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Adding time diversification
to risk diversification
Presented by Michel M. Dacorogna
Moscow, Russia, April 23-24,2008
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Although all reasonable care has been taken to ensure the facts stated herein are accurate and that the opinions contained herein are fair and
reasonable, this document is selective in nature and is intended to provide an introduction to, and overview of, the business of Converium. Where
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available information. These statements are often, but not always, made through the use of words or phrases such as 'expects', 'should continue',
'believes', 'anticipates', 'estimated' and 'intends'. The specific forward-looking statements cover, among other matters, the reinsurance market, the
outcome of insurance regulatory reviews, the Company's operating results, the rating environment and the prospect for improving results, the amount
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and uncertainties. Actual future results and trends could differ materially from those set forth in such statements due to various factors. Such factors
include general economic conditions, including in particular economic conditions; the frequency, severity and development of insured loss events
arising out of catastrophes; as well as man-made disasters; the outcome of our regular quarterly reserve reviews, our ability to raise capital and the
success of our capital improvement measures, the ability to exclude and to reinsure the risk of loss from terrorism; fluctuations in interest rates;
returns on and fluctuations in the value of fixed income investments, equity investments and properties; fluctuations in foreign currency exchange
rates; rating agency actions; the effect on us and the insurance industry as a result of the investigations being carried out by US and international
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Please further note that the Company has made it a policy not to provide any quarterly or annual earnings guidance and it will not update any past
outlook for full year earnings. It will however provide investors with perspective on its value drivers, its strategic initiatives and those factors critical to
understanding its business and operating environment.
This document does not constitute, or form a part of, an offer, or solicitation of an offer, or invitation to subscribe for or purchase any securities of the
Company. Any securities to be offered as part of a capital raising will not be registered under the US securities laws and may not be offered or sold in
the United States absent registration or an applicable exemption from the registration requirements of the US securities laws.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
2
Agenda
1
Bank and insurance as risk bearer and the
challenges ahead
2
The example of natural catastrophes reserving
3
An investors’ perspective on catastrophe risks
4
Conclusion and perspective
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
3
Changing Risk Landscape
Peak risks are growing due to:
Demographic changes: concentration of population in hazardous
areas, movements of populations favors the spread of diseases
(AIDS, SARS, …)
Social & political changes: better leaving standards, more demanding
people (e.g. liability), changing of legal systems, terrorism, political
instabilities in oil rich regions, …
New technologies could bring along new risks: nanotechnology,
cellular phones, new drugs (VIOXX) …
New financial products (especially in life insurance and credit)
More demanding & more attentive stakeholders: policyholders
concerned with financial stability, regulators revisit insurances,
better informed investors (Return on Equity ROE).
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
4
250 billion –trillion More than 1 trillion
50-250 billion
10-50 billion
The 26 Core Global Risks: Likelihood with Severity by
Economic Loss
Retrenchment from
globalization (developed)
Asset price collapse
Slowing Chinese economy (6%)
Oil and gas price spike
Infectious disease, developing
Pandemic
world
CII breakdown
Transnational
Chronic disease, developed world
crime and
corruption
Middle East instability
Cyclone
NatCat:
Heatwaves & droughts
Earthquake
Liability
NatCat:
Major fall in US$
regimes
Interstate & civil wars
Retrenchment from globalization (emerging)
Fiscal crisis in
Food insecurity
advanced
Extreme climate change related weather
economies
NatCat:
Emergence of
Failed & failing states
Extreme
nanotechnology risks
inland
International terrorism
flooding
Loss of freshwater
Collapse of NPT
2-10 billion
Severity (in US$)
New Risks are Multiplying with Varying
Severity and Likelihood
below 1%
1-5%
5-10%
Likelihood
10-20%
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
above 20%
5
Urban population concentrates
in riskiest areas
Source : Sherbinin, Shiller & Pulsipher (2007)
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
6
Number of Terrorist Attacks is Rising Dramatically
Number of international (since 1968) and domestic (since 1998) incidents
INCIDENTS
5000
4000
3000
2000
1000
0
Source: MIPT terrorism knowledge base
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
7
Issues in Risk Management
Society is asking more and more financial markets and
insurances to be the main providers of risk mitigating solutions
as far as the financial impact of risk is concerned.
