What's new

Dowd - Chapter 4 - Non-Parametric Bootstrapping

brian.field

Well-Known Member
Subscriber
Hi Friends - looking to confirm my understanding of the bootstrapping approach described in this chapter.

@David Harper CFA FRM - in your video, it looks like the example is assuming a portfolio of stocks. For instance, if there are 10 stocks and 100 days of histroical returns, we would have a 10x100 matrix of returns or 100 10x1 vectors. Then we would choose a vector at random (with replacement) to generate a larger sample.

I assume this also applies to a single asset or to the averages of the assets in David's example.

For instance, assume we take the weighted average return or portfolio return for each day in David's example. This is equivalent to having one stock rather than a portfolio of stocks. Then we would have a 1x100 matrix or 100 returns.

Can we apply the bootstrap by simply picking one of the returns (with replacement) to generate larger samples?

Thanks!
 

brian.field

Well-Known Member
Subscriber
The whole point of bootstrapping is to create a larger "sample" with which to work.....so yes, larger sample size.
 

brian.field

Well-Known Member
Subscriber
It seems to me that we should be able to choose portfolio returns from row 7 at random rather than selecting return vectors at random......my point is that they should be equivalent but the lecture doesn't specifically say this....essentially, we are collapsing a portfolio of 10 assets into a portfolio of 1 asset and then bootstrapping on the returns of the single asset. So, bootstrapping from the returns in green rather than from the vectors in blue (equivalently).


\upload_2016-2-23_14-13-25.png
 

ami44

Well-Known Member
Subscriber
Hi Brian,

you can use bootstrapping with a sample of random vectors or just a sample of random numbers. It doesn't matter.

Your row 7 would be a sample of random numbers. E.g. You can calculate the standard derivative of that sample and use Bootstrapping to estimate the quality of that estimated standard derivative.

Bootstrapping is a general tool to estimate the properties of sample statistics. If your samples are iid you can use it, apart from that it does not matter how you got your sample.
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @Tania Pereira Here is my simple bootstrap illustrator (I don't have it updated yet, but eventually I will include a version in an learning XLS for Brooks Ch 13 Simulation (P1.T2). I hope this is helpful, it color codes the four steps
https://www.dropbox.com/s/4vu6hspdp4t6657/0923-bootstrap.xlsx?dl=0

 
Top