Figures 2.1-2.2 illustrate the aggregate incurred loss estimates of workers’
compensation market according to Chain-Ladder and Bornhuetter-Ferguson methods.
The plots in figure 2.1 represent the reversal direction of loss development and the failure to recognize such information in the actuarial reserving models. More specifically, the incurred losses were favorably developed during year 1992-1996 but began to increase in year 1996. However, the Chain-Ladder and Bornhuetter- Ferguson assume that incurred loss would remain decreasing just like before 1996. As a result, the actuarial estimates yield the underestimated forecast of losses. This idea is clearly shown in figure 1.1 in which actuarial estimates are materially deviated from the actual losses since 1996.
Similarly, the loss reserve error created by the actuarial reserving models is demonstrated in figure 2.2. The incurred loss was rapidly growing during year 1996- 2000, and though it keeps on increasing, the growth rate diminished in year 2000.
Unfortunately, the Chain-Ladder and Bornhuetter-Ferguson approaches expect that the incurred loss would be decreasing at the same growth rate of years prior to 2000.
Consequently, the incurred losses are actuarially overestimated in this scenario.
Based on the individual company data, we demonstrate an empirical analysis of actuarial reserving model risk. The Chain-Ladder method, which is popularly used for loss reserve estimations, is chosen as a representative of the traditional actuarial reserving model.
In addition, the insurance companies are also characterized by size of the insurers. As pointed out by Wang and Faber (2006) who applied some selected insurers as an example, the Chain-Ladder estimation error is likely to be pronounced in large insurers and this method seems to work well with the small insurers.
Accordingly, we speculate that Chain-Ladder method could be a source of loss reserve errors and can create the unfavorable errors especially for the large insurers.
Other than using some selected insurers as a sample, we investigate the actuarial
estimate errors of every insurer. We also group the insurance companies by size of their premium using each line of business for comparison of the effectiveness of the Chain-Ladder method on different size of insurers. Mean and median of the errors are presented for each class of insurers, and we will base our analysis on the median of the errors for the outlier effect exclusion.
Applying the Chain-Ladder method, we project the incurred loss for accident- year 1996, 1999, and 2001. We select these years for the actuarial reserve error analysis in that they are the turning points of the underwriting cycle in most of the lines of business. The medians of squared errors from the Chain-Ladder estimation are exhibited in tables 9.1-9.3 for year 1996, 1999, and 2001 respectively. The positive error means that the chain-ladder model underestimate the incurred loss while the negative error implies that the model overestimate the incurred loss. However, the estimation error depend upon both direction of loss pattern and the growth rate of loss, we do not restrict ourselves to expect to see only underestimation in the year that loss changes from decreasing to increasing. Therefore, we will focus on the magnitude of the errors and the difference of the errors by size of insurers
In general, the results suggest that the insurers tend to actuarially overestimate the losses in the year that the loss pattern changes from moving upward to downward.
On the other hand, the estimates of loss from the Chain-Ladder technique are likely to be undervalued when the loss that was diminishing in the prior years begins to rise in the current year. We will discuss the actuarial loss reserve errors created by the Chain-Ladder method together with the loss ratio pattern by line of business. Note that not only does the actuarial estimate depend on the direction of the movement of the losses in prior years, it also depends on the rate of losses development. As a result, both loss overestimation and underestimation can be observed in the soft and hard
markets. In addition, we also explore the actuarial reserve errors by premium size of the companies. As there is not a significant variation of the loss ratio in homeowner insurance market, we only include this line as a sample of the property line of business.
Considering the Chain-Ladder estimation errors in the commercial multiple peril market, the loss ratio is quite stable from 1991-2000. There is a small jump of loss ratio in 2001 and a huge drop in 2002. We focus on the loss estimation error occurred in 2001 when a major change of the pattern of the price movement is presented. According to table 9.3, the medians of the errors indicate that the Chain- Ladder method underestimates the losses of the policies that were written in 2001.
Nevertheless, small, large and giant insurers exaggerate the incurred loss and the overestimation is considerable in giant insurers. An explanation for the underestimation could be that the increase rate of losses in these classes of insurers is small relative to the overall decrease rate of losses in the recent years. In addition, for these insurers, the company loss ratios may not track with the industry loss ratios.
Nevertheless, the considerable errors in large and giant insurers agree with Wang and Faber (2006) who suggested that this method do not work well with large insurers.
Next, we examine the Chain-Ladder reserve error in the commercial auto liability industry. The industry plot of loss ratio states that the insurance price had a reversal direction and began to increase in 1999. The Chain-Ladder method underestimates the losses in this year, and the magnitude of the error is material for large and giant insurers as shown in table 9.2.
In the other liability market, the results confirm our hypothesis that the Chain- Ladder method is a source of loss reserve estimation errors. In 1996 is the year just before the arrival of softening market. Nevertheless, while for the small and midsize
insurers the Chain-Ladder method tends to over-estimate loss reserves in this period, for the large and giant insurers the Chain-Ladder method tends to underestimate the loss reserves. When the market went deep into the soft market in 1999, the Chain- Ladder method appears to have underestimated the loss reserve for every size of insurers. The magnitude of the error is considerable in the large and giant insurers.
The results in medical malpractice industry also suggest the existence of the actuarial estimation errors. In year 1996, insurers have a tendency to underestimate the loss reserve if they utilize the Chain-Ladder method as a tool for loss predictions.
As expected, large and giant insurers show the greater magnitude of the errors in comparison to the small insurers. In contrary, the incurred loss appears to be underestimated, especially for the large and giant companies, in 2001 when the price continues to decrease. The reason for the actuarial underestimation in 2001 could be that the rate of decrease in losses is greater than that in the recent years.
In product liability market, there are two turning points of the price trend in the studied period. In 1999 when the market has a sudden jump of the loss ratio, the Chain-Ladder technique seems to provide the underestimation of the loss in every size of insurers. The result, therefore, is consistent with the hypothesis that the actuarial method can create the loss reserve understatement when loss is adversely developed.
The similar analysis is performed in workers’ compensation industry. The price of workers’ compensation insurance was growing during 1991-1994. It began to fall in 1995 and continued to decrease until 1999. The price began to go up again from year 1999 onward. With exception of the giant insurers, the other sizes of insurers overestimate the loss reserve in 1996 as expected. When the market is in the mature soft market in 1999, the Chain-Ladder method appears to underestimate the loss reserve except for the giant insurers. In particular, the figure shows that, though it
is small in magnitude, the Chain-Ladder technique exaggerates the loss reserves in the group of giant insurers.
Finally, we explore the loss reserve errors that are generated by the Chain- Ladder estimation in private passenger auto liability. The industry loss ratios indicate that the market price does not vary to a great extent during 1991-1998. The price, however, has gradually declined since 1999. By projecting the incurred losses, the empirical analysis shows that the Chain-Ladder technique underestimates the loss reserve in 1999. The loss reserve is underestimated when the incurred loss pattern changes in the adverse manner, the actuarial reserve error in large and giant insurers is greater than the smaller insurers. This finding substantiates the idea that small insurers set the loss reserves more conservatively than the large insurers.