You are given the following information:

1. Case reserves = 187,047
2. Losses paid-to-date = 243,005
3. Age-to-ultimate incurred loss development factor = 1.08
4. IBNR using Bornhuetter-Ferguson method = 47,387

Calculate the absolute difference in the IBNR based on the chain-ladder method and the expected loss ratio method.

• 12,983
• 43,787
• 98,101
• 146,754
• 175,268

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: E

First, use the Borhuetter-Ferguson method to calculate the estimated ultimate loss as 47,387/(1-1/1.08) = 639, 724.5. Next, calculate IBNR under the expected loss ratio method as 639,724.5 − (187,047 + 243,005) = 209,672.5. Then, IBNR under the chain-ladder method is (187,047 + 243,005)*0.08 = 34,404.16 . The absolute difference is 209,672.5 − 34, 404.16 = 175, 268.34.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.