P1.T4.R25 Allen - Parametric VaR Autocorrelation

[Roberto Hernández]

Hi Team,

I hope you're having a great day. I was wondering if you could help me understand the below idea, on page 8 of reading 25, there's a table in which it is calculated the parametric VaR for a 1D horizon and then extended to a 10D horizon using the square root rule.

My question is, from the below table and taking into account the autocorrelation as 0, 0.2 and -0.2 respectively how those 3 rows were computed?


I believe this is not a tested concept, but I would like to understand.

Thanks a lot.
-Roberto

 

[David Harper CFA FRM]

Hi @Roberto Hernández

Thanks, I hope you are having a great day, too Here is the XLS in case you want to experiment with autocorrelated volatility/VaR https://www.dropbox.com/s/2608gzpnqj9ga69/0408-autocorrelated-var.xlsx?dl=0
The formula, and its derivation, is shown below from Carol Alexander's MRA Vol II (see starting at page 92 https://forum.bionicturtle.com/reso...ractical-financial-econometrics-volume-ii.91/ (This is where I got it, years ago I carefully studied her entire 4-book series). You will notice that, if you input her Example II.3.2. (0.05, h = 12 months, and autocorrelation ρ=0.25), you'll get her answer of 21.86%. You are of course correct that the exam won't (cannot realistically) test the computation of autocorrelated volatility/VaR, but conceptually per longstanding T4 LOs (Calculate conditional volatility with and without mean reversion. Describe the impact of mean reversion on long horizon conditional volatility estimation), the exam does expect us to know the directional impact of auto-correlated returns (which this concretely illustrates). I hope that helps, thanks!

 

[Roberto Hernández]

Hi @David Harper CFA FRM, thank you very much for this amazing response, I will definitely play around with the excel file provided and take a look into the suggested literature.

Thanks a lot and enjoy the rest of the weekend!
-Roberto