Title: Modeling%20Contagion%20Risk%20and%20a%20Tax-Carry-Forward%20Program%20in%20an%20Insurance%20Guaranty%20Fund:%20The%20Case%20of%20PACICC%20in%20Canada
1Modeling Contagion Risk and a Tax-Carry-Forward
Program in an Insurance Guaranty Fund The Case
of PACICC in Canada
- Gilles Bernier, Ph.D.
- Professor of Finance and Insurance
- Faculty of Business Administration
- Laval University
- Chairholder
- and,
-
- Ridha Mahfoudhi, Ph.D.
- Chief Analyst
- Securitization ALM
- National Bank of Canada
- ARIA, Quebec City, August 7, 2007
- www.fsa.ulaval.ca/chaire-industriellealliance
2 Content
- Purpose and Research Question.
- Literature Review on Contagion Risk in the
Financial Services Industry. - Description of the Basic Model of the Insurance
Firm. - Modeling the Impact of Ex-Post Assessments in a
Guarantee Fund such as PACICC - With/Without a TCFP.
- Optimality Criteria for TCFP.
- Model Calibration and Implementation.
- Numerical Results and their Interpretation.
- Conclusions.
3Purpose and Research Question
- Contagion risk is a source of concern for members
of PACICC here in Canada. - Purpose of our research
- Study how contagion risk can come into play as a
result of ex-post guarantee fund assessments. - Research Question
- Can a tax-carry-forward program be a plausible
solution for the contagion problem, while
maintaining protection for policyholders and
claimants?
4Literature Review on Contagion Risk in the
Financial Services Industry
- Definition of contagion risk
- Spill over effects of shocks from one or more
firms to other firms. - Topic largely studied in banking
- Evidence of different transmission mechanisms
(liquidity and/or asset-quality problems,
rumors/panics, etc.) at both levels - domestic
and international. - Fewer studies in the insurance literature
- Brewer Jackson (2002) observed evidence of
intra inter industry contagion effects in
the LH sector - Angbazo Narayanan (1996) also found contagion
effects in the PC sector due to catastrophic and
regulatory events.
5Our Basic Model of the Insurance Firm
- EBIT-based default risk model of an insurance
firm that allows for stochastic CFs and interest
rates. - Main features
- Revenue and costs are described by a
mean-reverting Gaussian process (eq 3.1) - Investment portfolio contains short and long-term
bonds with term structure dynamics as in Vasicek
(1977) (eq 3.2-3.3) - The franchise value is accounted for as the PV of
future economic rents for an identical unlevered
firm (eq 3.4 3.5) - Financial leverage is considered through a
stationary debt structure for which there is an
interest charge and a repayment of principal each
year (as in Leland Toft, 1996). This leads to
the firms annual net income (eq 3.6)
6Our Basic Model of the Insurance Firm (cont)
- Main features
- The insurer pays dividends out of its cash
reserves which includes all other marketable
securities - If the cash reserves fall below zero, then the
insurer bankrupts (eq 3.8) - Bankruptcy time is random (eq 3.10)
- Ultimately, if the insurer has not defaulted, the
firm is liquidated and SHs are entitled to a
residual claim (eq 3.11) - At any time t, the economic value of the
insurance firm is given by the PV of expected
payoffs to all claimants (equity, debt and
government) less bankruptcy costs (eq 3.12 to
3.15).
7Modeling the Impact of Ex-Post Assessments in a
Guarantee Fund such as PACICC
- Extension of basic model without a TCFP
- Members of the guaranty fund are all identical
and similar to the insurance firm described in
our basic model. - Upon a failure event at time t0, the funds
remaining solvent companies become engaged in a
sort of loss-recovery program - The firm we are modeling must pay a periodic
amount to PACICC in order to meet obligations
toward clients - Size of the amount (h) and time schedule of
recovery program t1, Th are negotiated among
fund s members - PACICC becomes a claimant of the failed company
and will receive a fraction of the liquidation
proceeds, which will be later returned to its
solvent members in the form of dividends - Hence, the firms cash reserves fall below normal
level so that both leverage and failure risk are
increased (eq 4.1 4.2). - Under such a default contagion model, the values
of both equity and government claims of the
insurance firm will decrease due a probability
distribution of cash reserves being more skewed.
