The Choice of Trigger in an Insurance Linked Security – The Case of Brevity Risk ARIA Annual...

The Choice of Trigger in an Insurance Linked Security

– The Case of Brevity Risk

ARIA Annual Meeting, Quebec City , August 5-8, 2007

Richard MacMinn (Illinois State U)

Andreas Richter (Ludwig-Maximilians U Munich)

Institute for Risk and Insurance Management · LMU Munich School of Management

Institute for Risk and Insurance Management

Munich School of Management

MacMinn / Richter ARIA Annual Meeting, Quebec City, August 2007

Agenda

1. Introduction

2. The Model

3. Results

• Limited Liability and Incentives

• Introducing Indemnity and Index Hedge

• Incentive Effects of Hedging

4. Conclusion




Potential Triggers in an ILS

Indemnity/company-based trigger: Payout to the issuer is based on actual losses

Industry index: industry losses resulting from catastrophic events

Parametric index: Physical characteristics of a catastrophe (e.g., strength of an earthquake)

Modeled-loss trigger: uses physical parameters of a catastrophe as input into an ex-ante agreed-upon model which generates a “loss” value

Hybrid trigger: uses more than one trigger type in a single transaction, for instance, hurricane in the U.S. and flood in the UK (more complex: sequential event triggers)




Insurance Securitization vs. Traditional (Re)Insurance

Some aspects for a comparison

• Basis risk

• Moral hazard

• Transparency for investors

• Default risk

• Transaction costs

• Speed of availability of necessary information




Cat Bonds – Growing Importance of Non-Indemnity Triggers

Source: Guy Carpenter (2007)




Related Literature

Securitization versus traditional (Re)Insurance

• Overview/Introduction: Doherty (1997), Croson/Kunreuther (2000)

key aspects: default risk, transaction cost, basis risk vs. moral hazard

• Insurance economics modeling approaches:

Doherty/Mahul (2001), Doherty/Richter (2002), Nell/Richter (2004), Laux/Brandts (2007)

Incentive distortions because of limited liability / “Judgment Proof Problem”

• Jensen/Meckling (1976), Shavell (1986), Garven/MacMinn (1993)

Fisher-Model

• MacMinn (1987) (2005)




Scope of this paper

• Shareholder value maximizing (re)insurer

• Effort / care affects underwriting results

• (Re)insurer is subject to insolvency risk judgment proof/underinvestment problem

• ILS based on actual losses vs. index moral hazard vs. basis risk

• What are the incentive effects of ILS?




The Model

In the absence of any ILS, the (re)insurer’s stock market

value is the value of its book of business:

: set of states of nature

: premium income

: loss on book of business (with and

: (cost of) effort

0S(a) max , a, dP

a,

L a,

a

L a, a

0

L

2

0L

)a




Limited Liability and Incentives in the Unhedged Case

If bankruptcy risk exists, we find:

au < ae

What is the effect of introducing hedging instruments?

au: Shareholder value maximizing effort level

ae : Socially efficient level, maximizing total firm value

(taking into account the potential consequences of a bankruptcy for other stakeholders).




• Payoff function for an indemnity-based transaction:

• Payoff function for the index hedge:

0max ,L a, i

0max ,I i

where i is the trigger and I() an index with

0dId

Modeling the Hedge




Incentive Effects of Hedging (with Asymmetric Information)

• Can hedging improve the incentive deficit due to the judgment proof problem?

• With the hedge in place, the organization maximizes shareholder value. This determines the underwriting effort a(i) (reaction function).

• Indemnity hedge creates moral hazard

• Index hedge creates basis risk, but no moral hazard




With indemnity-based hedging ...

• the reaction function increases in i, i.e. the more protection, the lower the effort.

• incentives are completely eliminated if the trigger is sufficiently low.

Incentive problem is aggravated.

a

i*i **i

a(i)

Incentive Effects of Hedging – Results




In the case of index-linked hedging ...

• under certain assumptions regarding basis risk, the reaction function decreases in i, i.e. the more protection, the greater the effort.

• if an exists, such that bankruptcy risk can be entirely avoided through the hedge, even the first-best optimum is reached. (a(i)=ae, )

a(i)

ii i

a

i i

i

Incentive Effects of Hedging – Results




Conclusion

• Insolvency risk / limited liability causes underinvestment in effort.

• Shareholder value maximization vs. other stakeholders’ interests.

• How does hedging affect incentives?

– Under asymmetric information, an indemnity hedge reduces the underwriting effort.

– An index hedge can improve incentives.

– If the index hedge can eliminate insolvency risk, it induces the first-best-optimum.

The Choice of Trigger in an Insurance Linked Security

– The Case of Brevity Risk

ARIA Annual Meeting, Quebec City , August 5-8, 2007

Richard MacMinn (Illinois State U)

Andreas Richter (Ludwig-Maximilians U Munich)

Institute for Risk and Insurance Management · LMU Munich School of Management




Future Research

• Model the shareholder value indirectly created by an ILS

– Hedging as a signal that decreases capital cost

– How does hedging affect incentives with respect to investment decisions etc.?

• Longevity risk




Related Literature

Doherty, N. A. (1997). "Financial Innovation in the Management of Catastrophe Risk." Journal of Applied Corporate Finance 10(3): 84-95.

Croson, D. C. and H. C. Kunreuther (2000). "Customizing Indemnity Contracts and Indexed Cat Bonds for Natural Hazard Risks." Journal of Risk Finance 1(3): 24-41.

Doherty, N. A. and O. Mahul (2001). Mickey Mouse and Moral Hazard: Uninformative but Correlated Triggers. Working Paper. Wharton School.

Doherty, N. A. and A. Richter (2002). "Moral Hazard, Basis Risk and Gap Insurance." Journal of Risk and Insurance 69(1): 9-24.

Richter, A. (2003). Catastrophe Risk Management - Implications of Default Risk and Basis Risk. Working Paper. Illinois State University.

MacMinn, R. D. (1987). "Insurance and Corporate Risk Management." Journal of Risk and Insurance 54(4): 658-77.

MacMinn, R. (2005). The Fisher Model and Corporate Finance. Taipei, forthcoming.




The Model (cont.)

Assumption

The reinsurer’s payoff R and the loss satisfy the principle of

decreasing uncertainty (PDU):

• After compensating for the change in the mean, the PDU provides a decrease in the risk, in the Rothschild-Stiglitz sense (MacMinn and Holtmann 1983).

0

L

2

0L

)a

and




Limited Liability and Incentives

Judgment Proof Problem

(Shavell 1986, Kahan 1989, MacMinn 2002)

If , the level of care selected by the (unhedged)

reinsurer is less than the socially optimal level,




Indemnity Hedge

0 0

0

: (a, ) max{ ,L(a, ) i}

: L(a, ) i

L

i

0(a, ) max{ ,L(a, ) i}

L

R(a, )




: (a, ) I( ) i 0

: I( ) i 0

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