4 General/health/property and casualty insurance
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NON PROFIT LIFE AND GENERAL INSURANCE FIRMS
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damaged, and must be rebuilt from scratch, the policy pays out the full
market reconstruction costs of the property at the point of claim.
We model a portfolio of 100,000 policies and also assume that each
policy is written for a maximum term of ten years, with the book of policies running off over this ten year period. Both premiums and property
reconstruction costs are assumed to increase in line with UK HPI, as generated by the stochastic model, parameterized according to Table 7.11.
The full details of the assumptions that underlie the general insurance
example are given in Appendix 9.4.
9.4.2
General insurance firm corporate structure
The general insurance firm corporate structure that we have assumed is
shown in Figure 9.13. Note that this structure again follows the same
broad corporate firm structure model as for our previous examples.
This firm structure is relatively simple and the firm cashflows are also
displayed in the figure.
9.4.3
Stochastically modeled response variables
We use the stochastic model described in Chapter 7, parameterized
according to Table 7.11, to generate the stochastic elements of the
Commission,
expenses, …
General insurance business fund
Claims
General
insurance
business
fund
Financing
Capital model
Premiums
General insurance
business fund profits
Tier 2 capital
Tier 1 capital
Shareholders
Customers
Tier 1
capital
Cost of Tier 1 capital
and capital repayment
Tier 2
capital
Cost of Tier 2 capital
Tier 2 capital
providers
Cost of Tier 2 capital
and capital repayment
Investment income
On Tier 1 and Tier 2
capital
Figure 9.13 General insurance firm corporate structure
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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT
example. However, the stochastic claims distribution, as described
below, and in full detail in Appendix 9.4, is developed outside of our
Chapter 7 stochastic model.
The following response variables are stochastically modeled:
1. The general insurance firm’s fixed expenses are assumed to increase
in line with UK RPI, as generated by the stochastic model.
2. The number of claims in the portfolio in month t is assumed to follow a binomial distribution. The probability of a claim depends on
whether or not a catastrophic event has occurred. In particular, if a
catastrophe has occurred, then claims are certain to happen for all
in force policies in the portfolio. By a catastrophic event, we have in
mind a flood, or earthquake, which destroys all of the properties in
the portfolio when it occurs. In practice, general insurance firms
will diversify their businesses geographically to reduce the concentration risk of the firm being exposed to a catastrophic event in one
region, or they will attempt to place this concentration risk with the
reinsurance markets. For the purposes of this example, however, we
will assume that the firm takes all of the catastrophe risks, so reflecting the position of the firm, gross of risk mitigants.
3. In our base case example, we assume that the probability of a claim
occurring, given that a catastrophe has not occurred, is 0.0001 in
that month. The probability of a claim occurring, given that a catastrophe has occurred is assumed to equal 1, and where the probability
of a catastrophe occurring is assumed to equal 0.000025 per month.
The full details are provided in Appendix 9.4.
4. Claim amounts are assumed to follow a log normal distribution,
increased in line with UK HPI, as generated by the stochastic
model. The log normal distribution models the distribution of property reconstruction costs in the firm’s portfolio.
5. The Pillar 1 regulatory capital requirement is calculated as the general insurance capital requirement described in Appendix 9.4.
Based on the stochastic elements of this example, the economic
capital requirement that is generated by the stochastic model is the
amount of capital required by the general insurance firm to cover its
aggregate
Claim experience risks
Expense risks
NON PROFIT LIFE AND GENERAL INSURANCE FIRMS
9.4.4
155
Stochastic economic capital calculation
The method described in Section 8.2.3.2, which was used for our
stochastic retail mortgage bank example is again used. We use 10,000
simulations in our runs.
9.4.5
Results
Our results are provided graphically in the form of a series of figures.
Each figure compares average Pillar 1 capital with 95th, 99th, 99.5th and
99.9th percentile economic capital.
Note that, in our figures, we plot the natural logarithm of each capital
amount. This is because certain of the economic capital amounts, 99.9th
percentile economic capital for example, are too large to be plotted
meaningfully without transformation.
9.4.5.1 Base case example
Note that, with the assumptions described in Appendix 9.4, where we
assume a catastrophe probability of 0.000025 per month, we expect that
0.000025 ϫ 12 ϫ 10 ϫ 10,000 ϭ 30 catastrophes will occur in total
over all of the 10,000 simulations, for the entire ten year projection term
of each simulation. Therefore, for this example, we expect catastrophes
to impact 99.9th percentile economic capital, but not 99.5th, nor lower
percentile, economic capital.
Note also that, for each simulation, the further into the projection term
that one is, the less likelihood there is of catastrophes occurring over the
remaining lifetime of the projection term from that point onwards.
Therefore, we expect that catastrophes will impact economic capital at
the shorter durations, with the impact reducing, and ultimately there
being no impact at all at the medium and longer durations.
Figure 9.14 shows the results for our base case.
As expected, catastrophes only affect 99.9th percentile economic capital and only at the shorter durations. Catastrophes cause the 99.9th economic capital to be at the initial very high levels shown in Figure 9.14,
before dropping back down to the level of economic capital at the other
percentile levels.
