Intro to Quant Finance: Value at Risk (VaR)

[TheStormPulse]

Does anyone know if there is a bionic turtle video about "spectral risk measure"? - I can't find one at least

[bionicturtledotcom]

@TheStormPulse I don't think we have one, I added to our requested topics list, thanks for your interest!

[riddd9]

Hi! I also do not think this is correct. You say that VaR is z-alpha*std away from zero which you implicitly assume to be the mean. This would only be the case if you assume that the distribution is standard normal. Nevertheless, your mean is -0.71% so sth is wrong here. What about VaR=z-alpha*std - 0.0071 ?

[KoalaBearWarrior]

Bionic Turtle, you are a God among Quants.

[akathetruthteller]

dude, i don't think your VAR calculation is correct. your assuming that the distribution of the return has mean 0 then the var is simply a scaled variance.but you didn't mention anywhere that your are assuming that the access return is 0. or risk free

[bionicturtledotcom]

@akathetruthteller right, agreed but it's not incorrect so much as i should have clarified this is a relative VaR not an absolute VaR where the relative VaR ignores the drift (i.e., relative to future expected value) and the absolute VaR--to your point-- is the VaR reduced by the drift (if drift is zero, they are the same).

Please note my comment from two years ago has the terms mistakenly reversed, should be:

relative VaR = volatilty*deviate

absolute VaR = -mean + volatilty*deviate

thanks!

[samiwistler]

Like

[kumaisobele]

Very helpful indeed, thanks a lot for sharing. Just one question, what is the difference between the losses wont exceed -1.80% and the losses wont exceed say 1.80%?

[Sashaeagle]

David, thank you! Simplification of the complex things makes me understand quant finance.

Also could tell me please how to create a chart of density in Excel?

[briano8713]

The Gaussian has proven to be a terrible predictor of extreme events in this context, and other methods (like using a "power law" or a polynomial with scale invariance) have been much more accurate. What gives?

[bionicturtledotcom]

Brian, of course you are correct. The reason the normal is used (here and often) is merely to introduce VaR as the quantile of a distribution (i.e., any distribution!) ... those normal is friendliest to the new learner...once we explain how VaR is "merely a quantile" then we can deal in the various approaches, parameteric or otherwise...although re: power law & heavy-tail distributions, you still have the issue of "does any parametric distribution" *really* fit the tail? David

[prodigee411]

@briano8713 Trend Following.

[briano8713]

@prodigee411 Do you mean to say trend-following (as an approach) creates the observed fat-tailed/asymmetric distributions of returns?

[prodigee411]

@briano8713 Yes, historically, bubbles and crashes appear when the markets move several standard deviations beyond the "historical mean"(historical mean is useless, since the inputs to that mean are changing every second with new data/behavior).

[briano8713]

I am a casual student of econ/finance, and this has always perplexed me.

If the normal distribution is so clearly an false assumption for the distribution of many different types of asset returns, does mathematical expediency truly make its use necessary? Why not use (at least) a "fat-tailed", or even a skewed (asymmetrical) variant as the standard density function for financial practice, depending on the historical data?

[social90climber]

Dear Mr. Harper,

I am really a great fan of yours. I have really learned a lot from these sort of videos from you.

Please keep uploading these, I have recommended many friends of that.

Thanks n Regards,

Samran Habib

Dubai

UAE

[bionicturtledotcom]

Samran, belatedly: thank you for liking the videos! David H

[mport365]

I have question. How did you draw that normal distribution graph in the excel?

[arihant11]

Statistical functions are available in excel.

[earth1ing]

David,

Thanks for posting these videos. I'd like to point out one oversight in this illustration. When the mean is non-zero (here, it is -0.71%), you must take it into account. So in your spreadsheet, C18 should =C14+C16*C17.

Of course, the mean is commonly approximately zero and can be ignored, but in this example it's worth including.

Thanks again for posting these videos, they are useful!

Aviad

[bionicturtledotcom]

Thanks Aviad, I appreciate that.

And I agree, I am showing the so-called absolute VaR without reference to the mean; which is sort of okay for short trading (daily or less) periods. But yours (so-called relative VaR) is just better as it is the general case and treats VaR as the unexpected loss. Thanks for making this point!

David

[Arteaisgoodman]

I liked it. Very informative staff.

[bionicturtledotcom]

Hi Mahyar: History informs params but that's all: it gives us average & volatility. But then I don't use history, i.e., for normal (parameteric) distribution. I use only the smooth (but unrealistic) curve. A HISTORICAL SIM has NO params. For historical sim, you only need to SORT the historical return and look down the list to 95th-99th %ile, etc. You have a point, under most VaR approaches, historical series at least implicitly informs going-forward model. Thanks for viewing!