is doing to make his simulated returns look more
> like the real thing?
>
> Googling around turned up some articles regarding scaling volatility to the
> square root of time, but the scaling in the code here doesn't look quite
> like what I've seen. Re-scalings I've seen involve multiplying some short
> term (i.e. daily) measure of volatility by the root of time, but this isn't
> quite that. Also, the documentation for the package doesn't include this
> chunk of re-scaling and re-centering code. Documentation: https://cran.r-
> project.org/web/packages/pbo/pbo.pdf
>
> So:
>
>    -
>
>    Why is the data transformed in this way/what is result of this
>    transformation?
>    -
>
>    Is it only necessary for this simulated data, or do I need to
>    similarly transform real returns?
>
> I read in the posting guide that stats questions are acceptable given
> certain conditions, I hope this counts. Thanks for reading,
>
> -Joe
>
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