However, the finance service industry and particularly insurers
are faced with two major issues in risk management:
1. New regulation: Basel II (banks) and Solvency II (European
insurers)
2. New accounting rules: IFRS
Academic research should help the industry facing them by
providing better tools and models.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
8
Challenge for the
Financial Service Industry
Both questions challenge the industry and the academic world in
terms of the methods used to model for instance operational risk or
in the insurance industry to account for the reserves.
Often the rules applied to insurers are derived from those applied
to banks because the latter have already been in place for a few
years and have been quite successful.
After all they are both risk bearers. Aren’t they?
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
9
Banks and Insurers as Risk Bearers
Banks have traditionally been taking credit risks on their books in
their wholesale lending operations, but also market risks through
their securities trading operations.
Insurers and reinsurers have been taking most other kinds of
risks: mortality and interest rate risks for life insurers, natural
disasters, liability and accident risks for non-life insurers.
The traditional providers of risk management solutions are
investment banks and reinsurers.
Recently, banks by securitizing most of their credit risks are
moving away from their traditional risk bearing function.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
10
Banks and Insurances
as Risk Bearers (continued)
For banks the risk assumption on the balance sheet is only a
small part of their activity; the main activities are intermediation
and other services.
The investment bank is a sort of broker (financial intermediary) to
access the financial markets. It is taking little risk except when
trading securities for its own account.
The reinsurer on the other hand provides its own capital and
balance sheet to carry the risk. It is a sort of risk warehouse and
risk appears on both sides (asset and liability) of its balance
sheet.
That is why capital-to-asset ratio is substantially higher for nonlife insurers, somewhat smaller for life insurers, but still higher
than for banks.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
11
Regulators and Accountants
Regulators want insurers to develop internal models for riskbased capital (RBC) (first and second pillar of Solvency II).
Accountant standard setters want insurers to mark-to-market
their assets (IAS 39) and eventually their liabilities.
Most of those rules are inspired by the bank regulations and
accounting.
The purpose is to protect the policyholders (regulators) and to
bring more transparency in the value creation of the industry
(accountants).
Is the industry ready for these challenges?
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
12
Challenges and Questions Ahead
First of all, the insurance industry needs still to adopt a common
language and disseminate best practices to build models.
Are we able to model the complexity of the business and the
risks to a good level of accuracy? Do we have the methods and
data in place?
Is the requirement for transparency (Pillar III of Solvency II and
IFRS) going too far and introducing artificial volatility?
Is the principle of conservatism in accounting still followed:
“anticipate no profit but anticipate all losses”, when using
probabilities or NPVs in balance sheets?
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
13
More Questions and Challenges
Are we insuring verifiability and limiting the amount of discretion
that managers may exert in deciding what the “right” numbers
are: marking-to-market the liabilities might open Pandora’s box ,
because there is no financial market for insurance liabilities?
Despite their obvious similarities, have we really considered the
major differences between banking and insurance?
In insurance reserving is crucial and very difficult. Insufficient
reserves account for two third of insurance insolvencies.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
14
The Example of CAT Reserving
Reserving for natural catastrophes (CAT Reserving) is a good
example of the problems that face the insurance industry in
applying the new accounting rules
US-GAAP and the new IFRS rules do not allow to carry over
reserves for future business. If no loss has occurred during the
year then the reserves must be released: equalization reserves
are not allowed anymore
Two main arguments speak for the introduction of those rules:
1.
It is in the interest of shareholders to diminish the amount of free
cash flows at the disposal of managers for fear of misuse.
2.
