Demand/Supply in Insurance

• insurance market in a country is a product of the environment in the country

• two sides of the market: supply/demand

• demand depends on price and quantity

• what is the “price” and the “quantity” of insurance bought?

How is insurance demand generated by households?

• an individual derives utility from the consumption of goods

• an individual is subject to budget constraint• insurance is an inherently intertemporal

decision• intertemporal budget constraint• an example with two periods• extended with uncertainty

a simple intertemporal model without uncertainty

u(c1, c2) = log(c1.c2) = logc1 + log c2

where c1 is consumption in period 1 and c2 is consumption in period 2

individual can convert good from period 1 to period 2 at the rate of (1+r) [r is interpreted as the rate of transformation or the interest rate]

Assuming income in period 1 is y and no income in period 2….

a simple intertemporal model without uncertainty

…we can write the intertemporal budget set as (1+r)c1 + c2 = (1+r)y + 0

Now solve for the optimal consumption pattern

c1 =

c2 =

Note that the optimal consumption pattern depends on the intertemporal “price”(what is that?) and income

a simple intertemporal model with uncertainty

In the previous model suppose that the person can die at the end of period 1 with probability 1-p

How will the utility function change?

How will the budget constraint change?

The role of the availability of insurance in the model

The role of probability/price and income in the demand function generated

Elasticities of demand: price and income elasticties

• demand elasticity of x is defined as the percentage change in the demand divided by the percentage change in x

• x can be any factor affecting demand

• what does it mean to have price elasticity of -2.5? -0.5?

• what does it mean to have income elasticity of +1? -1?

Some examples of price and income elasticities of demand

Country price elasticity income elasticity

Chile

fire -0.9 to -1.2 3.0 to 4.0

motor -0.8 2.8

Japan

fire -1.0 1.7

What do these numbers mean in terms of development and insurance demand?

By lines of business

• Personal auto, homeowners, etc are generally bought from domestic companies

• Why? Generally in OECD countries only locally operated firms are allowed to compete in compulsory nonlife business

• Changing in some European countries

• Justification: Government can keep a better tab on local insurance companies

Commercial insurance

• Less local

• Companies have more information

• They have more options

• Companies can form their own captives

• General question: If a company can diversify, why should it buy insurance in the first place?

Corporate demand for insurance

We have shown that risk averse individuals, faced with risky situations, will pay more than the expected value to transfer the loss exposure to another party

But corporations are assumed to be risk neutral

What does that imply about the corporate utility function? Marginal utility of wealth is constant

Implication of risk neutrality

utility

wealthWhat does it say about risk premium?

Is it strange to assume that corporations are risk neutral?

Definition of corporation: A legal mechanism where parties come together to produce a product or service for earning profits

Shareholders typically hire outside managers to operate the business

If shareholders are risk averse individuals, is it not reasonable to assume that owners of the firm would want to reduce risk-taking by the firms?

What a shareholder can do

• Shareholders do not need to have each individual companies to minimize risk

• They can do that on their own by holding diversified portfolios

• Therefore, owners of the firm will hire managers to maximize the expected value of the firms

(Another implication: Firms do not need to pick debt equity mix to maximize value)

So, why does the corporation buy insurance anyway?

• Insurance companies have comparative advantage in risk bearing

• The purchase of insurance can lower the costs of financial distress

• Insurers may have real-service efficiencies

• Regulation/legal requirements

• Purchase of insurance can lower the firm’s expected tax liabilities

Comparative advantage of insurance companies in risk

bearing

If…..

risk bearing can be diversified by widely dispersed ownership

Then….

Closely held corporations should have higher demand for insurance

They do! (Other parties: bondholders)

Costs of financial distress

Financial distress affects the cost of capital of the firm:

(1) If a firm has an accident, it cannot borrow money at the same cost as it did before the accident

(2) Regulators may ask a firm to have an audit

(3) Bankruptcy costs can be substantial

Real service efficiency of insurer

• Insurers provide more than simple loss reimbursement

• For example, liability insruance may provide legal defense when the insured is sued

