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Through the Cycle – PD Scalar March 16, 2007

Posted by riskopedia in Basel II, Economy, PD, Regulator, Retail Risk, Risk Management, scorecard.
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For Basel modellers, a common problem is a relatively short period of data. In most firms, they might not even able to get up to 5 years worth of data. Hence, the PD models would normally reflecting a Point in time (PIT) estimate or a Short run cycle (SRC) estimate.

Now, its nothing wrong having a PIT estimate. It is really up to the Bank’s senior management to decide if they want:

  • Estimate a default risk over a fix period, which is a PIT approach.
    • PROS
      •  Less regulatory capital requirement during good time, in comparison to TTC
    • CONS
      • Capital is more volatile
      • Capital is more senstive to economy
      • More regulatory capital requirement during a bad time, in comparison to TTC
  • Take the volatility effect out of the estimation, which is Through the Cycle (TTC)  approach
    • PROS
      • Less volatile
      • Less sensitivity to economy
      • Less regulatory capital during bad time
    • CONS
      • Hold more capital during good time

The graph below illustrated the point:

ttc-vs-pit.JPG

From the regular and firm’s point of view, they would a stable regulatory capital position. However, it is hard to achieve when having such a limited period of data. Hence, there is a proposed approach that transform the PIT PD estimate into a TTC PD estimate.

To illustrate the idea, a common approach is to apply a TTC scalar to the PIT PD estimate. This is usually a one off exercise (since you should capture the data going forward).

Using the above graph as an example:

  • Let say you can model PIT estimate at portfolio level between time 15 – 17. The portfolio PIT estimate is around 0.35% (for argument sake).
  • Then, you either do a econometric type model or using external data, you can map out the TTC estimate is around 1.25%.
  • Hence, the TTC scalar = 1.25% / 0.35% = 3.57. Then, you apply this scalar to the segment PIT PD.

Another way of coverting a PIT PD estimate to TTC estimate via the score in scorecard.  Often a scorecard follows a set of parameters, e.g. Good Bad Odd 20:1 at score of 600,  points double odd (PDO)  is 50. Then, as long as there is a scorecard calibration from time-to-time, the PIT estimate should be a proxy of TTC estimate.

Here are couple of key points from my view on the Scalar approach:

  1. Somehow I think the industry missed two key points
    1. Once a scalar is done and convert PIT into TTC. In theory, there is no more adjustment on the estimate going forward. Unless, during the on-going monitoring, the current TTC estimate is proven to be significantly different from the one you have previously. But, if you pick between the line, you probably wouldn’t able to prove that until the next cycle.
    2. Even you have applied a TTC estimate in hoping to achieve stable capital. But, during different economic environment, the homogenous pool distribution will change. E.g. a shift to “bad” homogeneous pool during downturn. Hence, no matter how stable the TTC estimate, the capital will still fluctuate due to the shift of portfolio pool distribution. (In saying that, TTC does take away a certain degree of volatity).
  2. The TTC conversion is based on the “past”, not predicting the “future”.  Especially with the change in credit use in the last 15  years or so (look at the increase of sub-prime lenders and use of credit cards in comparison to the past). As stated a concerning pt in #15(a) and #18 by FSA. So, firm should of try to “predict” the portoflio risk profile going forward instead of looking back into the past.
  3. But regardless of the above, a scalar would at least give a degree of conservatism in the immediate period and the converted TTC estimate can be acted as a bench mark. But firms would still need to adjust the estimate in the future.
  4. Firms should start looking forward then stay in the past, when, risk management framework, risk profiles, operation, market strategy etc. have changed significantly. (Who has online application back in early 90s?)

This approach has been proposed to FSA, the following link is their response

http://www.fsa.gov.uk/pubs/international/crsg_procyclicality3.pdf

I think I will let this to be an open debate. You can read it and form your own opinion. Welcome any comments from you guys.

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Comments»

1. Paul Hodges - July 4, 2007

“Then, as long as there is a scorecard calibration from time-to-time, the PIT estimate should be a proxy of TTC estimate.”

Hi
Isn’t it the other way around? It would be a PIT estimate?

2. BHC - February 14, 2008

Now, I thot that Basel 2 is to ensure that the regulatory capital estimate is risk-sensitive. If the model is a TTC model, very likely the capital estimate would be flat over time also.

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