[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 21:42:24 CET 2017
Hi Eric,
Thank you, that helps a lot. If I'm understanding correctly, if I’m wanting
to use actual returns from backtests rather than simulated returns, I would
need to make sure my risk-adjusted return measure, sharpe ratio in this
case, matches up in scale with my returns (i.e. daily returns with daily
sharpe, monthly with monthly, etc). And I wouldn’t need to transform
returns like the simulated returns are in the vignette, as the real returns
are going to have whatever properties they have (meaning they will have
whatever average and std dev they happen to have). Is that correct?
Thanks, -Joe
On Tue, Nov 21, 2017 at 5:36 AM, Eric Berger <ericjberger at gmail.com> wrote:
> [re-sending - previous email went out by accident before complete]
> 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 returns would have mean MU_D = MU_A / 252 and
> standard deviation SIGMA_D = SIGMA_A/SQRT(252).
>
> He calls MU_D by the name mu_base and SIGMA_D by the name sigma_base.
>
> His loop now converts the random numbers in his matrix so that each column
> has mean MU_D and std deviation SIGMA_D.
>
> HTH,
> Eric
>
>
>
> On Tue, Nov 21, 2017 at 2:33 PM, Eric Berger <ericjberger at gmail.com>
> wrote:
>
>> 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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>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
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>>
>>
>
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