Economics of Insurance

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Economics of Insurance

• Lecture 4
• Reducing Insurance Company Risk and Catastrophes

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Lecture 4 More method of reducing or avoiding
risk
Ensuring the survival of an insurance company
Last week, we showed that insurance company risk,
in situations where underlying client risk was
well known, was based on the variability of claim
numbers.
On the assumption that claim numbers were
normally distributed around the mean number of
claims (determined by underlying probabilities),
companies could manage the risk with a
quantifiably sized reserve fund.
This fund mainly consisted of premiums charged
but not yet used to pay compensation (unearned
premiums). This arose because of the LAG between
premium payment and likely compensation payment.
The calculation of such funding for excess claims
is known as RESERVING. Insurance companies are
also required to carry direct financial
reserves. There are legal regulations underlying
the size and calculation of reserves.
BUT THE MAIN POINT IS THAT THE FIRST METHOD
COMPANIES USE TO REDUCE RISK OF INSOLVENCY IS TO
CARRY RESERVES.
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Lecture 4 More method of reducing or avoiding
risk
VARIETY OF RISK
A company underwriting a variety of types of risk
reduces risk of insolvency or serious loss of
profit through excess claims
Suppose an insurance company insured cars
AND housing
In any year excess claims on, say, house
insurance would probably not coincide with excess
claims on motor insurance
So the unexpected claims submitted by
householders could be paid for by the premium
income from motoring insurance
(Provided that motoring risk was unrelated to the
risk of theft or damage to household contents)
And vice versa when motor insurance claims are
excessive but house claims normal
Risk of excess claims would be reduced through
DIVERSIFICATION.



Each company would have a diversified RISK
PORTFOLIO
This works to the extent that risks are
NEGATIVELY correlated
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Lecture 4 More method of reducing or avoiding
risk
Profits and diversification
Notice what this does to our profits identity
E ( ? )    R    E(G)    A     v.V 
V,
the size of the nominal reserve fund now depends
on
The ratio of standard deviation to mean
(which in turn depends on the number of clients,
n)
and
The COVARIANCE of claims of different types
Diversification works to the extent that risks
are NEGATIVELY correlated
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Lecture 4 More method of reducing or avoiding
risk
Covariance and risk
If claims on the two funds are negatively
correlated
covariance will be negative
so risk will be reduced
so in the profits identity
E ( ? )    R    E(G)    A     v.V 
V will be reduced for any given underlying
(i.e.client) risk
and profits per client will be higher
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Lecture 4 More method of reducing or avoiding
risk
Risk swapping
Risk swapping between insurance companies
reduces riskiness
It effectively diversifies risk between the two
companies
each of two primary insurance companies
transferring part of their compensation liability
to the other company.
But enables each company to retain its special
expertise in a narrow area.
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Lecture 4 More method of reducing or avoiding
risk
REINSURANCE
A reinsurance company INSURES INSURANCE
COMPANIES It POOLS the risk of all participating
PRIMARY companies.
It can compensate one primary company for excess
claims in a particular year from the pool of
premiums from other companies who do not have
excess claims
Risk of excess claims is reduced through a
diversified portfolio of primary insurance
companies.
This diversification is what gives reinsurance
companies a comparative advantage over primary
companies and so enables them to maintain a
profitable trade.
Worlds Top 10 Re-insurers (m premiums
written).2001  
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Lecture 4 More method of reducing or avoiding
risk
CATASTROPHES
An assumption (explicit in Lecture 3) made so far
is that
Primary claims arise from large numbers of
independent events normally distributed
Catastrophes, such as hurricanes, create serial
damage, each claim arises from same event. So the
claims are NOT INDEPENDENT and not normally
distributed.
So claims are not easily manageable.
Could in fact destroy insurance companies e.g.
Hurricane Andrew in 1992 created such widespread
damage it nearly bankrupted a big US insurance
company Allstate
It is generally considered that for an event to
be a catastrophe there also has to be a high
value of compensation claims
One bad event cannot be balanced against many
other good events
Hurricane Andrew 1992
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Lecture 4 More method of reducing or avoiding
risk
REINSURANCE AND CATSTROPHES
Reinsurance can POOL catastrophic risks
Hurricane in Florida can be set against non
happening of an earthquake in Tokio
BUT reinsurance companies must


BE BIG

HAVE A GEOGRAPHICALLY

DIVERSIFIED RISK PORTFOLIO

HAVE A DIVERSE TYPE OF

RISK PORTFOLIO
Hence their size and status
But cant pool SYSTEMIC WORLD WIDE RISK

Climate
deterioration Political cataclysms such as war,
occupation or terrorism
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CATSTROPHE BONDS
Lecture 4 More method of reducing or avoiding
risk
Worldwide risks now so big that companies seek to
use equity markets to finance insurance or
securitize risks
For example, reinsurance companies can issue
CATASTROPHE BONDS.

INVESTORS buy apparently high yield
bonds from the reinsurance company against a bad
event and - Lose all or
some of their investment if the bad event
occurs Receive their stake back plus their
return if no bad event happens
Cat bonds raises cash and divest reinsurance
companies of some risk
BUT cat bonds have perverse informational effects
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Lecture 4 More method of reducing or avoiding
risk
Risk reduction and avoidance and profits
Methods outlined in this lecture will of course
have costs, and these will effect insurance
company profitability.
Simplifying methods discussed previously into the
use of reinsurance, our accounting definition of
company profits now becomes
E ( ? )    R    E(G)    A     v.V    E(U) 
  u.U
Where E(U) is the expected value of compensation
from the reinsurance company to the primary
company
u.U is the premium payments from the primary
company to the reinsurance company
There is not, at present, a general formula to
determine optimum proportions of reserves to
re-insurance.