Securitization, Insurance, and Reinsurance

J. David Cummins

Temple University

Conférence en Finance et Assurance

du Fonds Conrad-Leblanc, Université Laval

April 1, 2011Copyright J. David Cummins, 2011.

Outline of Presentation

The catastrophe risk financing problem Reinsurance: The traditional risk warehouse model

The risk warehouse: strengths and limitations Pricing with correlated risks

Securitization: Focus on insurance-linked bonds Financing risk through securitization Strengths and weaknesses

Reinsurance and CAT bonds: Market size & pricing Conclusions

The Catastrophe Risk Financing Problem

Number of Worldwide Insured Catastrophes

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

0

50

100

150

200

250

300

350

400

450

Man-MadeNatural

No.

of

CA

Ts

No. Cats increases from < 150 per year to > 300 per year.

Source: Swiss Re (2010).

Worldwide Insured Catastrophe Losses

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

0

20

40

60

80

100

120

Man-made Natural

Bil

lion

s (2

009

$)

Cat losses increase from < $10B per year up to > $100B.

Source: Swiss Re (2010).

Fifteen Most Costly Insured Disasters Worldwide: 1970-2009 (2008$)

H Katrina 05H Andrew 92WTC 9/11 01

Northridge 94H Ike 08

H Ivan 04H Wilma 05

H Rita 05H Charley 04

Typh Mireille 91H Hugo 89

Wstorm Daria 90Wstrm Lothar 99

Eur Storm 07Eur Storms 87

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000

Loss US$ Millions

Disasters: 13 of top 15 since 1990, 8 of top 15 since 2000

Source: Swiss Re (2009, 2010).

Financing Catastrophes: Conclusions & Questions

Costs of catastrophes have increased over time Significant increases in both frequency and severity

Can the global (re)insurance industry adequately finance this type of risk? Resources of insurers and reinsurers Market imperfections impeding risk financing

Can securitization play a significant role in financing catastrophes?

Reinsurance: The Traditional Model for Financing Catastrophic Risk

Traditional Insurer Model: Risk-Warehousing and Risk-Bearing

Risk Warehouse:

Primary Insurer

Internal Risk Diversification

Risk-Bearing:

Equity Capital

Hedgers: Individuals & Firms

Risk Transfer

& Premium

Contingent Payment

Shareholders: Portfolio Diversif.

Equity

Capital

Dividends

Risk Warehouse:Reinsurer Contingent

Payment

Risk Transfer

& Premium

How the Risk Warehouse Works

Hedgers transfer risks to the risk warehouse The risk warehouse internalizes risk diversification

Across policyholders Across lines of insurance Geographically

Diversification does not eliminate all risk Some risk is transferred to reinsurers but reinsurance can

be expensive, so residual risk remains Residual risk is borne by the insurer’s stockholders, who

diversify by holding stocks and bonds in other industries across the economy

Limitations of Risk Warehousing

Risk warehouses are very efficient in handling relatively small, independent risks & many larger risks that are not correlated

Factors exist that create inefficiencies such that warehousing may become too costly Events causing extremely large losses relative to the

(re)insurance industry’s equity capital Risks that are correlated (theory of insurance is mostly

based on independent risks) Capital market imperfections that raise the cost of capital

for insurers and reinsurers

Limitations of Risk Warehousing II

Premium = E(L) + Expense Loading + Risk Loading Risk loading = Required capital*Cost of capital

Large risks and correlated risks raise the required capital for a given insolvency or VaR target

Capital market imperfections for such risks raise the costs of capital

Therefore, the risk loading may be excessive, destroying “gains from trade” in the insurance market

Illustrating Effects of Correlated Risks on Cost of Capital and Insurance Pricing

Diversification and pricing illustrated using a simple mean-variance model Insurance portfolio consists of N risks, X1, . . ., XN

Risks have finite means and variances Risks have pairwise covariances which are not

necessarily equal to 0 The average mean in the sample is , the average

variance is and the average covariance is In the limit, the sum of the risks is assumed to

approach normality Results would hold even more strongly for skewed risks

i 2i

ij

2 ij

Assumptions About the Insurer

Insurer is assumed to set premiums to cover expected losses plus a risk-charge

The risk charge is calculated to achieve a target probability of insolvency, ε (Tail VaR)

The insurer raises equity capital in the capital market at unit price

( )

( ) expected value of loss

risk charge

P E X

where E X

cr

Why Is Ruin Probability Not = 0?

Capital is costly due to Agency costs of operating an insurance company Regulatory costs Corporate income taxation Informational asymmetries between insurers and capital

market Accounting rules regarding treatment of reinsurance, etc.

