Case Study 1: Multiple Line of Business and DFA
This study examines two related lines of business, LOB1 and LOB3. We show how to calculate the diversification benefit to assess the combined liability for these two lines, and illustrate a method of allocating capital between them. The information required as input to Dynamic Financial Analysis is also available, for example, probability distributions of calendar totals and correlations between calendar totals.

If these two lines are modelled separately, the calendar year trends are very similar. Both have a sharp increase in calendar year trend in 2000. There are also similarities in the variation about those trends.


If we put these two models together in a two triangle model, first of all, we find that the residuals are correlated (a correlation of 0.36). What does this mean? Well, if the actual losses for LOB1 are above the trend line, it is more likely than not that the losses for LOB3 will also be above the trend line (and vice versa).


Each line has a trend starting in the year 2000. In LOB1 it is 11% +- 3% and in LOB3, it is 8% +- 3%. Correlations in the residuals often induce correlations in the parameters. If we look at the correlation between the calendar year trend estimates, it is 0.32. Assuming that this relationship continues into future years, this will mean that if the actual future trend in LOB1 is higher than the “expected” value (say 14%), it is more likely than not that the actual future trend in LOB3 will be higher than expected (say 10%). This will tend to increase the spread of the aggregate forecast losses, compared to what we would estimate if the trends in the two triangles were completely unrelated.