1 15.3 bearing and eliminating risk why do people buy insurance? why do people buy extended...
TRANSCRIPT
1
15.3 Bearing and Eliminating Risk
•Why do people buy insurance?•Why do people buy extended warranties?•Why are extended warranties so expensive?•What is a reasonable extended warranty?
These questions are answered by:1)Actuarially Fair Insurance2)Risk Premium
2
15.3 Actuarially Fair Insurance
Actuarially Fair Insurance-insurance where the premium is equal
to the expected value of the payout
)()(
)(
payoutfpayoutAFI
payoutEAFI
3
Risky Income: p($100,000 )=0.2, p($25,000)=0.8
1) Calculate Actuarially Fair Insurance Premium
Actuarially Fair Insurance Example
Assume that you could buy fire insurance. You have a $100,000 job, and an 80% chance to lose $75,000 (house fire). Your utility is U=√I.
000,60$
)8.0)(000,75($
)(
AFI
AFI
payoutEAFI
4
U=√I Risky Income: p($100,000 )=0.2, p($25,000)=0.8
2) Utility without Insurance
Actuarially Fair Insurance Example
If you didn’t get insurance, your utility would be:
7.189)(
)8.0(000,25)2.0(000,100)(
)()(2/12/1
UE
UE
UUfUE
5
U=√I Risky Income: p($100,000 )=0.2, p($25,000)=0.8Insurance: $60,000
2) Utility with Insurance
Actuarially Fair Insurance Example
With fair insurance, your utility would be:
200)(
)1()000,40()(
)8.0()000,75000,60000,25(
)2.0()000,60000,100()(
)()(
2/1
2/1
2/1
UE
UE
UE
UUfUE
6
Income
Utility
Uinsure
25K $40K=E(I) 100K
U
0
AFI gives you the expected income of a risky situation
D•
Chapter Fifteen
Actuarially Fair Insurance
Uno insure
7
15.3 Is Insurance ever Fair?
Actual insurance premiums are rarely actuarially fair, partially due to a firm making profit, but also due to other factors: •administration•moral hazard•adverse selection(which will be covered later)What is the maximum amount someone will pay above actuarially fair premiums?
8
15.3 Risk Premium
Risk Premium-Maximum amount of money that a
risk-averse person will pay to avoid taking a risk
-Maximum amount a person will pay in premiums above actuarially fair
premiums
Note: Even risk loving people consider themselves risk averse for large purchases.
9
Income
Utility
E(U)
E(I)
U
0 Is
Risk premium = horizontal distance ED
DE• •
Chapter Fifteen
Risk Premium
10
Calculating Risk Premium
1) Calculate E(I) of risky choice.
2) Calculate E(U) of risky choice
3) Calculate sure income Is of E(U)
4) Risk Premium = E(I)- Is
5) Conclude
11
U=√I Risky Income: p($100,000 )=0.2, p($25,000)=0.8
1) Calculate E(I) of risky choice
Risk Premium Example
000,40$)(
)8.0(000,25$)2.0(000,100$)(
)()(
IE
IE
IIfIE
2) Calculate E(U) of risky choice
7.189)(
)8.0(000,25)2.0(000,100)(
)()(2/12/1
UE
UE
UUfUE
12
U=√I Risky Income: p($100,000 )=0.2, p($25,000)=0.8E(I) = $40,000 E(U) = 189.7
3) Calculate Is of E(U)
Risk Premium Example
s
s
s
I
I
IUE
986,35$
7.189
)(
4) Calculate Risk Premium
014,4$
986,35$000,40$
)(
RP
RP
IIERP S
13
This person would spend a maximum of $4,014 above actuarially fair insurance premiums to avoid the risk in his job.
This person would accept a job paying at least $35,986 instead of taking the risky job.
Risk Premium Example
•This person is willing to buy additional insurance against his risky job
14
Income
Utility
E(U)
25K E(I) 100K
U
0
4,014
IS
Risk premium = horizontal distance $4,014
DE• •
Chapter Fifteen
Risk Premium
15
15.3 Administration and Profit
Providing insurance isn’t free, there are administration costs:•Paying employees•Overhead•Legal Costs•Etc
Insurance firms also desire profits. Many extended warranties carry 40%-80% profit margins.