Therefore, insurer does not hold enough capital to reduce insolvency probability to zero

Calculating Ruin Probability: Central Limit Theorem

1Pr 1

N

ii

N

X Nz

Equity Capital Per Policy to Achieve Ruin Target: Correlated Risks

2 ( 1) ijNN N Nz

N N

“Equity capital per policy to achieve ruin probability target = ε.”

Capital Per Policy: Limiting Value

lim

where average covariance

Nij

N

ij

zz

N

Therefore, unlike the case of independent risks, the risk charge does not go to zero in the limit

Cost of Capital for New Policies

where market beta of insurance risk

random return on existing insurance portolio

random return on new policy i

asymmetrical component of existing portfolio

, risk premia 0

i

i

p

i i

w

( ) [ ( ) ]

( , ) ( , )

i f i m f

i i i p i

E r r E r r

Cov Cov

Cost of Capital for New Policies: Discussion

Incorporates the conventional CAPM beta term Adds a term reflecting non-systematic covariability

with existing risk portfolio Adds a term for the contribution of the new risk

(risk i) to portfolio return skewness Again this does not have to be market systematic risk in

the conventional CAPM sense Model is based on Froot, Journal of Risk and

Insurance (2007).

Why Non-Systematic Risk is Priced

Non-systematic covariability and skewness risk increase the probability that the firm will need to raise external capital due to loss shocks

External capital is more expensive than internal capital (retained earnings) Following a shock, cost of external capital rises, leading

insurers to have to pass up attractive projects Therefore, policies with high contributions to

covariability and skewness have higher costs of capital Insurance buyers are more sensitive to insolvency

risk than bond holders in corporations because insurer insolvency not diversifiable for buyers

Why Is External Capital More Costly

Informational asymmetries between insurers and capital markets Insurer knows more about its risk exposure and project

riskiness than investors Investors demand a premium to protect against possibly

higher risk levels Agency costs of monitoring managers who may act in

their own interests rather than the owners’ interests Insurers invest in informationally intensive, illiquid

assets that cannot be fully hedged in financial markets, e.g., liability insurance policies, catastrophe insurance

Capital, Convexity, and Risk Premia

Information asymmetries, agency costs and other factors lead to convex costs of raising new capital Per unit cost of capital increases in the amount of capital

required The risk premia ( ) are

Increasing in convexity of the cost of capital Decreasing in the amount of internal funds held

Thus, firms with high costs of external funds and relatively low capital charge higher prices

Helps to explain (re)insurance underwriting cycles

,i i

Premium With Correlated Risks

( )

cost of capital

average covariance

standard normal variate

c ij

c

ij

P E X r z

where r

z

“Expenses assumed to equal zero.”

Premium With Correlated Risks: XOL Reinsurance

RX {Max[X M,0] Max[X U,0]}

Effects of covariability likely to be larger for excess of loss (XOL) reinsurance, which is more risky and highly skewed

Payoff to XOL reinsurance is similar to a call option spread:

Where XR = reinsurance payoff α = coinsurance proportion M = point of attachment (lower strike) U = coverage limit (upper strike)

U > M

Premium with Correlated Risks: Assumptions for Illustration

Portfolio of identically distributed risks Frequency distribution: Poisson (λ = 0.1) Severity distribution: Lognormal (μ = 10, σ = 0.8) Average correlation among risks varies from 0 to 0.35 in

increments of 0.05 Lognormal

Mean = 30,333.3 Standard deviation = 28,720.3

Total claims distribution Mean = 3,033.3 Standard deviation = 13,209.7

Premium with Correlated Risks: Assumptions for Illustration

Cost of capital 10% to illustrate CAPM-type cost of capital 15% to illustrate cost of capital with loadings for non-

systematic covariability and skewness Premiums for a layer of reinsurance

Attachment point M = 25,000 Upper limit U = 45,000

Expected value of loss in the layer = 582.66

Premium with Correlated Risks: Function of Average Correlation and Cost of Capital

00.

05 0.1

0.15 0.

20.