Moreover, the tax authorities want to avoid artificial reserve
increases that diminish tax payment.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
15
Agenda
1
Bank and insurance as risk bearer and the
challenges ahead
2
The example of natural catastrophes reserving
3
An investors’ perspective on catastrophe risks
4
Conclusion and perspective
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
16
Premiums and Claims
We have seen that insurance premiums are computed on the
basis of the expected loss:
Premium = Expected Loss + Cost of Capital + Expenses
It is in the nature of CAT business that most of the time the
claims will be much below expectation
Once in a while though, a catastrophe will occur with claims
much above expectation and the yearly premiums would not
suffice to cover the liabilities
To survive such situations, insurance companies have learned to
diversify their risks
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
17
Mitigating Catastrophic Risks
Diversification is usually thought in terms of geography and of
type of risks.
For instance a reinsurance company would reinsure European
windstorm and Japanese earthquakes as well as American
hurricanes.
Given this type of risk, geographical diversification will not suffice
to avoid large fluctuations in the results, as we have seen
recently.
Uncertainty in the results is penalized by investors. They will
require higher reward for their investments.
This will, in turn, increase the cost of insurance policies.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
18
Time Diversification Helps
Traditionally, insurers have built equalization reserves to dampen
the effects of natural catastrophes on their balance sheet.
This is nothing else than diversifying the risk over time.
Some countries particularly exposed to catastrophic risks like
Japan even require their insurance companies to hold
equalization reserves.
The idea is simple: the years without natural disaster are used to
build up reserves for the years where such a catastrophe occurs.
Since the probability of occurrence is low, it is possible on
average to build substantial reserves before large claims
happen.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
19
Capital or Reserves, That is the Question !
The argument against equalization reserves is that capital is
here to be used when the premiums do not cover the claims.
If not actively invested, analysts would argue that capital should
be given back to shareholders and again raised only when it is
needed.
Unfortunately, if an insurance company tries to tap the market
when it is known to have several hundred million dollars of
claims to pay, it finds:
That there is less cash available from the market; and
That the cash that can be found is much more expensive than
keeping it on the balance sheet.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
20
Time Diversification is also Good
for Long-Term Investors
Clearly, it is to the benefit of the policyholders to keep an extra
cushion.
Is it also true for shareholders?
For short-term investors: the chances of getting high returns is
bigger, if reserves are released at the end of the year.
For long-term investors: the volatility incurred by an insurer that
releases its CAT reserves every year is high, thus the Sharpe
Ratio of the investment will be lower.
The extra-cash kept in the reserves differs from the capital:
1.
2.
it is not rewarded at the cost of capital and
no new risk is written against it.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
21
Agenda
1
Bank and insurance as risk bearer and the
challenges ahead
2
The example of natural catastrophes reserving
3
An investors’ perspective on catastrophe risks
4
Conclusion and perspective
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
22
An Illustrative Example
In a simple example we illustrate the view of a long-term investor:
We consider two companies that write only CAT risk against an
initial capital of 100,000 USD.
One company follows US-GAAP and the other one is allowed to
keep equalization reserves (time diversification).
We compute the yearly return on equity (ROE), Ri, which an
investor would make by investing in such companies (all profits are
paid as dividends) over a long period (10 to 30 years).
We also compute the Sharpe Ratio, S, for both investments
assuming a risk free rate (R0) of 3% and computing:
E[ Ri  R0 ]
S
 ( Ri  R0 )
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
23
Business Cycles and Cost of Capital
We introduce business cycles by assuming softening of the
market if the previous loss ratio is below 60%. The price is then
reduced by 20% for the next year.
The hardening of the market is modeled by a price increase of
200% if the previous loss ratio has reached 150%.
The cost of raising new capital is put at 5% of the sum raised,
which corresponds to the usual investment bank fees. We
neglect other costs due to distress.
The company is allowed to keep equalization reserves up to an
amount equivalent to the expected loss minus the paid losses.
