Part6: Fisher/Lester- Fall 2002 Exam Question

[Roasted Almond]

Q25a),Fall 2002 Exam.

The solution reveals that the Examiner has asked about the behaviour of different reserve estimation methods under Text's CASE4: "Deteriorating Loss Ratio With Reserve Strengthening".

I consider myself extremely dumb to admit that I can't figure-out how the Examiner is actually pointing out to CASE4 under the given scenario?

Thanks ALOT for your kind explanation.

[Basso]

The loss ratio is deteriorating because the pricing actuaries have not yet responded to the unusually high inflation by the evaluation period. As such, if price stays the same, and costs increase, loss ratio increases. The claims adjusters started responding after 12 months, meaning that they started increasing their reserves for the 1997 year due to the inflation in the question. The combination of the deteriorating loss ratio and the reserve strengthening is what is referred to in case 4.

[chinese_girl]

There are several variables(Expected loss ratio, LDF, inflation rate) that will affect the results. I put this into an excel worksheet and change the value to see the difference. I found the result varied under different input values especially for the B-F method.

The CAS solution for B-F method states “I would expect the expected loss method to understate reserves. Since the actuaries have made no adjustment, the expected loss ratio used is lower than what one would now expect.”

Well, that’s true just for the LR part. But the LDF will be overestimated if the inflation rate does not remain as high as in 1997. And the IBNR factor will be overestimated. So the result of the B-F method is not definite. It depends on the level of underestimation of the LR and the overestimation from the reserve strengthening.

Here is a numeric example.

Let’s say before 1997, the LDF is the following:
12-24 24-36 36-48
1.1 1.05 1.03

There are no more development after 48 months.

As of 12/31/96, the loss development triangle is:
AY 12 24 36 48
1993 900 990 1040 1071
1994 950 1045 1097
1995 1000 1100
1996 1050

The inflation rate in 1997 is 10%.

As of 12/31/97, the loss development triangle is:
AY 12 24 36 48
1993 900 990 1040 1071
1994 950 1045 1097 1243
1995 1000 1100 1271
1996 1050 1271
1997 1210

(for example, the incurred loss for accident year 1995 at 36th month is 1271=1100*1.05*1.1, all of the data in the most recent diagonal is constructed in this way.)


Now use B-F method to estimate the IBNR reserve for accident year 1997 as of 12/31/97.

Assume earned premium in 1997 is $2500 and the actuary estimates the LR = 60%

The actual LR is 70%.

The result of IBNR = 2500*60%*(1-1/1.415)=440
If the inflation rate return to normal level after 1997, then
The actual IBNR = 2500*70%*(1-1/1.19)=279

This is just one case of the situation. If you change the input value of the inflation rate and LR, you will see different result under different situation.

[Archen]

...
The actual LR is 70%.

The result of IBNR = 2500*60%*(1-1/1.415)=440
If the inflation rate return to normal level after 1997, then
The actual IBNR = 2500*70%*(1-1/1.19)=279

This is just one case of the situation. If you change the input value of the inflation rate and LR, you will see different result under different situation.

Well could anyone tell me where the 1.415 came from?

[carrytheCrøss]

Well could anyone tell me where the 1.415 came from?It appears that she may have squared (1.1*1.05*1.03). I haven't looked into why in her example she would have done so.

[Archen]

But 1.1*1.05*1.03 equals 1.190 rather than 1.415. F/L paper is hard for me to thoroughly understand.

Under the consistent loss ratio and reserve strengthening scenario, it is said that all three methods(BF,CL,PoP) tell out an overstated IBNR. I'm wondering what we do can result in a best estimated IBNR then. Should we use the Fixed Ult Loss Ratio Method (IBNR=EP*ELR-Cum Rptd Loss) and believe it's the best?