Video 2c, auto-correlation and VAR

[[email protected]]

Hi David.

It's around 24 min mark, and slide number shown is 39.

You showed that 10 day sigma and Var is greater with auto-correlation. However I think that would be the case if we were given 1 day variance, in the case we are given 1 year variance, the 10 day sigma and VAR should be smaller due to auto correlation.

Because auto correlation would make long run variance greater, and in this case, when the long run (1 year)variance is known, the short term variance(10) would be smaller under auto-correlation than under iid.

Maybe I am wrong, please help, thanks.

 

[David Harper CFA FRM]

Chugagc,

Really excellent point: I agree in regard to your concept. In this case (just to use vol instead), annual volatility is 15%. If we "scale down," then auto-correlated returns imply a 1 -day volatility of less than 15%. In this respect, I absolutely agree with you.

For reference here is the same spreadsheet: http://www.bionicturtle.com/how-to/spreadsheet/4.a.1_two_asset_var_relative_vs_absolute/

In this case, what I really did was:
1. I scaled the annual down to 10-day, to compute the 10-day i.i.d. VaR
2. Then I used the autocorrelation adjustment (as a factor) which really operates implicitly from a 1-day baseline; it uses the 10 to effectively adjust a 10-day i.i.d VaR into a 10-day autocorrelated VaR. I may need to improve the presentation (I had not frankly considered your interpretation), but the A/R never really "exits" the 10-day horizon in the XLS, it does not scale up/down..
… hence the increase
… in this way, I suppose, if we scaled back up, the annual autocorrelated VaR would be greater than 15%
… in this way, the 10-day A/R VaR is not consistent with the one-year VaR (which agrees with your point) but rather operated directly from the 10-day i.i.d. VaR

David

 

[[email protected]]

Thanks for the reply

After thinking about it for some times, I think it make sense. Do you think there will be question on exam where you can assume different things or they will be more clear cut?

 

[David Harper CFA FRM]

This is good example of operating one notch deeper than the exam questions. The exam is highly unlikely to get into the subtlety of scale up/scale down. Much more likely is a question that requires you to know scaling per square root rule assumes i.i.d. and, if autocorrelated, you will get a different answer.
(applying the square root rule is something you can expect to get quizzed on)

So, in the case, the exam is one notch more superficial generally:
* be able to scale per SRR (assume i.i.d.) from (eg) 1 day to 10 days
* Know that autocorrelation violates and gives different answer

David