25 0.3

0.35

1.0

1.5

2.0

2.5

3.0

3.5

4.0Rc = 10% Rc = 15%

Average Correlation

Pre

miu

m/E

(L)

Premium/Expected Loss, Reinsurance Layer, Ruin Probability = 0.001

Premiums with Correlated Risks: Conclusions Risk correlations raise the amount of capital

required to achieve a specified probability of ruin Moderate correlations (5% or 10%) produce premiums

1.5 to 2.5 times the expected loss Higher correlations (e.g., 20%) produce premiums 2.5 to

3.25 times the expected loss Raising the cost of capital also increases the

premium significantly At 10% risk correlation, raising cost of capital from 10%

to 15% raises the premium by 25% Therefore, correlations and capital costs can lead to

severe insurance market problems

Traditional Reinsurance Model: Advantages Internalizing the benefits of law of large numbers,

reinsurers achieve a high degree of diversification High diversification means that a small amount of

equity capital can support policy limits many hundreds of times large than the capital itself

By warehousing over a period of time, the reinsurer accumulates significant amounts of information on underwriting, pricing, and risk management Economies of scale in information acquisition & analysis Provides information to clients at low cost

Reinsurance Model: Disadvantages

Warehousing reinsurance contracts internally creates information opacities with securities markets Increases informational asymmetries Raises the cost of capital

Reinsurer capital costs are high because of agency costs, corporate income taxation, and other factors

Reinsurance market subject to underwriting cycles – periodic pricing and availability problems

Reinsurance market not efficient for correlated, highly skewed risks that are large relative to industry capital

Securitization: A New Model for Financing Catastrophic Risk

Securitization: Resolving Reinsurance Market Inefficiencies

Risks that are correlated within reinsurance markets may be uncorrelated with other economic risks

Magnitude of largest insured risks is large relative to equity capital of reinsurers But small relative to capitalization of securities markets $100 billion event has probability of 1 to 2% $100 billion is large relative to reinsurer equity but

< 0.5% of value of US stock and bond markets Securitization can reduce or eliminate credit risk

that is present in reinsurance markets

Hybrid and Securitized Products

Hybrid products Industry loss warranties (ILWs) Sidecars Collateralized reinsurance

Securitized products CAT futures and options Insurance-linked swaps CAT bonds Other insurance-linked bonds (e.g., auto insurance) Contingent capital Mortality and longevity bonds

Securitization Through Insurance-Linked Bonds

Hedgers transfer risks to the risk warehouse (reinsurer) Risk warehouse retains some risks through internal

diversification, equity capital, and reinsurance Efficient to securitize some risks

Risk transferred to special purpose vehicle (SPV) and held off-balance-sheet

SPV issues securities to investors and receives proceeds SPV puts proceeds in trust, invested in safe assets SPV issues a call option (XOL reinsurance) to reinsurer Insurer pays premium (expected loss + risk spread) to SPV SPV pays premium to investors

For correlated risks (e.g., catastrophes), reinsurance premiums may be too high Such risks are large relative to reinsurer capital Capital needed to achieve ruin target raise prices

Securitization transfers risk to investors holding broadly diversified portfolios CAT risk small relative to securities markets CAT risk uncorrelated with most events that move markets

Therefore, CAT bonds valuable for diversification

CAT bonds are a “pure-play” on catastrophe risk Not exposed to frictional costs of investing in insurer equity capital

Securitization Through Insurance-Linked Bonds II

Insurance-linked bonds are fully collateralized On occurrence of event, funds are released to reinsurer If no event, funds returned to investors at maturity

Full collateralization: Advantages Limited counterparty credit risk contingent on

Credit quality of swap counterparty Appropriate restrictions on investment of SPV assets

Funds available quickly following an event Full collateralization: Disadvantage?

Amount of coverage = funds in SPV No leveraging of equity capital as in traditional reinsurance

Securitization Through Insurance-Linked Bonds III

Why Use a Special Purpose Vehicle?

The SPV is a “passive financial intermediary” that exists to Insulate investors from sponsor’s credit risk Provide transparent servicing of asset/liability Structure tranches of debt to appeal to different classes of

investors Insulate investors from agency costs of issuer, creating a

“pure play” security Provide tax and accounting benefits to sponsor

Insurance-Linked Bonds: Advantages to Investors

Low correlations with other types of investments such as stocks, bonds, mortgage-backed securities

Full collateralization reduces credit risk Provide a “pure play” in catastrophe risk Less complex and more transparent than mortgage

backed securities and CDOs Lower moral hazard than mortgage-backed securities

Issuing reinsurer remains responsible for covered risks, providing incentives for proper risk management

Reinsurer and investors have incentive to invest trust assets in safe securities

Insurance-Linked Bonds and Reinsurance: Market Size and Pricing

Global Reinsurers: Resources

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

Equity Premiums

In 2009: $426 billion equity, $161 billion premiums

Top 10 Global Reinsurers: 2009

Group Name Country Gross Premiums

Swiss Re Switzerland $32,462

Munich Re Germany $22,892

Hannover Re Germany $13,341

Berkshire Hathaway U.S. $11,399

Lloyd's of London U.K. $9,732

SCOR France $8,314

RGA Reinsurance U.K. $5,725

Transatlantic U.K. $3,986

Partner Re Bermuda $3,942

Everest Re Bermuda $3,929

Source: A.M. Best 2010 Global Reinsurance Special Report, September 6, 2010.