The amount of 99.9th percentile economic capital that is required at
this higher level is extremely large, relative to Pillar 1 capital, although
the natural logarithm transformation hides this difference. In fact, 99.9th
percentile economic capital is nearly 700 times as large as Pillar 1
capital at the shorter durations.
Conversely, at the later durations, when future catastrophes do not
have adequate time to occur over the remaining lifetime of the
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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT
ln capital (£)
25
10
0
120
Duration (months)
99.9th Percentile
99.5th Percentile
99th Percentile
95th Percentile
Pillar 1 capital
Figure 9.14 General insurance economic capital versus Pillar 1
capital – base case
projection, Pillar 1 capital is higher than economic capital at all
percentile levels.
In practice, general insurance firms would not be prepared, or able, to
provide 99.9th percentile economic capital to cover the catastrophe risks
that they are running. Nor would they be able to reinsure these risks.
Instead, general insurance firms attempt to limit catastrophe risks by
diversifying their businesses. For example, they may put upper limits on
the proportion of their total business that they may accept in a particular
geographical region.
Note that the Pillar 1 capital calculation is conceptually flawed
because, as is described in Appendix 9.4, it is based on what has happened over the previous three years, rather than what might happen in
future. If a catastrophe has occurred in the previous three years, Pillar 1
capital will respond to this, although this will be after the event. So,
Pillar 1 capital reacts to past events, rather than being based on what
might happen in the future, as economic capital is.
We cannot see this effect in Figure 9.14 as the Pillar 1 capital shown
there is average Pillar 1 capital, averaged over all of the 10,000 simulations. We have therefore rerun the base case example and have graphed
the percentiles of Pillar 1 capital also. Our results are shown in
Figure 9.15.
ln capital (£)
25
99.9th
99.5th
99th
95th
Mean
50th
99.9th
99.5th
99th
95th
10
0
120
Duration (months)
Economic capital (percentile)
Pillar 1 capital (percentile)
157
Figure 9.15 General insurance economic capital versus Pillar 1 capital – base case with Pillar 1 capital percentiles
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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT
It can be seen that only 99.9th percentile Pillar 1 capital is affected by
catastrophes, and this occurs only when at least 10 of the 10,000 simulations has a catastrophic event in the previous three years. The odd shape of
99.9th percentile economic capital reflects the movement of these catastrophes through this retrospective three year window across simulations.
Figure 9.15 nevertheless shows that even 99.9th percentile Pillar 1
capital is not a good approximation to economic capital, as it is generally
too low. Moreover, as we have seen, Pillar 1 capital reacts to catastrophes after the event, when it is too late, rather than anticipating them.
9.4.5.2 Catastrophe probability increased from
0.000025 to 0.00005 per month
In this example, we double the catastrophe probability from 0.00025 to
0.0005 per month.
Note that, with the increased catastrophe probability assumption, we
expect that 0.00005 ϫ 12 ϫ 10 ϫ 10,000 ϭ 60 catastrophes will occur
in total over all of the 10,000 simulations, for the entire ten year projection term of each simulation. Therefore, for this example, we expect
catastrophes to impact 99.5th and higher percentile economic capital,
but not 99th, nor lower percentile, economic capital. Again, we expect
that catastrophes will affect economic capital at the shorter durations.
Figure 9.16 shows the results for this example.
Comparing Figure 9.16 with Figure 9.14 shows that, where 99.9th
percentile economic capital is being driven by catastrophic events, it
increases with the higher catastrophe probability and persists at the
higher catastrophic level for longer. This is simply because there are
more catastrophes around to drive up economic capital to higher levels
and for longer. As expected, 99.5th percentile economic capital is also
now being driven by catastrophes at the shorter durations, again because
of the increased numbers of catastrophes.
The lower percentile economic capital amounts, as they are not being
driven by catastrophic events, are relatively unaffected by the increased
catastrophe probability.
Pillar 1 capital increases slightly because more catastrophes occur,
giving higher claims and slightly higher technical provisions.
9.4.5.3 Non catastrophic claim probability increased from
0.0001 to 0.0002
The same numbers of catastrophes are expected in this example as for
our base case example. However, non catastrophic claims are more
likely to occur, so we expect to see economic capital increase at all those
NON PROFIT LIFE AND GENERAL INSURANCE FIRMS
159
ln Capital (£)
25
10
0
120
Duration (months)
99.9th Percentile
99.5th Percentile
99th Percentile
95th Percentile
Pillar 1 capital
Figure 9.16 General insurance economic capital versus Pillar 1
capital – catastrophe probability increased from 0.000025 to 0.00005
durations where economic capital is not being driven by a catastrophic
event. Similarly Pillar 1 capital should increase as actual claims and
technical provisions will increase.
Figure 9.17 shows the results for this example.
As the logarithmic scale makes it difficult to compare Figure 9.17 to
Figure 9.14, inspection of the capital amounts that underlie these figures
shows that, except for 99.9th percentile economic capital, all capital
amounts increase everywhere as a consequence of increasing the non
catastrophic claims probability.
