R help - Nov 2017 - Do I need to transform backtest returns before using pbo (probability of backtest overfitting) package functions?

[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
>>
>> <http://www.avg.com/email-signature?utm_medium=email&
>> utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>> Virus-free.
>> www.avg.com
>> <http://www.avg.com/email-signature?utm_medium=email&
>> utm_source=link&utm_campaign=sig-email&utm_content=webmail
>>
<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>> >
>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>>
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posti
>> ng-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posti
>> ng-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
	[[alternative HTML version deleted]]

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
>>>
>>> <http://www.avg.com/email-signature?utm_medium=email&
>>>
utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>> Virus-free.
>>> www.avg.com
>>> <http://www.avg.com/email-signature?utm_medium=email&
>>> utm_source=link&utm_campaign=sig-email&utm_content=webmail
>>>
<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>> >
>>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posti
>>> ng-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>         [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more,
see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posti
>>> ng-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>>
>
	[[alternative HTML version deleted]]

Correct 

Sent from my iPhone
> On 21 Nov 2017, at 22:42, Joe O <joerodonnell at gmail.com> wrote:
> 
> 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
>>>> 
>>>> <http://www.avg.com/email-signature?utm_medium=email&
>>>>
utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>>> Virus-free.
>>>> www.avg.com
>>>> <http://www.avg.com/email-signature?utm_medium=email&
>>>>
utm_source=link&utm_campaign=sig-email&utm_content=webmail>
>>>> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>>>> 
>>>>         [[alternative HTML version deleted]]
>>>> 
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and
more, see
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible
code.
>>>> 
>>>>         [[alternative HTML version deleted]]
>>>> 
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and
more, see
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible
code.
>>> 
>> 
> 
	[[alternative HTML version deleted]]