Loading Fee = Actual Premium – Actuarially Fair Premium
-Average loading ratio (actual premium/fair premium) for private US insurance companies is 1.2 (Phelps 2003)
-(typical laptop service plan is $200 for 3 years, working out to a Loading Ratio of 4.0 – 10% failure rate in year 2 and 3 for $500 laptop)
-keep in mind administration costs
15.3 Loading Fees
17
15.3 Asymmetric Information
Part of the additional costs of insurance, as well as items such as deductibles and mandatory insurance, arises from:ASYMMETRIC INFORMATION – when one party has information not available to another party•Typically, the person being insured has information the insurance company doesn’t:1)Hidden actions – Moral Hazard2)Hidden information – Adverse Selection
If people have insurance, their actions may change in two ways:
1)They are riskier (take laptop to beach, eat unhealthy – health insurance)
2)They over consume insurance since it’s free (Send laptop to be fixed, ask for unneeded tests based on “House” – health insurance)
This second effect can be shown through supply and demand:
15.3 Moral Hazard
19
D=MB
S=MC (constant)P0
Q
P
With insurance, repairs cost P1 and Q1 are made (where new S=D). This causes repair expenditures
of Area A +B (expenditures increase).
Without insurance, repairs
cost P0 and Q0 repairs are made
(where S=D).This causes repair
expenditures of area A.A B
Q0 Q1
P1
20
D=MB
S=MC (constant)P0
Q
P
The insurers are forced to cover waste, therefore insurance premiums increase.
This overcomsumption
causes deadweight loss where MC>MB:
DWL
Q0 Q1
P1
Moral Hazard can be decreased by:A) Including “reckless” situations that
invalidate warranty ie: Casio Calculator Warranty:
“The customer shall NOT have any claim under this warranty for repair or adjustment expenses if:”
1)The problem is caused by improper, rough or careless treatment;
2)The problem is caused by a fire or other natural calamity;
15.3 Fighting Moral Hazard
3) The problem is caused by improper repair or adjustment made by anyone other than a CASIO Service Center;
4) The problem is caused by battery leakage, bending of the unit, broken display or key;
5) The battery is damaged or worn…7) The proof of purchase is not presented
when requesting service-although it can be hard to prove that a
customer has been “reckless”: “Of course I didn’t drop my ipad!”
15.3 Fighting Moral Hazard
B) Introducing a cost to claim the warranty/insurance.
ie:1)Deductible2)Shipping Costs3)Cost of time
Long repair time Hard-to-get-to repair location
15.3 Fighting Moral Hazard
Insurance can break down due to Adverse Selection – an increase in insurance premium increases the average risk of the insured
Assume there are 3 laptop purchasers:Bill has a laptop failure rate of 10%
(he’s a computer technician)Charles has a laptop failure rate of 20%
(he’s average)Denis has a laptop failure rate of 30%
(he clicks on all the “you won” pop-ups)
15.3 Adverse Selection
Recall that actuarially fair insurance just charges enough to over expected repairs
AFI = ($500xP(failure)):Bill: $50Charles $100Denis $150
If you charge:$50 – Charles and Denis cause a loss$100 – Bill doesn’t want insurance and
Denis causes a loss$150 – Charles and Bill don’t want
insurance
15.3 Adverse Selection
If insurance is optional, those with higher risk would buyThis leads to more expensive claimsThis leads to higher premiumsThis leads to more people not buying
insuranceThe end result would be
UNDERPROVISION of insurance
15.3 Adverse Selection
5 Issues can keep Adverse Selection from killing a private insurance market:
i) Risk Aversionii)Group Insuranceiii)Insurance Choiceiv)Risk Categories/Risk Profilingv)Mandatory Insurance
15.3 Adverse Selection
i) Risk Aversion
Because people are risk averse, they are willing to pay a RISK PREMIUM above the actuarially fair premium.This may keep more people in the
marketii) Group Insurance
Larger companies can offer group insurance plans that automatically cover everyone (high and low risk)This doesn’t help small firms or the self-
employed
iii) Insurance ChoiceIf different levels of insurance at different
costs are offered, people will self-sort themselves into different categories:
Denis will pay $150+ for the full insurance (ie: Product Replacement Plan)
Charles will pay $100+ for partial insurance (ie: Product Service Plan)
Bill will pay $50+ for limited insurance (ie: manufacturer warranty included in price)
iv) Risk CategoriesAdverse selection occurs due to
asymmetric info – inability to know a person’s risk
HOWEVER, a company can charge premiums based on OBSERVABLE characteristics statistically linked to UNOBSERVABLE riskie: Male 20-year olds pay more for auto
insurance because they are STATISTICALLY more likely to have an accident than Female 20-year Olds
iv) Risk Profiling?The Supreme Court of Canada ruled this does
not violate the Canadian Charter of Rights and Freedoms because there is statistical evidence that 20-year-old males do have higher loss probabilities
Some ask how long until we are charged based on:EthnicityReligionSexual Orientation (marital status already
applies)If there is statistical evidence?