8Modeling the Impact of Ex-Post Assessments in a
Guarantee Fund such as PACICC (cont)
- Extension of basic model with a TCFP
- Under the TCFP, the government agrees to only
receive a fraction (ß) of regular taxes from
solvent members over t1, Th, but it is hopeful
to recuperate the difference later at time Th 1
- This will reduce the failure risk of the
insurance firm caused by PACICCs extraordinary
obligation imposed following the failure event. - However, these companies may also fail before the
full repayment of residual taxes at Th 1. So,
TCFP is risky to the government. - On the other hand, the same firms might also face
difficulty over t1, Th for other reasons that
could lead to an EBIT lt 0, so that no regular
taxes would have to be paid even without a TCFP. - In this setup, the TCFP can be viewed as an
indirect source of debt financing, where the
government has a prior claim over debtholders. - Equations 4.3 and 4.11 formulate both the
government and the equity claims under the
scenario of a default contagion model with TCFP.
9Optimality Criteria for TCFP
- Decision rule for government
- Maximize expected utility of future tax revenues.
10Model Calibration
- Model calibatred using financials (EBIT, TA, CA,
TL, Div) of 38 members of PACICC over 1997-2005 - Median sample value of the panel averages for
each variable.
11Model Implementation
12Numerical Results and their Interpretation
- In Table 1 and Figure 1 (varying the firms cash
reserves and dividend payout), we find that - Introducing ex-post assessments will increase the
failure rate of the insurance firm, thus lowering
the value of its claims (E and G) - Direct consequence of contagion effect
- Much lower for high initial cash reserves.
- In order to make the TCFP sustainable, it appears
that initial cash reserves must be high. - The default rates over time (credit curves) are
also indicative of a contagion effect due to
ex-post assessments - Appear to be lower when the TCFP is introduced,
independently from the level of initial cash
reserves. - TCFP adds value by lowering bankruptcy costs. The
higher the initial cash reserves, the more
solvent the firm is and the higher will the
optimal tax deferral rate (ß) be.
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15Numerical Results and their Interpretation
- In Table 2 and Figure 2 (varying the firms debt
and the guaranty funds ex-post assessment), we
find that - Again, there is a downward shift in value of the
firms claims (E and G) and an upward shift in
the default rates over time (credit curves)
following the introduction of ex-post
assessments. - TCFP does produce a systematic increase in the
governments claims (G) but it does have a mixed
impact on the value of the insurers equity claim
(E) - E increases (decreases) when the assessment is
low (high) - Same effect on E when the insurers debt level is
high - The optimal tax deferral rate drops rapidly as
the extraordinary obligation imposed by the
guaranty fund goes up. - Here, the tax authority does not find the option
of more deferral very attractive.
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18Numerical Results and their Interpretation
- In Figure 3, we find that
- The optimal tax deferral rate is highly sensitive
to the tax authoritys degree of risk aversion - W/r to the insurers dividend payout, a higher
risk-tolerance does not necessarily imply a
higher optimal deferral rate. - The tax authority is likely to be more tolerant
when the amount of assessment is lower. - A medium level of risk aversion leads to higher
tax deferral rates. - In Figure 4, we find that the appreciation rate
of the governments claim due to TCFP - is not very sensitive to the tax authoritys
degree of risk aversion - largely depends on the amount of assessment
charged by the guaranty fund and, to a lesser
extent, also upon the insurers dividend payout.
19Figure 3 The Optimal Tax-Deferral Rate
20Figure 4 The Appreciation Rate of the
Governments Claim Due to the TCFP
21Conclusions
- Overall, our results suggest that
- TCFP does effectively reduce the contagion
effect - TCFP does systematically increase the value of
the governments prior claim - TCFP does not always verify the incentive
compatibility condition w/r to equityholders as
shown in eq.4.14