Cholesky Decomposition: Take your Backtesting to the Next Level

[@lade_edal]

Great video Christian. You bang out one of these every few weeks and humanity gains.

[@dirtyquant]

Haha. Too kind.

[@AbhishekSingh-is6vo]

I'm a statistics student and it was a very interesting video. Thanks.

[@dirtyquant]

Thanks for watching mate. Tell all your classmates! :-) Let me know what else you would like to see

[@Smartskaft2]

I was looking for details about the Cholesky Decomposition for a completely different field. But this was really interesting, and something I will bring with me to _any_ application where Id like to create synthetic data with real life attributes. Cool stuff, thank you!

[@dirtyquant]

Welcome! It’s a super handy technique once you discover it. I really love it Welcome

[@saulobrendo8960]

This is so wonderful!

[@dirtyquant]

Glad you are enjoying it Saulo

[@Tyokok]

Hi one question, around 5:10, why you divide all the random data generated by 100? You didn't mention in the video. But can you please advise what's the purpose? thanks!

[@kevinalejandro3121]

I have a Big doubt about cholesky decomposition, because i have seen articles where they apply the cholesky decomposition in the covariance matrix and other articles where they apply it in the correlation matrix and i don't know really which one is correct, or both are correct. I don't know really.

[@dirtyquant]

Hi Kevin, You can still apply it to both, as correlation and covariance are very similar, with correlation a re-scaled version of covariance. Some workflows like mean-variance optimization need a covariance matrix, so sometimes you want to use that. Thanks for watching!

[@ezequiell.castano-espanol1088]

This is great! I've watched this and the copulas video, is it possible to introduce correlation by Cholesky when the different assets come from different distributions? Say for example gamma and beta like in the copula example (or more generally two continuos distributions). I know the copula approach is a way to fix it but I wanted to see if it is also possible with Cholesky

[@dirtyquant]

Good question. Give me some time to answer it. I think some transformations between different spaces are required. Top of my head I would convert your known marginals to uniforms, and the to normals, from there calculate the correlation matrix and use cholesky, and the work it backwards from the simulation, so normal to uniform to your beta/gamma. Hope that makes sense. Excellent idea for a video! Thanks for watching!

[@lade_edal]

Yeh good one I like it!

[@gvancakirvalidze2477]

Thank you, it was really informative. I do have problem with last plot, it doesn't give me an output, even tried display(widgets.VBox()). what might be the issue?

[@dirtyquant]

hmm....hard to know

[@guillermoalvarez2457]

Really useful video. If you can make one regarding Ornstein-Uhlenbeck Process would be amazing!!

[@nnamdiodozi7713]

Why use Cholesky? Doesn’t numpy have a mvnrnd function?

[@dirtyquant]

This is what numpy uses under the hood.

[@nnamdiodozi7713]

@@dirtyquant ok I enjoyed your copulas video. When using copulas to generate random realisations, when is it better to use ranked correlations rather than linear correlations. I understand that ranked correlations are preserved under various transformations while linear ones are not.

[@poisonza]

so does this mean if our algorithm passes the backtest using this simulated paths it will be profitable in the future? or what other assumption do we need more?

[@kevinshao9148]

Thanks for the great video! do you also have a video on how to use Cholesky to study the correlation of real data example? Thanks a lot!

[@gavandevirajabhinav5484]

I had a doubt, when you have two correlated stocks say X and Y, while generating the Brownian motion for X do we multiply the standard deviation of X to the cholesky-random_normal product? And btw, great video, you've earned yourself a subscriber.

[@dirtyquant]

Indeed you would need to scale each of the RVs by the correct SD and means. Thanks for subscribing!

[@gavandevirajabhinav5484]

@@dirtyquant Got it, Thanks

[@MrKhaledpage]

very usefull thanx aloot

[@dirtyquant]

Welcome mate!

[@erpangwang8398]

nice explanation, but distracting music and b-roll of keyboard.

[@abeerhamid]

True annoying background noise. I closed the video because of this

[@moganlarry1417]

you seems like showing your faces, keyboard, right?

[@dirtyquant]

Yes, I have the best face and the best keyboard.

[@jonathanl2757]

Is that just geometrically skewing the data set when you use one side of cholesky?

[@dirtyquant]

Hi Jonathan, not sure what you mean by that. The 2 sides of the Cholesky are the same, just transposed. By multiplying it by the data you add that correlation structure to them, that is all :-)

[@DanielTrivino-e9n]

Did you quit KZbin? :/

[@dirtyquant]

Hey Daniel. Yes, the fame and money got a bit too much. Could barely leave the house without some groupies wanting me to sign some part of their body, and these guys are HAIRY. I hope to be making more content soon. Thanks for reaching out. Tino