Transcript Price Monitoring: French XS Motor Market

AXIS Re Europe
Price Monitoring
French XS Motor Market
CAE Spring 2008 Meeting – London
Adrien de Tessières
26 July 2016
AXIS Re Europe
Motor Insurance market:
Frequency, Prices &
Inflation
26 July 2016
Frequency of bodily injury losses in France
BI Losses Frequency
8
7.5
Frequency per 1000 veh.
7
Introduction of
6.5
safety cameras
6
5.5
5
4.5
4
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Source: FFSA (Fédération Francaise des Sociétés d‘assurances)
Over 10 years, the frequency has decreased by 38%
26 July 2016
3
Original Price Change - MTPL
Average MTPL Premium in France (all classes of vehicles)
200.00
195.00
190.00
185.00
Euro
180.00
175.00
170.00
165.00
160.00
Based on FFSA data
Estimation
155.00
150.00
1990
1992
1994
1996
1998
2000
2002
2004
2006
Year
The cycle is limited to +/- 6% rate change
26 July 2016
4
2008
Inflation: Example of Cost of Care
Cost of Care (on a sample book)
Cost of Care (Eur/H)
CPI France
2001
2002
2003
2004
2005
2006
Year of Settlement
The Hourly Cost of Care has seen an annual inflation of more
than 10% between 2001 and 2006
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5
Inflation on Large Bodily Injury Claims

Annual average inflation of large claims was 9.4%
between 2001 & 2006

Cost of Care part has increased by 21.1% in the
same period
Large Claim: BI Losses with disability of more than 50%
Source: FFSA
26 July 2016
6
AXIS Re Europe
Reinsurance Motor
Market: Rates
26 July 2016
Historical Reinsurance Rates / France MTPL
Rate of the unlimited programs
multiplied by 4 in 8 years
Commercial Rates 2007
Commercial Rates 1999
multiplied by 5 in 8 years
multiplied by 8 in 8 years
multiplied by 12 in 8 years
0
0.5
1
1.5
2
2.5
Priority in Euro million
3
3.5
4
8
5
Source: Rough Estimation of AXIS' actuarial department
Huge Increases between 1999 and 2007
26 July 2016
4.5
Question

We’ve seen the original inflation, the frequency
trend, the price and the reinsurance price
Information

What do we need in addition to Monitor the
profitability of a treaty?

26 July 2016
The XS Inflation
9
AXIS Re Europe
Impact of the inflation to
the XS layers:
3 examples
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XS Inflation – Leverage Effect
1/3
Inflation on an XS Layer - With 10% FGU Inflation
4
3.5
Loss before Inflation
After 10% Inflation (FGU)
+ 15%
3
2.5
Layer
+ 20%
2
1.5
+ 110%
N/A
1
+ 0%
+ 0%
+ 0%
+ 10%
Retention
0.5
0
Loss 1
Loss 2
Loss 3
Loss 4
Inflation on the layer between 15 and 110%
On average +20% for those 4 Losses
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11
XS Inflation – Leverage Effect
2/3
Inflation on an XS Layer - With 10% FGU Inflation
4
3.5
Loss before Inflation
After 10% Inflation (FGU)
3
2.5
2
1.5
+ 0%
+ 0%
Layer
+ 110%
N/A
1
+ 0%
+ 0%
+ 10%
+ 0%
Retention
0.5
0
Loss 1
Loss 2
Loss 3
Loss 4
Inflation on average +10% for those 4 Losses
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12
XS Inflation – Leverage Effect
3/3
Inflation on an XS Layer - With 10% FGU Inflation
4
3.5
Loss before Inflation
After 10% Inflation (FGU)
3
2.5
Layer
2
1.5
+ 43%
+ 60%
+ 110%
N/A
1
+ 0%
+ 0%
+ 0%
+ 10%
Retention
0.5
0
Loss 1
Loss 2
Loss 3
Loss 4
Inflation on average +60% for those 4 Losses
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13
XS Inflation

Beside the original inflation, the inflation on XS
Layers depends on:
–
The Level of the layer (ex. 1 vs. 2)
And
–
26 July 2016
The Distribution of the losses (ex. 1 vs. 3)
14
XS Inflation and Index Clause

The index clause will increase the priority and the limit by
the inflation of a defined index between the “base” date and
the date of payment to share the increase *:
5'000'000
4'500'000
Unindexed Total Loss
Total Loss
4'000'000
+16.2%
3'500'000
3'000'000
39.8%
39.8%
2'500'000
+16.2%
2'000'000
30.1%
1'500'000
30.1%
+16.2%
1'000'000
500'000
30.1%
30.1%
1
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* For a Full Index Clause, without margin
15
XS Inflation and Index Clause
When we renew a treaty, what is the impact of the index
clause on the XS inflation?