The cumulated reserves are not allowed to exceed the
VaR(1%), i.e. 100,000 USD.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
24
Performance Comparison in a
Simple Deterministic Model
Models
US-GAAP
Sharpe Ratio
ROE
No Cycle Recapitalization
0.57
15.00%
1.26
15.00%
0.53
14.70%
1.25
14.90%
No recapitalization
0.46
13.23%
1.27
14.90%
Recapitalization
0.39
13.32%
0.63
13.32%
Recapitalization
Cycle
Time Diversification
Sharpe Ratio
ROE
with costs (5%)
Recapitalization
with costs (5%)
0.37
12.90%
0.61
13.20%
Recapitalization
with costs (5%) and taxes (25%)
0.15
4.90%
0.30
5.70%
Recapitalization
with costs (5%), taxes (25%) and interest (3%)
0.14
4.91%
0.29
5.89%
No recapitalization
0.17
5.79%
0.60
12.30%
No recapitalization with taxes (25%)
-0.03
-0.88%
0.28
5.10%
No recapitalization with taxes (25%) and interest (3%)
-0.05
-1.68%
0.25
4.78%
In all cases, the time diversification company presents better Sharpe
Ratios and most of the time better ROEs over 10 years (large loss 7th
year).
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
25
The Stochastic Models
We model the risk with a lognormal distribution:
f ( x) 
1
2 x
 (ln x   )2
e
2 2
The parameters are chosen so that the Value-at-Risk (VaR) at
the 1% level always equals 100,000 USD, assuming that this is
the risk-based capital (RBC).
We vary the coefficient of variation
allowing for various tails
to the distribution but keeping the same VaR.
The premium is computed according to the technical price:
Expected Loss + 15% of the RBC + Expenses
Expenses are taken to be 5% of the expected loss.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
26
The Stochastic Model (Fréchet Distribution)
We use also a fat-tailed distribution, the Fréchet distribution:
0,
x0


  x   
 , s ( x )  
exp    s   , x  0
   

1
We compute the expectation: E  , s   s  G 1  
 
1
G(1  )
1

And the expected shortfall: ES  , s ; r   s  G(1  ,  ln r ) 

1 r
z
Where G(a,z) is the incomplete gamma function:
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
a 1  x
x
 e dx
0

a 1  x
x
 e dx
0
27
Influence of the Parameters of the Distribution
on the Expected Shortfall
Lognormal distribution
Fréchet distribution
For all parameters the VaR
at 99% is 100’000
For all parameters the VaR
at 99% is 100’000
CoV
10
1
0.1
0.01
Expectation
6'787
20'388
79'686
97'705
ESF
192'346
135'788
104'288
100'430
Alpha
1.1
1.3
1.5
1.9
Expectation
ESF
16'041 1'104'613
11'465
434'696
12'476
300'755
16'607
211'490
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
28
Buildup of the Reserves Over Time
For Lognormal Ditributions
100'000
Expected Amount of Reserves
CoV=10
Cov=1
80'000
CoV=0.1
CoV=0.01
60'000
40'000
20'000
0
0
5
10
15
20
25
30
Years
We use 10,000 simulations over 30 years
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
29
Buildup of the Reserves Over Time (II)
For Fréchet Ditributions
Expected Amount of Reserves
100'000
80'000
60'000
40'000
alpha=1.1
alpha=1.3
20'000
alpha=1.5
alpha=1.9
0
0
5
10
15
20
25
30
Years
The CAT reserves’ buildup behavior is complex and depends on
the fatness of the tails of the distribution
(limit 100,000 USD).
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
30
Simulation Results
We simulate 10,000 times a period of 30 years and look at the
results for two corporate finance metric the Sharpe ratio of the
shareholder investment and the call option based on Merton’s
model.
We see that the company can on average build up sufficient
equalization reserves if the tails are sufficiently fat.
The fatter the tails the faster the equalization reserves buildup
for both stochastic processes.
