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NON PROFIT LIFE AND GENERAL INSURANCE FIRMS



153



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



158



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



160



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.



161



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



162



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

163



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