Historical simulation (HS VaR): Basic and age-weighted (FRM T4-2)

[here is my xls trtl.bz/2BmVoxW] Basic historical simulation value at risk (HS VaR) sorts the returns in the window and locates the return ranked (1-confidence)%*K+1. Age-weighted HS assigns greater weight to more recent returns.
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[@pb5721]

Very good explanation and so easy to understand 👍 thank you, sir.

[@bionicturtle]

You're welcome! Thank you for watching!

[@joshdundundun1154]

Well Explained. Thank You for the video

[@bionicturtle]

You're welcome! Thank you for watching!

[@alexandretaffet7019]

Thank you !

[@joseluissanchez4276]

muy bueno el video, gracias.

[@bionicturtle]

Thank you for watching!

[@investwithvincent6329]

What's the formula used for the mass centered weights column?

[@investwithvincent6329]

What's confusing here @10:00 is the reason for selecting 2.9 & 2.7%. Clearly, 3.3% is greater than 2.7%. Even when reviewing the results in the hybrid section, we observe that the weights are both the highest and lowest values that we could see. What's the reason for picking that combination of weights instead of the two largest weights? Lastly, how come results from 1 period ago are missing? I feel like that would be the largest exponentially weighted average because it is the period closest to the current moment.

[@bionicturtle]

Sounds like your missing the first step and the whole structure of exercisxe. Among K = 100 returns, this is showing only the tail: the worst six returns -3.30%, -2.90%, -2.70%, -2.50%, -2.40%, -2.30%. Yesterday's (i.e., the 1 period ago) return is "missing" because, in this simulation, it simply wasn't among the worst six returns (out of 100), it was somewhere among the other 94. The complete series is 100 rows, not just these six worst. Then the weight assigned is a function of the its recency: the worst return of -3.30% would earn a a weight of (1-λ)*λ^(3 - 1) = 1.92% if the window were infinite, but for K = 100, its weight is (1-λ)*λ^(3 - 1)/( 1-λ^100) = 2.21%. The sort is based on return, but each return's weight is sized by its recency; e.g., the third worst return of -2.70% was 65 days ago, so only earns a 0.63% weight. The reason for selecting (-)2.90% and (-)2.70% is that, by arbitrary selection, we are seeking the 95.0% VaR so we want to identify (cumulatively) the 0.050 quantile and their cumulative weights, respectively, are 4.47% and 5.11%. There is an XLS for further inspection, b/c I didn't even get to the final step of identifying the exact 0.050 quantile. Hope that's helpful,

[@investwithvincent6329]

​@@bionicturtle Ok... I'm back... I understand why we were looking at those two values mentioned. from my observation, the way we are going about making this decision has to do with the cumulative. The cumulative value of 5% (95% VaR) changes from the stationary method and the ewma method. Our goal is to select the observation that is greater than 5% in this case. The basic approach assigned a weight of 1 to each value, so we simply selected observation n+1. This equaled 6%. The hybrid approach assigned a exponentially weighted moving average to each weight, so we have to find the observation where the cumulative weights is the minimum value that's greater than 5%

[@bionicturtle]

@@investwithvincent6329 Yes, correct. VaR is (simply) the quantile of the probability distribution so that a 95.0% VaR is the location of the 0.050 quantile (which by definition is cumulative). In the age-weighted (aka, hybrid) approach, that 5.0% quantile is unequivocally at ("within" if you like) the third-worst loss. When n = 100, it is actually the basic HS that is equivocal because it falls right "in between " the 5th and 6th worst, hence although the "FRM correct" choice is the 6th worst, it is also okay to select the 5th worst or an interpolation between the 5th and 6th. But just to illustrate, when n = 100 the basic HS for 95.1% would be unequivocally the 6th worst and the 95.9% would be unequivocally the 5th worst. It's an issue of the quantile when the distribution is discrete.

[@estudoseprojetos9636]

Sensacional

[@bionicturtle]

Thank you!

[@gianninidario]

❤