Economic capital, at the 99.9th percentile level, is determined using a
relatively few number of simulations and, consequently, is volatile. For
the particular 10,000 simulations shown in Figure 9.17, economic capital consequently does not always increase with increased claim probability, relative to Figure 9.14, due to this stochastic volatility. It does,
however, increase for the majority of durations.
9.4.5.4 Standard deviation of the claim amount distribution
is increased by 50%
In this example, modeled claim amounts, whether they are due to a catastrophic event, or not, are more volatile as the claim amount standard
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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT
ln capital (£)
25
10
0
120
Duration (months)
99.9th Percentile
99.5th Percentile
99th Percentile
95th Percentile
Pillar 1 capital
Figure 9.17 General insurance economic capital versus Pillar 1
capital – non catastrophic claim probability increased from
0.0001 to 0.0002 p.m.
deviation is increased by 50%. Note that we have left the mean claim
amount value unaltered. We expect, therefore, to see economic capital
and Pillar 1 capital increase at all durations.
Figure 9.18 shows the results for this example.
Although it is difficult to see from comparing Figure 9.18 with
Figure 9.14, which shows the corresponding base case results, inspection of the underlying capital amounts shows that both Pillar 1 capital
and economic capital have increased as a consequence of increasing the
claim amount distribution standard deviation.
9.4.5.5 Rate of return on capital
For each of the 10,000 simulations, and for each example, we have
calculated the rate of return earned on capital for each of average Pillar 1
capital, 95th percentile economic capital, 99th percentile economic capital, 99.5th percentile economic capital and 99.9th percentile economic
capital. We can then study the distribution of these rates of returns on
capital over the 10,000 simulations.
Summary statistics for our base case example are shown in Table 9.7.
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NON PROFIT LIFE AND GENERAL INSURANCE FIRMS
ln capital (£)
25
10
0
120
Duration (months)
99.9th Percentile
99.5th Percentile
99th Percentile
95th Percentile
Pillar 1 capital
Figure 9.18 General insurance economic capital versus Pillar 1
capital – standard deviation of claim amount distribution
increased by 50%
Table 9.7 Rates of return on capital for base case general insurance
firm example
Capital amount
Pillar 1
Mean
Standard deviation
Skewness
Kurtosis
141%
17%
0.41
0.81
95th
99th
Percentile Percentile
economic economic
capital
capital
388%
73%
0.71
1.15
379%
71%
0.70
1.14
99.5th
Percentile
economic
capital
99.9th
Percentile
economic
capital
371%
69%
0.70
1.14
4%
0%
(0.10)
0.86
From Table 9.7, it can be seen that the rates of return on capital are
reasonably well behaved, although they are generally slightly more
positive skewed and fat tailed than for a Normal distribution.
The most striking aspect, however, is the difference between the rate of
return on 99.9th percentile economic capital and the rates of return on the
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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT
other capital amounts. The rate of return on 99.9th percentile economic
capital is very much lower than the other rates of return on capital.
It can be seen, therefore, that if firms price for extremely unlikely
risks, catastrophic risks in this example, rates of return on capital
amounts that do not reflect these unlikely risks, can be enormous.
This conclusion is predicated on the assumption that such catastrophic risk pricing will result in premium rates that are competitive
in the market place, although it is probably not likely that this will be
the case.
9.5
SUMMARY
In this chapter we have calculated both deterministic and stochastic
economic capital for a range of diverse insurance applications and have
compared our results to corresponding Pillar 1 regulatory capital requirements. Stochastic economic capital was determined using the stochastic
model developed in Chapter 7.
Our results show that the Pillar 1 regulatory capital requirements are
generally very poor approximations to economic capital and we have
illustrated the misleading impact that this can have on performance
measurement. Obviously, these results and conclusions have quite serious implications for insurers themselves, regulators, insurance firm customers and shareholders.
We now move on to consider in Chapter 10 asset management firms.
CHAPTER 10
Asset Management
Firms
10.1
INTRODUCTION
In this chapter we give a short discussion of economic capital for asset
management firms. This discussion is brief because, as we describe
below, the treatment of economic capital for asset management firms is
very similar to that for unit linked life insurance firms, as described
previously in Section 9.3.
10.2
R E G U L AT I O N O F A S S E T M A N A G E M E N T
FIRMS
It is first worth pointing out that, at least in the EU, asset management
firms are subject to the same regulatory capital regulations and requirements
as banks. That is, the EU’s implementation of the Basel 2 Accord, via its
corresponding Capital Adequacy Directive, applies to asset management
firms, as well as to banks. See Chapter 14, where this is described in
more detail. As asset management firms do not generally collect market
or credit risks, most firms will be required to set up a Pillar 1 regulatory
capital requirement for operational risk only, and this may lead to
increased regulatory capital requirements for many firms.
10.3
R I S K A N D E CO N O M I C C A P I TA L
Although asset management firms can provide a very wide range of
investment services, their business is often quite narrow comprising, in
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