step 3 Note
We could have instead compared projected ultimate losses at the cost level of the prospective policy period (i.e. developed and trended actual reported losses) to three-years worth of expected ultimate losses for the prospective policy period.
Comments
I hit enter by mistake above. Can you please help me understand why the detrending / undeveloping approach gives more weight to the latest year as compared to bringing the actual losses to ultimate? From step 3 notes:
"We could have instead compared projected ultimate losses at the cost level of the prospective policy period (i.e. developed and trended actual reported losses) to three-years worth of expected ultimate losses for the prospective policy period.
These two approaches are not equivalent.
One difference is that the approach we took here gives a bit more weight to the older policy period (36% = $115.0/315.2), while the alternate approach would give equal weight to all three years."
The best explanation I've got at the moment is this is to do with matching the time periods involved. We can project the expected ultimate losses for the prospective policy period. This covers one year. To use the actual loss history we trend and develop it to the prospective period, but then we've got three years of losses which is a mismatch with the one year of expected losses. So we divide the trended ultimate actual loss by 3 to remove the mismatch. This means we're giving 1/3 weight to each of the years of loss history.
Whereas when we start with the expected loss and detrend and de-develop, we're doing it once for each year so the time periods match and then the inverse of the product of the trend and development factors determines which year gets the most weight (not always the oldest year).
Thanks