We see that with both investment metrics the US-GAAP
company is valued lower than the company allowed to keep
reserves over time.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
31
Comparison of Sharpe Ratios
Lognormal
Cov
Fréchet
Alpha
10
73.2%
1.1
82.3%
1
96.3%
1.3
76.3%
0.1
97.7%
1.5
82.5%
0.01
100.0%
1.9
89.5%
In general, the Sharpe ratio for time diversified companies
is better than for US-GAAP companies.
The percentages are influenced by what happens at the
beginning of the experiment. If the company is bankrupted
after one or two years the US-GAAP company is better off.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
32
The Merton Model Applied
to CAT Reserving
The Merton model views the share as a call option on the assets
of a company.
In this case, we value the call options using the NPV of the cash
flows over 30 years of both the time diversified company and the
US-GAAP company.
We discount the cash flows with a risk free rate at 3%.
The result is that the option for the time diversified company has
a higher value than the one of the US-GAAP company, in line
with our Sharpe ratio results.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
33
Costs and Benefits of
Setting up Cat Reserves
The economics literature discusses two types of cost that could
play a role in the determination of the optimal amount of cat
reserves:
1.
“Agency Costs of Free Cash Flows” (Jensen, AER, 1986)
Instead of paying out free cash flows to shareholders, managers
might use “free money” to engage to investment activities that
(unverifiably) are not in the best interest of shareholders (e. g.
negative NPV “empire building”, unduly diversify operations).
2.
“Costs of Financial Distress” (e. g. Warner, JoF, 1977)
Companies in distress face constraints on operating and
investment decisions (imposed by regulators, creditors, nervous
shareholders) that may prevent even good investment decisions.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
34
Tradeoffs between Agency & Distress Costs in
Cat Insurance
Higher cat reserves potentially accentuate the agency problem
of free cash flows:
More cat reserves increase the amount of “free money” available
for empire building.
Higher cat reserves potentially mitigate the financial distress
costs:
More cat reserves diminish the likelihood of the firm running into a
distress situation.
An Open Question:
How does the new cat risk modeling technology affect the optimal
amount of cat reserves that insurers should set?
The answer…
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
35
Consequence of CAT Modeling
The new catastrophe modeling technology has been
standardized and made the measurement of catastrophic risk
exposure more transparent :
This diminishes the potential for the abusive setting or using of
catastrophe reserves (for empire building, for engaging in or hiding
negative NPV projects, for tax evasion etc).
The existence of standard cat modeling tools
and the application of financial valuation over
the long-term reinforce the argument for
allowing cat reserves – even from a
shareholder’s view
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
36
Agenda
1
Bank and insurance as risk bearer and the
challenges ahead
2
The example of natural catastrophes reserving
3
An investors’ perspective on catastrophe risks
4
Conclusion and perspective
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
37
Conclusion
It is dangerous to simply apply rules designed for banks on
insurance risks.
To mitigate risks insurers need all the diversification they can get
including time diversification.
New technology allows for more transparency without
abandoning some old prudent habits (equalization reserves).
The integration of risk management, however, will demand more
and more solutions that should imply a strong cooperation
between insurances, banks and academics.
The lack of capacity requires also that financial markets bear
some of the risks instead of the reinsurers.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
38
Outlook
There are three important axis of development for research in risk
management:
1.
Develop the stochastic models to truly multi-period models where
time plays a key role.
2.
Apply financial valuation methods to risks: this will accelerate the
transfer of risks to financial markets and thus open up new
investment opportunities.
3.
Fully integrate the concepts of fat-tails and non-linear dependence
in the pricing of risks.
Progress in this field can only help us coping with the growing
risks and offer further economically sound risk management
solutions.
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
39
Looking for New Risk Transfer Avenues
Capital
Market Risks
Insurance
Risks
Insurance /
Reinsurance
“Securitization”:
Insurance-linked
securities (CatEPut,
Surplus Notes)
Investment /
Hedging
Securitization, CAT
bonds, longevity bonds,
etc.
(Re)Insurance
Balance sheets
Capital Markets
Economy of Risk in Insurance
Michel M. Dacorogna
April 23-24, 2008
40