Risk Metric

carmensdiez · Post by **carmensdiez** » Thu Jul 25, 2019 4:09 pm

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 · Post by **nikol** » Thu Jul 25, 2019 7:06 pm

Why 360? Is it in degrees?

carmensdiez · Post by **carmensdiez** » Thu Jul 25, 2019 7:29 pm

they put 360 days in a year (rather than 252 which is the standard)

nikol · Post by **nikol** » Thu Jul 25, 2019 9:22 pm

A year is 365. Sometimes it is 366.

I like more 256 because it is all square.

carmensdiez · Post by **carmensdiez** » Thu Jul 25, 2019 10:41 pm

Thanks, but that’s not the point

nikol · Post by **nikol** » Sat Jul 27, 2019 7:50 pm

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 · Post by **carmensdiez** » Sun Jul 28, 2019 12:23 am

How do you account for correlation? Thanks for your answer, amazing

nikol · Post by **nikol** » Sun Jul 28, 2019 7:06 am

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.