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What is the best way of measuring default rates for a portfolio which contains mostly loans which are either 30, 60 or 90 days term?

Normally I use the following methodology

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Look at all loans which are in the portfolio on a specific date. Any loan which does not default within the next 12 months is a Good loan irrespective if the loan ends within those 12 months or not. Any loan which defaults within those 12 months is a Bad loan. Loans which start within the 12 months are disregarded.

What is the best way of doing this?

  • Keep everything the same way
  • Scale down from 12 months to 90 days and multiply resulting default rate by 4.
  • Other suggestions?
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    $\begingroup$ A simple approximation would be to downscale the PD as $1-(1-PD(0,T))^{t/T}$. $\endgroup$ Jul 26, 2021 at 19:40
  • $\begingroup$ I would change the observation period to 3 months and then use the formula to upscale to 12 months (12 months is what i need for reporting and regulatory purposes). Makes sense. $\endgroup$
    – PalimPalim
    Jul 28, 2021 at 6:22
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    $\begingroup$ Yes, that could work as well. Effectively, if your PDs are quite small, you'll see that the annualized PD is of course roughly $PD(0,1) \approx 4 \times PD(0,0.25)$. $\endgroup$ Jul 28, 2021 at 9:20

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