Age-weighted historical simulation

[afterworkguinness]

Hi David,
Dowd says that large losses receive a higher weight under age weighted HSIM than under the equally weighted HSIM. I don't understand why this is, my understanding from the notes and Google is there is no special treatment for large losses just each day that passes gets a lower weight.

Thanks in advance.

 

[IRENA BLAZINCIC]

Hi David,
Dowd says that large losses receive a higher weight under age weighted HSIM than under the equally weighted HSIM. I don't understand why this is, my understanding from the notes and Google is there is no special treatment for large losses just each day that passes gets a lower weight.

Thanks in advance.

Hi,
I agree there is no special treatment of large losses
But, If we observe large loss event that today, it will receive a higher weight in next day VaR calculation than under equally weighted HS.
It means that age-weighted HS is more responsive to large loss observations, than equally weighted HS.

 

[afterworkguinness]

Thanks @irenab

 

[David Harper CFA FRM]

I agree with @irenab . Dowd's text below. In isolation, it does read "a large loss event will receive a higher weight than under traditional HS" but he's referring to the volatility from the realistic perspective of updating the estimate as time marches forward. It's easy to forget that it's an estimate that gets updated each day! So, when does any loss enter the sample? On the most recent day, which under age-weighed approach, gets the highest weight. A similar perspective informs his third advantage concerning the "ghosting effect:" as the data sample is a window that rolls forward, any loss enters with a heavy weight and leaves not with a bang but a whimper:

Dowd: 4.4.1 Age-weighted Historical Simulation: Second, a suitable choice of λ can make the VaR (or ES) estimates more responsive to large loss observations: a large loss event will receive a higher weight than under traditional HS, and the resulting next-day VaR would be higher than it would otherwise have been. This not only means that age-weighted VaR estimates are more responsive to large losses, but also makes them better at handling clusters of large losses. Third, age-weighting helps to reduce distortions caused by events that are unlikely to recur, and helps to reduce ghost effects. As an observation ages, its probability weight gradually falls and its influence diminishes gradually over time.

 

[afterworkguinness]

Hi David,
So you mean by "more responsive to large loss observations" he's referring to both the overcoming of the ghosting effect and the better weighting scheme ?

 

[David Harper CFA FRM]

Hi @afterworkguinness

When he writes "a large loss event will receive a higher weight than under traditional HS, and the resulting next-day VaR would be higher than it would otherwise have been," I think he is just referring to when the large loss initially enters the historical data sample (which is where it would enter!). The ghosting effect is related because it is addressed by the same age-weighting but I think it's a different point:

• A large loss initially "appears" as yesterday's (the most recent) negative return. Under simple HS, it's weight is 1/n where n is the number of days; Under age-weighting, it is significantly higher, is the point of "a large loss event will receive a higher weight than under traditional HS"
• Then go forward n-1 days in time. Under HS, this large loss still has a weight of 1/n; for example, it may be the worst loss every single day, between t(0) and t(0)+n-1. And, under HS, the ghosting effect refers to how it goes from this 1/n weight to being entirely dropped out the subsequent day. But under age-weighted, as time goes form t(0) to t(0)+n-1, the weight of this large loss is gradually declining. On its "final day" inside the window, it has barely any weight, and then the next day it drops (or under an infinite series, it "never" drops). But, either way, it "fades out" rather than dropping abruptly from 1/n to zero. This is the meaning of "but also makes them better at handling clusters of large losses."

So, while simple HS weights all returns equally (1/n), age-weighting both gives greater weight to recent returns ("more responsive"), and at the same time by definition, lesser weight to distant returns ("reduce ghosting effect"). I hope that helps,

 

[afterworkguinness]

Hi @afterworkguinness

When he writes "a large loss event will receive a higher weight than under traditional HS, and the resulting next-day VaR would be higher than it would otherwise have been," I think he is just referring to when the large loss initially enters the historical data sample (which is where it would enter!). The ghosting effect is related because it is addressed by the same age-weighting but I think it's a different point:

• A large loss initially "appears" as yesterday's (the most recent) negative return. Under simple HS, it's weight is 1/n where n is the number of days; Under age-weighting, it is significantly higher, is the point of "a large loss event will receive a higher weight than under traditional HS"
• Then go forward n-1 days in time. Under HS, this large loss still has a weight of 1/n; for example, it may be the worst loss every single day, between t(0) and t(0)+n-1. And, under HS, the ghosting effect refers to how it goes from this 1/n weight to being entirely dropped out the subsequent day. But under age-weighted, as time goes form t(0) to t(0)+n-1, the weight of this large loss is gradually declining. On its "final day" inside the window, it has barely any weight, and then the next day it drops (or under an infinite series, it "never" drops). But, either way, it "fades out" rather than dropping abruptly from 1/n to zero. This is the meaning of "but also makes them better at handling clusters of large losses."

So, while simple HS weights all returns equally (1/n), age-weighting both gives greater weight to recent returns ("more responsive"), and at the same time by definition, lesser weight to distant returns ("reduce ghosting effect"). I hope that helps,

Thanks for the detailed reply, much appreciated.