Global Reinsurers: Equity & CAT Losses

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

-

100

200

300

400

500

600

0%

5%

10%

15%

20%

25%

30%

35%Equity CAT Loss/Equity

Equ

ity

(200

9 $U

S B

)

CA

T L

oss/

Eq

uit

y (%

)

Dollar values deflated to 2009 real values using the CPI. Equity from S&P GRH (various years), CAT Losses from Swiss Re (2010).

Reinsurance Cycles: World Rate on Line Index for Cat Reinsurance

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

50

100

150

200

250

300

350

400

Rate on line = Premium/Maximum Contract Payout

Source: Guy Carpenter (2010).

Reinsurance Rates on Line: Comment

Rates on line are Highly cyclical Correlated across national markets, reflecting the truly

global market for reinsurance Tend to spike after large catastrophes such as

Andrew (1992) World Trade Center (2001) Katrina-Rita-Wilma (2005)

Rate on line spikes correlated with supply restrictions

CAT Bonds: New Issue Volume & Deals

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

0

5

10

15

20

25

30

Volume No. Deals

Vol

um

e ($

US

Mil

lion

s)

Num

ber

of D

eals

Source: Swiss Re (2010), GC Securities (2008). A.M. Best Reinsurance Study (2008), AON (2009), 2010 data through July 31.

CAT Bonds: Risk Capital Outstanding

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

US

$ (

Mil

lion

s)

Source: Swiss Re (2010), 2010 data through July 31.

Reinsurance: Post-Disaster Capital Raising

1992-1993 2001-2002 2005-20060

2,000

4,000

6,000

8,000

10,000

12,000

Start-ups Recap CatBonds

Sidecars

US

$ (

Mil

lion

s)

“Cat Bonds and Sidecars accounted for 34% of new capital following 2005 hurricanes.”

Source: Guy Carpenter (2009).

CAT Bond InvestorsYear-ending June 30, 2010

Cat Funds39%

Institutions31%

Rein-surers20%

Hedge Funds

6%

Mutual Funds4%

CAT Bonds By Peril Year-ending June 30, 2010

US EQ30%

Japan1%US

Hurr55%

EU Wind8%

Other6%

Example: The Mexican CAT Bond

In March 2006, the Mexican government purchased $US 450M earthquake catastrophe coverage

$160 million was raised through a CAT bond Parametric bond – payoff based on earthquake

characteristics Bond premium very low: 2.5%

Reflects diversification relative to “peak risks” in the U.S., Europe, and Japan, i.e., Mexico “off peak”

The Mexican CAT Bond Characteristics

Class A Notes Class B Notes

Principal: US$150M US$10M

Covered Territory: Zone B Zones A and C

Annual Expected Loss: 0.96% 0.93%

Principal Reduction Mechanism: Binary

Binary, first Zone to Trigger

Rating (S&P): BB+ BB+

Investor Spread (bps) LIBOR + [235] LIBOR + [230]

Multiple (spread/exp loss) 2.45 2.47

CAT Bonds vs. Reinsurance: Why Price Comparison is Difficult

CAT bonds usually multi-year whereas reinsurance tends to be for one year

Reinsurance contracts contain reinstatement provisions whereas CAT bonds usually do not

CAT bonds have very low or no credit risk whereas reinsurance has credit risk

CAT Bond Pricing: Premium/Expected Loss

2001

Q3

2002

Q2

2003

Q1

2003

Q4

2004

Q3

2005

Q2

2006

Q1

2006

Q4

2007

Q3

2008

Q2

2009

Q1

2009

Q4

2010

Q3

0

1

2

3

4

5

6

7

Pre

miu

m/E

(L)

Source: Lane Financial (2010).

Reinsurance Prices: Rate on Line versus Loss on Line

0

2

4

6

8

10

12

14

1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0%

Loss on Line (LOL)

Ra

te o

n L

ine

/LO

L

2005 2006

2007 2008

Source: Guy Carpenter.