v) Manditory InsurancePublic Health Insurance, Car insurance, etc
is MANDATORY, and therefore Adverse selection is avoided since the low risk individuals can’t drop out
PRO’s:Mid and High-risk individuals are covered
at a reasonable rate ($100 in our example)Con’s:Low risk individuals would rather not be
covered at a high rate (for them)
Risk can also be managed through:Diversification – Reducing risk by
allocating resources to a variety of activities whose outcomes are not closely related
ie:a)Stock Market – buying a variety of stocksb)Sales – selling a variety of productsc)Insurance – buying a variety of good
without the warranty.
15.3 Diversification – Insurance Alternative
Diversification works because of:Law of Large Numbers – as the number
of samples increases, the average of these samples is likely to reach the mean of the whole population (investopedia)
ie: Stock has 50% fail rateFull fail chance of 1 stock = 50%Full fail chance of 2 stocks* = 25%Full fail chance of 8 stocks* = 0.39%
*stocks must be unrelated
-extreme outcomes reduce, expected outcome increases
15.3 Law of Large Numbers
Assume: You spend $5000 on electronics over 10 years, with an average FULL failure rate of 10%
No Extended Warranty: You spend $500 on repairs and replacement E(repair)=cost * f(cost)E(repair)=$5000 * 0.10 = $500
Extended Warranty: You spend $1000 on extended warranties (assume 50% profit margin)
15.3 Diversification – Extended Warranties
Probabilities can be combined with Game trees from chapter 14A player who MAKES decision is
replaced by an outcome that is chosen by chance
These game trees or decision trees can be FOLDED BACK in a method similar to backward induction to reduce the tree to the simple trees seen in chapter 14:
15.4 Risk and Game Trees
Circles represent CHANCE NODES (choices made by chance), while squares represent DECISION NODES (choices made by players).
15.4 Risk and Game Trees Example 1
Chance Nodes are FOLDED BACK by replacing them with the expected payoff:
E(B)= Σ$f($)=0.5($50)+0.5($10)=$30
15.4 Risk and Game Trees Example 1
Now new best responses lead to an overall Equilibrium
15.4 Risk and Game Trees Example 1
Sometimes the process takes multiple steps
15.4 Risk and Game Trees Example 2
1) Backward
induction of E and F
2) Expected return of B and C
15.4 Risk and Game Trees Example 2
30$)(
)5.0(10$)5.0(50$)(
($)$($)
IE
IE
fE
25$)(
)5.0(20$)5.0(30$)(
($)$($)
IE
IE
fE
3) Expected Return of D
15.4 Risk and Game Trees Example 2
30$)(
)5.0(10$)5.0(50$)(
($)$($)
IE
IE
fE
35$)(
)5.0(20$)5.0(50$)(
($)$($)
IE
IE
fE25$)(
)5.0(20$)5.0(30$)(
($)$($)
IE
IE
fE
4) Final Backward Induction
15.4 Risk and Game Trees Example 2
This previous example highlights the VALUE OF INFORMATIONThe firm expected return increases by $5
(million) if it is able to do a free testThe firm will pay up to $5 million for the
testValue of Perfect Information – increase in a
decision maker’s expected payoff when they can conduct a costless test to determine the outcome of a risky event
VPI = E($)with test- E($)without test
15.4 Value of Information
People pay money for information in a variety of ways:
1)New house inspections2)Car inspections3)Consumer Report subscriptions4)Online dating sites5)Etc.
15.4 Value of Information Examples
1) P(a) = Prob(a) = probability that event a will occur2) E($) = Σ$f($)3) E(U) = ΣUf(U)4) People can be risk averse, risk neutral, or risk
loving depending upon their preferences between certain and uncertain incomes.
5) Actuarially Fair Insurance=E(loss)6) Most people are willing to pay a RISK PREMIUM
above Actuarially Fair Insurance
Chapter 15 Conclusions
7) Insurance Premiums are increased by Asymmetric Information (Moral Hazard and Adverse Selection), which can be reduced but never eliminated.
8) Diversification is an alternative to insurance9) Game trees including risky outcomes can be
“Folded Back” using expected values and analyzed normally
10) Information is valuable11) Unless you can’t sleep at night without one, say
“no” to the extended warranty.
Chapter 15 Conclusions