Excluding AY for ECR calculation
In some problems from past exams, when calculating the ECR, we are expected to exclude the year we would like to calculate ultimate for from the ECR calculation.
For example, if we want to calculate 2025 ultimate using ECR, we should take the simple average of claim ratios for AY 2022-2024.
Why should we exclude AY 2025 from the calculation of the ECR?
As an extension, how come we can include AY 2025 in calculating the ECR using Cape Cod method? The examples I see for CC method will take the sum of trended reported from AY 2022-2025 divided by the sum of UUP from AY 2022-2025 to calculate ultimate for AY 2025.
Thank you.
Comments
The reason for excluding the year for which you want to calculate the ultimate (in this case AY 2025) from the calculation of the Estimated Current-to-Ultimate (ECR) ratio is to avoid any potential bias or distortion in the results. ECR is used to estimate the ultimate value of a certain parameter (e.g., claim ratios) based on historical data. By excluding the year you want to predict (AY 2025), you ensure that your estimate is based on data from previous years only, which provides a more unbiased and accurate prediction.
When you calculate the ECR for 2025 by taking the simple average of claim ratios for AY 2022-2024, you are essentially assuming that the historical pattern of data from these three years is representative of what you might expect for AY 2025. This approach assumes that there won't be any significant changes or shifts in the data pattern between the years, and the average of previous years' ratios will be a reasonable estimate for 2025.
On the other hand, the Cape Cod method, also known as the Bornhuetter-Ferguson method, is a more sophisticated reserving technique that can handle the inclusion of the year you want to predict (AY 2025) in the calculation. It is based on the concept of "trending" historical data to predict future values. The method calculates a trend factor that represents the historical growth or development pattern in the data and then applies this factor to the most recent data (AY 2025 in this case) to estimate the ultimate value.
The reason you can include AY 2025 in calculating the ECR using the Cape Cod method is that this method explicitly takes into account the trend and development pattern observed in the historical data. It assumes that the trend observed in the historical data is likely to continue into the future. By applying the trend factor to the most recent data, you can make a more informed prediction for AY 2025 without introducing significant bias.
In summary, the main difference between excluding AY 2025 in the simple ECR calculation and including it in the Cape Cod method is the handling of trend and development patterns. The Cape Cod method allows for a more sophisticated estimation, considering the observed trends, while the simple ECR approach assumes a constant pattern in the historical data and avoids potential biases by excluding the year in question.