If the base date is the inception date (most common case):

The Index Clause doesn’t offset the XS Inflation
Underwriting Year 2008 vs. 2009
4
3.5
3
Loss as if 2008
Loss as if 2009
2.5
2
1.5
1
0.5
0
Loss 1
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Loss 2
16
Indexed
Layer
08/09
XS Inflation and Index Clause

If the base date is defined as a specific date (e.g. 1/1/01):

The Index Clause offsets the XS Inflation if this date
doesn’t change when we renew the layer.
Underwriting Year 2008 vs. 2009
4
3.5
3
Loss as if 2008
Loss as if 2009
Indexed
Layer 08
2.5
Indexed
Layer 09
2
1.5
1
0.5
0
Loss 1
Loss 2
If the index is very close to the real inflation, it could completely offset the XS inflation
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AXIS Re Europe
Impact of the inflation to
the XS layers,
Real Market Data
26 July 2016
Data - Assumptions

We have the Renewal Loss information of ~90% of
the French Motor market

We use a flat index to revaluate the losses to the
underwriting year 2008, and UWY 2009

First index used is 6% per annum (see example)

We compare the loss to the unlimited layer in
2008 and 2009
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Data - Results

The increase on the From Ground Up Losses is
6% between 2008 and 2009 (cf. assumptions)

The increases of the losses to the unlimited
layers are the following:
Priority
(millions
EURO)
6% per year
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4.0
5.0
18%
6.0
21%
7.0
25%
8.0
28%
20
9.0
31%
10.0
33%
11.0
35%
12.0
35%
39%
Data - Results
If we use different assumptions for the inflation:

Priority
(millions
EURO)
2% per year
3% per year
4% per year
5% per year
6% per year
7% per year
8% per year
9% per year
10% per year
4.0
5.0
7%
9%
12%
15%
18%
20%
22%
25%
27%
6.0
8%
12%
15%
18%
21%
24%
28%
31%
34%
7.0
11%
14%
18%
21%
25%
29%
32%
34%
38%
8.0
13%
19%
21%
24%
28%
31%
35%
40%
44%
9.0
13%
19%
25%
27%
31%
34%
37%
41%
47%
10.0
14%
21%
25%
31%
33%
37%
40%
43%
48%
11.0
13%
20%
27%
31%
35%
39%
43%
47%
50%
12.0
12%
21%
29%
33%
35%
38%
45%
47%
51%
For an unlimited layer XS 10mio the increase of the loss to the
layer is 5 times the original inflation!
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13%
17%
24%
33%
39%
38%
43%
49%
52%
AXIS Re Europe
Impact of the inflation to
the XS layers,
Pareto Distribution
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Pareto Distribution - Characteristics

If x follows a Pareto distribution with an alpha
parameter of a,  x*(1+i%) also follows a Pareto
distribution with the same parameter a

For an unlimited layer, average loss= priority/(a -1)

The increase of the loss to an XS layer only derives
from the frequency and not from the severity

The increased frequency is: freq’= freq * (1+i%)a

The inflation to the layer is (1+i%)a -1
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Pareto Distribution - Result

Inflation to the layer for alpha between 0.9 and 5 and
Original
inflation
inflation between 2.5% and 10%:

2.5%
5.0%
7.5%
10.0%
0.9
2.2%
4.5%
6.7%
9.0%
1
2.5%
5.0%
7.5%
10.0%
Alpha Pareto
2
3
5.1%
7.7%
10.3%
15.8%
15.6%
24.2%
21.0%
33.1%
4
10.4%
21.6%
33.5%
46.4%
5
13.1%
27.6%
43.6%
61.1%
The results from the French Market for the layer
unlimited XS 10mio are similar to the results of a
Pareto with an alpha of 5
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Priority
(millions
EURO)
2% per year
3% per year
4% per year
5% per year
6% per year
7% per year
8% per year
9% per year
10% per year
4.0
5.0
7%
9%
12%
15%
18%
20%
22%
25%
27%
6.0
8%
12%
15%
18%
21%
24%
28%
31%
34%
7.0
11%
14%
18%
21%
25%
29%
32%
34%
38%
8.0
13%
19%
21%
24%
28%
31%
35%
40%
44%
9.0
13%
19%
25%
27%
31%
34%
37%
41%
47%
10.0
14%
21%
25%
31%
33%
37%
40%
43%
48%
11.0
13%
20%
27%
31%
35%
39%
43%
47%
50%
12.0
12%
21%
29%
33%
35%
38%
45%
47%
51%
13%
17%
24%
33%
39%
38%
43%
49%
52%
Distribution of BI Losses vs. Pareto

This empirical distribution is common for BI Losses:
Estimated alpha=2.5
We can see that Pareto doesn’t fit the data:
Underestimates the low part, and overestimates the high part
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25
Distribution of BI Losses vs. Pareto

We can have a good fit on a small band:
Estimated alpha=2.5
Estimated alpha=1.8
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Distribution of BI Losses vs. Pareto

Next band:
Estimated alpha=3.3
Estimated alpha=2.6
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Distribution of BI Losses vs. Pareto

This result is very common for BI Losses:
–

The alpha increases with the priority!
•
very low layers: a ~1
•
Very high layers: a > 4
Impact when there is inflation:

it increases the frequency (same as for Pareto)

it reduces the a at the same time, which increases
the average loss [ priority/(a -1) ].

