How to translate volatility over time; i.e., scale volatility per the square root rule (FRM T1-3)

We typically scale volatility with the square root rule, but keep in mind the key assumption (i.i.d. returns). I APOLOGIZE that the bottom-right corner is obstructed by my web camera. It contains Expected return = +10.0% such that the Absolute VaR = -10%*10/250 + 2.326*20%*sqrt(10/250); i.e., the drift scales linearly. [Here is the XLS I used if you are interested: trtl.bz/2wJaJEf]
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[@rohitjoshi637]

Hi David great explanation as usual . Just want to clarify that in case of time varying volatility iid will hold or not ( IMO not hold ) and to tackle it can we apply EWMA approach ? Thanks and regards

[@bionicturtle]

Thanks Rohit! Yes, you are correct, great point!. I wish I would have mentioned the implicit assumption here that volatility is constant. The square root rule assumes (requires) i.i.d. returns; but the assumption of i.i.d. returns also does imply constant volatility. As technically EWMA also assumes i.i.d. returns, I do not consider it a time-varying volatility model (the estimates change due to a generalization of the same weighting model used for constant standard deviation; e.g., EWMA can make no other forecast aside from flat). To model "time-varying volatility" easily the most popular approach is GARCH(1,1) which, in its basic flavor, actually assumed uncorrelated returns but not identical returns (hence, it does not assume i.i.d). Thanks!

[@rohitjoshi637]

Thanks David. You're the Best !

[@Mike-cp1tj]

lower left formula, shouldn't right hand side be squared (variance) as well?

[@bionicturtle]

Yes, indeed! It's my typo, should be: σ^2(T) = (ΔT/Δt)σ^2(Δt). Thank you!

[@arnaldolc]

Great video, David. Thanks. One question: I thought if we took 2 SD that would give me 95% confidence level. However, you used 1.645. What am I missing ? Thank you.

[@bionicturtle]

Thank you! You are correct that a two-tailed 95% confidence region occupies +/- 1.96 σ, which corresponds to 2.5% in each tail. Value at Risk (VaR) however is ALWAYS one-tailed: it is a risk measure of the loss potential only. So a 95% confidence level is implicitly (always) one-tailed such that the associated quantile is given by =NORM.S.INV(95%) = 1.645 or 1.65. Interestingly, it's okay to round to 1.65 b/c risk measurement is not valuation. While valuation seeks to be precise, in risk we always know we are approximating. Thanks!

[@arnaldolc]

Thanks David. You are absolutelly right. I completly overlooked the fact that it is indeed one-tailed...Cheers.

[@ashayvaradkar6227]

Really helpful vdeos. Thanks a lot David!

[@bionicturtle]

Thank you Ashay!

[@kmarcucci23]

It would be nice to see the Expected return, per annum and absolute T-day VaR, % but your picture is covering these pieces of information Please move your picture so it can be viewed on how to do the calculations for these numbers. Please HIDE YOUR picture in the bottom right-hand corner of the video. Thank you.

[@bionicturtle]

I didn't mean to do that (have the picture coverup the final calculations), but they are easily inferred

[@lesterwong5032]

i’d say it’s going to be 9.305%-(10/250)*10% = 0.4%. Put a negative to the value, the absolute Tday VaR would be -0.4% + 9.305% = 8.905%. It’s slight lower because it counted in the potential profit into it. Correct me if I’m wrong.