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

Joe O joerodonnell at gmail.com
Tue Nov 21 07:02:04 CET 2017

```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