CAT Bond Yields vs. Reinsurance

In the 1 to 2% loss on line range, reinsurance price spreads versus Cat bond spreads 2005: 4 to 6 reinsurance vs 2 to 3 Cat bonds 2006: 7 to 13 reinsurance vs 5 to 7 Cat bonds 2007: 4 to 5 reinsurance vs 4 to 5 Cat bonds 2008: 3 to 4 reinsurance vs 3 for Cat bonds

Therefore, Cat bonds are priced comparably with reinsurance in recent years

Yields: CAT Bonds & Corporates (BB)J

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10

11

12

13

14

15

16

BB CORP (1-10 year) BB Catastrophe Bonds

YT

M O

R C

OU

PO

N (

%)

CAT Bond Yields vs. BB Corporates

During most of period, CAT bonds priced comparable to corporates

However, during significant part of the period, CAT bonds had higher yields

CAT bond yields also more volatile than for corporates In part, reflects thinness of market

CAT Bonds: Explaining the Spreads

Original pricing argument: CAT risk is “zero-beta” Therefore, CAPM implies pricing at the risk-free rate

However, spreads are much higher than risk-free rate – why does this happen? “Novelty premium” – investor unfamiliarity –

however, we now have dedicated CAT mutual funds High costs of issuance – however, cost have declined So the reason is ????

CAT Bonds: Explaining the Spreads

“Habit-based” consumption CAPM (Campbell and Cochrane, 1999; Dieckmann, 2008)

Investor risk aversion increases as consumption falls towards its “long-run” habit level

Therefore, investors are averse to assets that have low payoffs during adverse states of the world (economic downturns or catastrophes)

Explaining the Spreads: Habit-Based Consumption Model

Campbell and Cochrane (1999), Dieckmann (2008).

1

0

( ) 1( , )

1

where r = discount rate

C consumption in period t

subsistence level of consumption ("habit")

risk aversion parameter

rt t t

t

t

t

C XU C X e

X

Utility determined by present value of consumption

Consumption-Based Pricing Model II

( )

where S = surplus consumption ratio

C consumption in period t

subsistence level of consumption ("habit")

t tt

t

t

t

t

C XS

C

X

Relationship between consumption and habit determined by the surplus consumption ratio

St → 0 corresponds to unfavorable state of the world

Consumption-Based Pricing Model III

where = relative risk aversion

absolute risk aversion

surplus consumption ratio

tt

t

t

t

t

S

S

Relative risk aversion in this model is:

St → 0 corresponds to very high investor risk aversion

Implications of Consumption-Based Model

Investor risk aversion increases as consumption falls towards its “long-run” habit level

Therefore, investors averse to assets that have low payoffs during adverse states of the world (economic downturns)

Dieckmann provides evidence that natural catastrophes shock economic activity sufficiently to explain magnitude of CAT bond spreads Shock of 2% of GDP (similar to Katrina) sufficient to

explain the spreads

Conclusions

Conclusions Reinsurance is highly efficient in dealing with the

usual types of insurance market risks Losses relatively small compared to reinsurer capital Risks with relatively low covariability Risks with manageable variance and skewness

Reinsurance facilitates long-term relationships between ceding insurers and reinsurers, reducing informational asymmetries and leading to more efficient risk sharing

Reinsurance available to insurers of all sizes, whereas securitization most efficient for large firms

Conclusions II

Securitization more efficient for relatively large risks with high covariability and skewness CAT bonds have established a market niche for CAT

risk financing and post-shock recapitalization Securitization provides needed capacity to mitigate

the effects of reinsurance price and availability cycles, periods when Reinsurance prices rise Supply of reinsurance is restricted

Securitization reduces or eliminates credit risk

Conclusions III

Risk-capital raised with insurance-linked securities has grown significantly Still small relative to reinsurance Recently, bonds issued for “low layer” coverages such

as automobile insurance Spreads have been declining

Now comparable with corporates, reinsurance, ILWs Prices remain volatile and subject to spikes following

large loss events “Off-peak” bonds (Mexican, etc.) may stabilize market

and reduce spreads

Conclusions IV

Bonds have attracted broad market interest – dedicated CAT funds now account for majority of the market

Because they are transparent and fully collateralized, CAT bonds less exposed to the problems that befell credit default swaps (CDS) and MBS CAT bonds generally much less complex than MBS & CDOs Except for a small number of bonds with Lehman as

counterparty, CAT bonds did well during the 2007-2010 crisis Therefore, CAT bonds provided valuable liquidity for trading

banks during the crisis

Conclusions V

Other securitized structures may provide additional capacity in the future Catastrophe futures & options Swaps Sidecars

However, for futures & options to succeed, insurers need to develop trading expertise Continual hedging operations versus Buy reinsurance once a year

The EndThank you!