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This is what we see in France for Motor
28
AXIS Re Europe
Conclusion
26 July 2016
Conclusion

XS inflation effect could be enormous:
Example of Price Monitoring with an Alpha Pareto of 1 (e.g. MTPL low layer)
100
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Alpha of 1
(no effect)
Frequency
Trend -2%
Reinsurance Rate
decrease (-0.13%)
–
No additional effect for alpha=1
Ultimate Loss Ratio
90
80
70
60
50
40
–
Previous Year
Loss Ratio
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio
For an alpha parameter of 2, it
Example of Price Monitoring with an Alpha Pareto of 2 (e.g. MTPL mid layer)
Alpha of 2
Frequency
Trend -2%
100
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Reinsurance Rate
increase +6.9%
90
Ultimate Loss Ratio
doubles the effect of the original
110
80
70
60
inflation
–
50
40
Previous Year
Loss Ratio
In some examples like French Motor,
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio
Example of Price Monitoring with an Alpha Pareto of 5 (e.g. MTPL high layer)
130
Alpha of 2
120
it could multiply by up to 5 the effect
Ultimate Loss Ratio
110
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Frequency
Trend -2%
Reinsurance Rate
increase +6.9%
100
90
80
70
60
50
40
Previous Year
Loss Ratio
of inflation

Do not forget this impact for the Price
Monitoring!
26 July 2016
30
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio
AXIS Re Europe
Q&A
26 July 2016
AXIS Re Europe
Appendix
26 July 2016
Assumptions - Example
original info
UWY
1995
1997
2003
1995
2003
1996
total
FGU AS IF
Loss FGU
1'312'438
1'227'577
1'432'905
1'322'220
1'003'219
1'110'818
7'409'177
with index 6%
unlimited XS 2 mio
index to 08 AS IF 2008 AS IF 2009 increase 08/09
2.133
2'799'336
2'967'297
6.0%
1.898
2'330'308
2'470'127
6.0%
1.338
1'917'550
2'032'603
6.0%
2.133
2'820'200
2'989'412
6.0%
1.338
1'342'533
1'423'085
6.0%
2.012
2'235'183
2'369'294
6.0%
13'445'112
14'251'819
6.0%
AS IF 08 XS Loss AS IF 09 XS Loss increase 08/09
799'336
967'297
21.0%
330'308
470'127
42.3%
32'603
0.0%
820'200
989'412
20.6%
0.0%
235'183
369'294
57.0%
2'185'028
2'828'734
29.5%
Original
inflation
French Motor Market - Results
Priority
(millions
EURO)
2% per year
3% per year
4% per year
5% per year
6% per year
7% per year
8% per year
9% per year
10% per year
4.0
2.5%
5.0%
7.5%
10.0%
5.0
7%
9%
12%
15%
18%
20%
22%
25%
27%
0.9
2.2%
4.5%
6.7%
9.0%
6.0
8%
12%
15%
18%
21%
24%
28%
31%
34%
1
2.5%
5.0%
7.5%
10.0%
7.0
11%
14%
18%
21%
25%
29%
32%
34%
38%
Alpha Pareto
2
3
5.1%
7.7%
10.3%
15.8%
15.6%
24.2%
21.0%
33.1%
8.0
13%
19%
21%
24%
28%
31%
35%
40%
44%
4
10.4%
21.6%
33.5%
46.4%
9.0
13%
19%
25%
27%
31%
34%
37%
41%
47%
5
13.1%
27.6%
43.6%
61.1%
10.0
14%
21%
25%
31%
33%
37%
40%
43%
48%
11.0
13%
20%
27%
31%
35%
39%
43%
47%
50%
12.0
12%
21%
29%
33%
35%
38%
45%
47%
51%
13%
17%
24%
33%
39%
38%
43%
49%
52%
Price Monitoring – Example Alpha Pareto 1
Example of Price Monitoring with an Alpha Pareto of 1 (e.g. MTPL low layer)
100
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Alpha of 1
(no effect)
Frequency
Trend -2%
Reinsurance Rate
decrease (-0.13%)
Ultimate Loss Ratio
90
80
70
60
50
40
Previous Year
Loss Ratio
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio
Price Monitoring – Example Alpha Pareto 2
Example of Price Monitoring with an Alpha Pareto of 2 (e.g. MTPL mid layer)
110
Alpha of 2
Frequency
Trend -2%
100
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Reinsurance Rate
increase +6.9%
Ultimate Loss Ratio
90
80
70
60
50
40
Previous Year
Loss Ratio
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio
Price Monitoring – Example Alpha Pareto 5
Example of Price Monitoring with an Alpha Pareto of 5 (e.g. MTPL high layer)
130
Alpha of 5
120
Ultimate Loss Ratio
110
5% Price
Increase
7% Inflation
Primary
Rate
Original
Inflation
Frequency
Trend -2%
Reinsurance Rate
increase +31.1%
100
90
80
70
60
50
40
Previous Year
Loss Ratio
XS Additional
Inflation
Frequency Trend
Reinsurance
Rate Change
Current Year
Loss Ratio