Loss reserving - a science, yes, but not rocket science.

This page demonstrates the incurred loss development and Bornhuetter-Ferguson methods of loss reserving using real-world data from the International Group Pool, available on the Web thanks to Elysian Insurance Services and Marsh (UK).

The experience of the International Group Pool is good for this purpose for two reasons: the composition of the fleet hardly changes from year to year (although the increasing number of large passenger ships bears watching) , and the conditions of cover have not changed much, either. The underlying retention (US$5 million), probably the most important single factor, did not change at all from 1995-2005.

The first step, once the data have been validated, is to array the data in a triangle.


International Group Pool Incurred losses at 20 February 2003 USD millions
Policy Year 12m 24m 36m 48m 60m 72m 84m 96m
1995 89 96 125 133 133 130 123 139
1996 101 127 158 158 155 158 159
1997 61 144 161 164 156 166

1998 25 103 110 118 128


1999 21 50 90 95



2000 101 136 144




2001 36 42





2002 97







The second step is to calculate the year-on-year percentage change for each policy year, and then find the average of those changes. (In this example, I took out one value I thought was anomalous, so it would not distort the analysis.)


Year-to-Year Loss Development Factors
Policy Year 12m 24m 36m 48m 60m 72m 84m 96m
1995 1.08 1.30 1.06 1.00 0.98 0.95 1.13 1.00
1996 1.26 1.24 1.00 0.98 1.02 1.01

1997 2.36 1.12 1.02 0.95 1.06


1998
1.07 1.07 1.08



1999 2.38 1.80 1.06




2000 1.35 1.06





2001 1.17






average 1.60 1.27 1.04 1.00 1.02 0.98 1.13 1.00
cumulative 2.38 1.49 1.18 1.13 1.13 1.10 1.13 1.00

The cumulative average is the product of all the averages to the right. (Eventually the average year-on-year change reaches 1.00, and you can stop multiplying.) The cumulative average, also known as the Loss Development Factor ("LDF"), is then multiplied times the actual losses at the relevant stage to project the ultimate losses for each policy year.


Projected ultimate losses

Actual LDF Ultimate
1995 139 1.00 139
1996 159 1.13 180
1997 166 1.10 183
1998 128 1.13 144
1999 95 1.13 107
2000 144 1.18 170
2001 42 1.49 63
2002 97 2.38 231

The same analysis can be applied to paid losses, with the caveat that there is usually a lot more variation in the year-on-year changes to paid losses, because so much depends on the timing of payments, especially with large claims. As a result, the paid loss development method requires more data to produce reliable results. The principal benefit to using paid losses is that the data points are more objective than incurred losses which are based in large part on the judgment of claims handlers.

Refining projections with the Bornhuetter-Ferguson method

  The incurred and paid loss development methods should be followed up  with the Bornhuetter-Ferguson analysis  to ensure that the projected ultimate  losses in  the immature years are realistic.  The B-F method  requires an exposure measure (usually tonnage in the case of a P&I Club).  The projected ultimate losses in the mature years are divided into the exposure measure to obtain a value  known as "pure premium".  An average (or selected) pure premium, properly trended, if appropriate,  can then be multiplied times the exposure measure for the immature years to provide an alternate projection  which can be compared to the projections determined  by the incurred and paid loss development methods. 

Expected Pure Premium

Actual LDF Ultimate G.T. P.P.
1995 139 1.00 1.39 700 0.20
1996 159 1.13 180 700 0.26
1997 166 1.10 183 700 0.26
1998 128 1.13 144 700 0.21
1999 95 1.13 107 700 0.15
2000 144 1.18 170 700 0.24
avg P.P



0.22
2001 42 1.49 63 700 0.09
2002 97 2.38 231 700 0.33

For example, if we assume that the tonnage entered in the International Group has remained steady at 700 million gross tons from 1995-2002, and look back at the last table, we can see that the ultimate losses projected for 2001 and 2002 (marked in red) both diverge from the expected pure premium of 0.22 (derived from the average of the preceding years).  Therefore, we should project that both 2001 and 2002 will move in the direction of $154 million, the figure that the results in the previous years lead us to expect.  It would probably be unduly optimistic to expect that the losses in 2001 will be less than those in the best year so far, and overly pessimistic to expect that 2002 will be worse than 1996 and 1997 (adjusted for inflation).  So, without more data, or other justification, an appropriate figure for 2001 would be in the range from $107m-$154m, and an appropriate figure for 2002 would be in the range from $154m-$200m.  The economic slowdown in the United States in 2001 and the reaction to the 9/11 attack give us reasons to keep the 2001 projection on the low side; I am not aware of any special factors affecting 2002, but to be conservative, I would reserve at least $200 million at this point, (remembering that I previously adjusted the average year-on-year change in the first year following expiry because I thought one of the values was anomalously high).  Therefore, the final results of this analysis would look like this:

Projected ultimate losses

Actual LDF Ultimate
1995 139 1.00 139
1996 159 1.13 180
1997 166 1.10 183
1998 128 1.13 144
1999 95 1.13 107
2000 144 1.18 170
2001 42 n/a 110
2002 97 n/a 200

One problem with this type of analysis is that tonnage (which, after all, is just a measure of the cubic capacity of a ship) is an imprecise measure of the exposure presented by a fleet, and works best with very large fleets such as the Group Pool.  Use it with caution when rating individual fleets, especially if your fleet has substantial passenger vessel or U.S. crew exposure.  Also remember that most fleets, unlike the Group Pool, can change substantially from year to year.

Update (January 2007)

Thanks to Martin Hubbard of Tysers, who sent me a copy of his firm's 2006/07 Annual P&I Report, I had a chance to see whether my projections were at all accurate.

International Group Pool Incurred losses at 20 Aug 2005 USD millions
Policy Year 18m 30m 42m 54m 66m 78m 90m 112m124m
1996 118 151 156 156 160 159 158 159
158
1997 122 148 155 158 162 177 178
 153
1998 78 108 112 126 127 130 134
1999 47 90 90 94 96
 98

2000 132 145 143 142
 145


2001 42 40 39
 42

2002 158 170
 178


2003132138
2004179

Oddly, the losses in 2001 have hardly developed.  As of  20 Aug 2005 (and  20 Feb 2006), notified Pool claims for the 2001 year stood at $42 million, unchanged from the position at 20 Feb 2003. The losses in 2002 are developing more in line with the projections, having reached $177.7 million as of 20 Aug 2005.

In general, however, the losses have not developed as much as I expected. The results of the 2001 year could be considered an anomaly, perhaps one caused by the effect of the events of 11 Sept 2001 on the world economy. Looking at the recent figures, however, makes me wonder whether a paradigm shift took place around 20 Aug 2002. The reserves in the older years (1996-2000) grew only a little after 20 Aug 2002, and the reserves in the more recent years show very little growth from their initial positions 6 months after expiry.  According to Tysers' chart, almost no growth in the figures was recorded between 20 Aug 2005 and 20 Feb 2006. 

Either Clubs started putting up more realistic initial reserves in 2002, or they are sitting on a lot of reserve increases that will appear in the figures that come out after 20 Feb 2006.

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