• Insurance companies have more efficient claims management procedure

• They provide assesment of loss and methods of risk control

Under progressive income tax, insurance reduces tax

Example: A company has the following income stream: 40, 45, 50, 55, 60, 65

It suffers a loss of 45 every three years

It can buy an actuarially fair insurance for 15

Assume a tax schedule: income to 30@20% and income above 30@35%

Calculate the income streams

Assume a zero discount rate: Calculate NPV

Table 5-1:The Levered, Uninsured Firm (B=$200,t=.34)

State Pr(s) V L(s) V-L(s) D(s) Dep T(s) S(s)noloss 50% $1000 $0 $1000 $200 $400 $136 $664loss 50% $1000 $800 $200 $200 $400 $0 $0value xx $1000 $400 $600 $200 $400 $68 $332

Another example to show that tax interacts with insurance (without insurance)

Another example to show that tax interacts with insurance (with insurance)

Table 5-2:The Levered, Insured Firm

State Pr(s) V L(s) V-p D(s) Dep T(s) S(s)noloss 50% $1000 $0 $600 $200 $400 $0 $400loss 50% $1000 $800 $600 $200 $400 $0 $400value xx $1000 $400 $600 $200 $400 $0 $400

Insurance supply

• Insurance supply is a function of expected profits

• But what we observe in the market is the interaction between supply and demand

• We never observe supply by itself!

• Insurance supply is positively related to risk bearing capacity

• Risk bearing capacity depends on insurer capital and surplus

Theory of Cycles

• Insurance “capacity” (at the national level) is a function of the total capital that investors are willing to put at risk and the intensity with which managers expose the capital to risk

• If bottlenecks arise: capacity crisis-hard market

• Profit rises, prices rise-leads to more capital and eventually a soft market

What are the causes of cycles?

• Macroeconomic factors: interest rates, inflation rates, uncertainty etc.

• Regulatory factors

• Other institutional differences

• Country wide factors such as the level of education

• Openness of economy

• Presence of monopoly

Classifying companies

• Largest ones are not necessarily large international ones– Nippon, Zenyoren, Dai-Ichi, Sumitomo, Pru,

Allianz, UAP, Meiji, AXA, Met, AIG– AIG, CIGNA, Aetna, Royal, Zurich, Allianz are

truly international

• Largest reinsurance companies are Europeans• Captives

International insurance supply

• Capacity with international presence is enhanced

• Risk is spread better across borders (in the same way international portfolio of assets spreads the risks for international investment funds)

• Insurance service can be offered either by cross border insurance trade or by establishment

International insurance supply

• Establishment insurance trade is via domestic but foreign owned entity: through local agents, through authority to underwrite using branch office or through local insurer

• Countries with large international trade component has this component very large

• Holland and Singapore

Establishment of insurance trade

• Agency– typically distributes, sometimes underwrite

• branches– have local reserves

• subsidiary– domestic company wholly owned by foreign

• representative office– promotion agency

Successful international insurance lines

• Most successful– Marine, Aviation and Transport– Why?– Complexity, and the nature of business– Personal lines domestic– Why?– High local knowledge required (for verification

of the states)

Foreign acquisitions

• With trade blocks, foreign acquisitions have accelerated

• NAFTA, EU, ANZAS

• But, foreign acquisitions have not all been very successful

What are the problems in expansion across borders?

• Government regulation

• Cross corporate linkages– keiretsu: more than 80% of Japanese nonlife market

is controlled by 11 keiretsus and some of the companies are vertically linked with other companies

– chaebol in South Korea– princelings in China– Grupos in Mexico

Governmentregulation, tax

Individualsbusinesses

Reinsurers

Insurance Company

Rating agenciesbankers

Distribution: ownindependent, direct,brokers, banks

shareholders

Underwritingpricingclaims settlement

Investmentmanagement

Problem of insurance

• Pricing before claims settlement– tradeoff: investment high or risky means better

price (premium) but may mean higher possibility of low return (or zero return!) however, if the investment is low, premium would be higher than otherwise

– Similarly, high discount rate may be prudent but bad for business!

Who handles internal matters?

• Actuary– does not have to be local except for regulatory

reasons

• Underwriter

• Claims personnel– have to be people on the ground

• Investment manager– can be global

Customer interface

• Direct solicitation

• agents are representative agents of insurer

• brokers are representative of customers

• tied agent

• independent agent

• bank-insurance nexus: bancassurance– ING