Mack(1994)

Question 1

Major consequence of Mack Assumption 1

Answer 1

It assumes development factors are uncorrelated. Therefore we should not apply the chain-ladder to business where we usually observe a small increase in development factors if the previous development factor is higher than most other AYs

Question 2

Mack’s 3 assumptions underlying the chain ladder method

Answer 2

1. The expected losses in the next development period are proportional to losses-to-date. (The chain ladder method uses the same LDF for each accident year, uses most recent losses-to-date to project losses, ignoring losses as of earlier development periods)
2. Loss are independent between accident years
3. Variance of losses in the next development period is proportional to losses-to-date with proportionality constant alpha^2 that baries by age

Question 3

Major consequence of Mack Assumption 2

Answer 3

It cannot be used for triangles where CY effects affect several AYs in the same way

Question 4

Examples of calendar year effects that may cause loss development data not to be independent by accident year

Answer 4

1. Changing inflation
2. Changes in payment processes
3. Changes in setting case reserves
4. Changes due to court decisions

Question 5

How to test Mack assumption 1

Answer 5

• Plot of cumulative losses from adjacent periods.
  If the assumption holds, you should see: linear relationship between Loss(k+1) and loss (k) through the origin. The line should go through the data points

Question 6

MSE of the total reserves greater than the sum of the MSE from the reserve for individual accident years

Answer 6

Because the same LDFs are used for all accident years, the loss reserve estimates are positively correlated between accident years, increasing the total MSE

Question 7

Higher standard error percentage for the oldest accident years

Answer 7

The absolute standard error should be the lowest for the oldest accident years, but since the size of the loss reserve is so small, the standard error percentage will be higher

Question 8

Higher standard error percentage for the most recent accident years (or two)

Answer 8

Uncertainty in forecasting future losses is highest for the most recent accident years because losses are immature, so the standard error percentage will be higher

Question 9

Advantage of using Spearman’s rank

Answer 9

1. The test is distribution-free (doesn’t assume LDFs are from a normal distribution)
2. Differences in variances of LDFs between development periods is less important because it uses ranks

Question 10

Weakness of the Chain Ladder Method

Answer 10

1. Estimators of the last 2 or 3 LDFs rely on very few observations
2. Does not work well for the most recent accident year where losses-to-date provide a very uncertain base to project ultimate losses. (another method, such as the least squares method would put less credibility on the immature losses)

Question 11

Two problems when using the normal distribution as an approximation to the true distribution for reserves

Answer 11

1. If data is skewed, it is a poor approximation
2. The confidence interval can have negative lower limits, even if a negative reserve is not possible