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

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