Venter Factors

Question 1

If future loss emergence is a constant plus a percent of emergence to date, what method should be used

Answer 1

A factor plus constant development method

Question 2

If future loss emergence is proportional to ultimate losses rather than to emerged to data, what method should be used

Answer 2

BF

Question 3

Testing implications of assumption 1- significance of factor f(d)

Answer 3

In general, the absolute value of a factor f(d) is required to be at least twice its standard deviation for the factor to be considered significantly different from zero

Question 4

Testing implications of assumption 2 - Superiority of factor assumption to alternative emergence patterns

Answer 4

To compare development methods, we should use the sum of the squared errors (SSE), adjusting for the number of parameters used (goodness of fit)

Question 5

Describe alternative emergence pattern: Linear with constant

Answer 5

f(d)c(w,d) + g(d)
often significant in the age 0 or 1 state, especially for highly variable and slowly reporting lines such as excess reinsurance.
If the constant is significant and the factor is not, the additive chain-ladder method may be appropriate

Question 6

Describe alternative emergence pattern: Factor times parameter

Answer 6

f(d)h(w)
States that the next period’s expected emerged loss is a lag factor f(d) times the expected ultimate loss amount h(w) for an AY
This is the parameterized BF method
To outperform the chain-ladder method, the BF method must produce lower fit errors.
To test the BF model against the chain-ladder model, we calculate the SSE test statistic and see which one is better.
If BF is better, that would suggest that loss emergence is more accurately represented as a proportion of ultimate losses rather than a percentage of previously emerged losses

Question 7

Alternative emergence pattern: testing implication 1&2

Answer 7

By graphing the age d+1 loss against the age d loss.
A factor-only model (no constant) would show roughly a straight line through the origin with slope equal to the development factor.
A constant-only model (no factor) would show roughly a horizontal line at the height of the constant

Question 8

The additive chain-ladder method and the Cape Cod method will always produce the same adjusted SSE, why is that?

Answer 8

For each age d, both models result in a constant f(d) across all accident years.
If we fit the Cape Code model, we can define g(d) = f(d)h, where g(d) is the additive development amount for age d.
If we fit the additive model, we can define f(d)h = g(d).
As long as the parameters are fit using least squares, the equation will always hold.

Question 9

Ways to reduce the number of parameters in the BF model

Answer 9

1. Grouping AYs using apparent jumps in loss levels and fitting a single h parameter to each group
2. Assume that subsequent periods all have the same expected percentage development.
3. Fit a trend line through the BF ultimate loss parameters

Question 10

Chain-ladder method assumption

Answer 10

Assumes that future emergence for an AY will be proportional to losses emerged to date

Question 11

BF method assumption

Answer 11

It takes expected emergence in each period to be a percentage of ultimate losses

Question 12

Cape Cod and additive chain-ladder method assumption

Answer 12

It assumes that years showing low losses or high losses to date will have the same expected future dollar development (because they assume a constant h over all accident years)

Question 13

Testing implication of assumption 3- test of linearity - Residuals as function of previous cumulative losses

Answer 13

A scatter plot of the raw incremental residuals (actual emergence - expected emergence) against the previous cumulative losses
The chain-ladder method assumes that the incremental losses are a linear function of the previous cumulative losses.

Question 14

Testing implication 4: Tests of stability - residuals over time (Stability Test 1)

Answer 14

Plot the incremental residuals against time

Question 15

Testing implication 4: Tests of stability - residuals over time (Stability Test 2)

Answer 15

Look at a moving average of a specific age-to-age factor.
If the moving average shows clear shifts over time, then instability exists and we may want to use a weighted average of the factors.
If the moving average shows large fluctuations around a fixed level, this does not mean we should focus only on recent data. In this case, a broader range of data is actually better

Question 16

Testing implication 4: Tests of stability - residuals over time (Stability Test 3)

Answer 16

The state-space model compares the degree of instability of the observations around the current mean to the degree of instability in the mean itself over time.
This helps us determine whether to use all of the data OR a weighted average that favors more recent years

Question 17

Two options when the factors are unstable

Answer 17

1. Use a weighted average of the available factors, with more weight going to the more recent years.
2. Adjust the triangle for instability. For example, if there are changes in the settlement rate of claims ,we can adjust the triangle to the latest pattern