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Mean of Ratios or Ratio of Means: statistical uncertainty applied to estimate Multiperiod Probability of Defaul

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  • Matteo Formenti

Abstract

The estimate of a Multiperiod probability of default applied to residential mortgages can be obtained using the mean of the observed default, so called the Mean of ratios estimator, or aggregating the default and the issued mortgages and computing the ratio of their sum, that is the Ratio of means. This work studies the statistical properties of the two estimators with the result that the Ratio of means has a lower statistical uncertainty. The application on a private residential mortgage portfolio leads to a lower probability of default on the overall portfolio by eleven basis points.

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  • Matteo Formenti, 2014. "Mean of Ratios or Ratio of Means: statistical uncertainty applied to estimate Multiperiod Probability of Defaul," Papers 1409.4896, arXiv.org.
    • Handle: RePEc:arx:papers:1409.4896
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    1. Larivière, Vincent & Gingras, Yves, 2011. "Averages of ratios vs. ratios of averages: An empirical analysis of four levels of aggregation," Journal of Informetrics, Elsevier, vol. 5(3), pages 392-399.
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