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carmensdiez


Total Posts: 5
Joined: Jun 2019
 
Posted: 2019-07-25 16:09
In my department we calculate a risk metric R and the process is the following:

•We divide the company portfolio into maturity buckets

•We calculate the Gap (asset-liab) for each bucket

•We multiply each GaP for the RISKFACTOR

RISK FACTOR=((1/ (1+Zero rate i) ^ (Average term i)/360) – (1/(1+Zero rate i + s) ^ (Average term i /360)))

•We sum the results for each bucket and that’s our R calculation.

To calculate the RISK FACTOR we are using an annualized Zero rate but a daily volatility (s), is this making any sense?? Shouldn’t be annualized the volatility?

any help?

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-07-25 19:06
Why 360? Is it in degrees?

carmensdiez


Total Posts: 5
Joined: Jun 2019
 
Posted: 2019-07-25 19:29
they put 360 days in a year (rather than 252 which is the standard)

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-07-25 21:22
A year is 365. Sometimes it is 366.
I like more 256 because it is all square.

carmensdiez


Total Posts: 5
Joined: Jun 2019
 
Posted: 2019-07-25 22:41
Thanks, but that’s not the point

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-07-27 19:50
You can try to solve this problem yourself. I will give you a guidance.

Your formula is doing the following:
- Asset-Liability Gaps is exposure, which is driven by cash flow mismatch, dCF_i (you call it gap)
- dCF_i is source of your PnL, which is PnL = Sum_i dCF_i
- It is vulnerable to the Present Value (PV) of your cash, or discounted cash: PV(dCF_i) = discount(ZeroRate_i, dT). Discount(x, dT) = 1/(1+x)^(dT/dcc), where dcc is day-count-convention (360, 365, or A - you should know the reason why you choose one).

It looks like your formula measures sensitivity with respect to daily movement of ZeroRate_i. Daily movement is proxied with volatility (s). Ask yourself, why daily? Are you able to exit from project in one day? No? How long does it take to get out? May be month? or two? Define it as risk horizon.

If risk horizon is not standard for all projects in portfolio, then you have to take this feature into account by modelling:
vol ~ s*sqrt(horizon)*Z(CL),
where Z(CL) is a number of standard deviations if you require confidence level, CL, e.g. Z(CL=84%)=1 or Z(CL=98%)=2 assuming Normal distribution).

From the assumptions I mention (CL, horizon, Normal, dcc etc) or adding your own you can cook up the model as complex as possible.

By the way, dont forget that your end number is also sensitive to bucket grid schema you choose. Also, I recommend to account for correlation corr(ZeroRate_i, ZeroRate_j)

carmensdiez


Total Posts: 5
Joined: Jun 2019
 
Posted: 2019-07-28 00:23
How do you account for correlation? Thanks for your answer, amazing

nikol


Total Posts: 850
Joined: Jun 2005
 
Posted: 2019-07-28 07:06
use dispersion formula.

PS. perhaps, I answered in too extended way by giving description closest to capital type of measure. In fact you formula is a 1-day sensitivity. Cross-term sensitivity (~correlation) is missing though.

If you still want to calc the capital and want to involve variable horizon feature, then you naturally come to the credit counterparty modelling, where probability of default of the project should be involved and that becomes even more complicated.
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