Hi
@amresh If I can work your queries last in first out (LIFO), your 3rd question is easiest. From Dowd:
Dowd (page 94, emphasis mine): "Finally, we can also modify age-weighting in a way that makes our risk estimates more efficient and effectively eliminates any remaining ghost effects.
Since age-weighting allows the impact of past extreme events to decline as past events recede in time, it gives us the option of letting our sample size grow over time. (Why can’t we do this under equal-weighted HS? Because we would be stuck with ancient observations whose information content was assumed never to date.) Age-weighting allows us to let our sample period grow with each new observation, so we never throw potentially valuable information away. This would improve efficiency and
eliminate ghost effects, because there would no longer be any ‘jumps’ in our sample resulting from old observations being thrown away.
However,
age-weighting also reduces the effective sample size, other things being equal, and a sequence of major profits or losses can produce major distortions in its implied risk profile. In addition, Pritsker shows that even with age-weighting, VaR estimates can still be insufficiently responsive to changes in underlying risk. Furthermore, there is the disturbing point that the BRW approach is ad hoc, and that except for the special case where λ=1, we cannot point to any asset-return process for which the BRW approach is theoretically correct."
It does appear to contradict, but I think the keys are (1) ghost-effect and (2) his term "effective." Say lambda is 0.92.
- The reduction of effective sample size refers to how, really, only the most recent returns are used. If λ = 0.92, then notice that the most recent ten observations constitute over half of the total weight (56.56%) and the most recent twenty constitute over 80% (81.13%). This is the meaning of reducing the effective sample size.
- This "reduction" is actually consistent with the first statement which is the alleviation of the dreaded ghosting effect; i.e., where under a simple HS, an outlier has equal weight for its entire participation in the the window, but then drops off abruptly. Here in age-weighted, the weights are getting small in the distant tail (they are not much informing the "effective" sample) so they feather out softly rather than ghost in and out abruptly.
Stay connected