Suspected Mistake in Level I Annotated Boot Camp

[Liming]

Dear David,
I’ve had some confusion, misunderstanding and doubts when doing 09 Level I Annotated Boot Camp. Appreciate your kind help on this!

Autocorrelation in scaling of Volatility: You mentioned on page 25 question 20 “Level1 Annotated boot camp” that if returns are positively auto correlated, the implied daily volatility will be less than what it would be without the autocorrelation. I’m quite confused over your statements because it seems to be very different from the FRM handbook 5ed, page 70, where the formula for two-day variance is: V(r2) = V(r1) + V(r1) + 2 ρ V(r1) = 2V(r1)(1+ρ) . I think it logically follows that hen ρ is positive, V(r2) should > 2V(r1) AND therefore S(r2) is larger than S(r1)* 2^1/2, not smaller.

Thank you for your enlightenment and correction!
Cheers
Liming
16/11/09

 

[notjusttp]

David,

I carry the same confusion as in your excel sheet 4.a.1 you have specifically mentioned the undermentioned words in your comments to scaling factor.

" don't worry about this formula, the point is that autocorrelation increases the VaR "

Pls clarify

Thanks & Best Rgds
Amit

 

[David Harper CFA FRM]

Liming & Amit,

But we are scaling down, not up. See Jack's fine take: http://forum.bionicturtle.com/viewreply/4627/
(I added this question b/c this is the sort of question the FRM asks; i.e., trip you up if you are too literal)

Liming, your formula is fine. if we use the SRR to scale annual vol of 30% over three years, then, indeed, positive autocorrelation implies 3-year vol > 30%*SQRT(3)
but by the same exact logic, if we scale down, daily vol (with +AR) < 30%*SQRT(1/252).
as i write in the solution e.g., if autocorrelation = 0.25, implied daily vol = 1.47% because:
1.47% * SQRT(252) = 23.3% but the positive A/R gives a *higher* 30%

David