Modeling Contagion Risk and a Tax-Carry-Forward Program in an Insurance Guaranty Fund: The Case of PACICC in Canada

1. Modeling 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.

3. Purpose 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?

4. Literature 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 L&H sector; • Angbazo & Narayanan (1996) also found contagion effects in the P&C sector due to catastrophic and regulatory events.

5. Our Basic Model of the Insurance Firm • EBIT-based default risk model of an insurance firm that allows for stochastic CF’s 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 firm’s annual net income (eq 3.6);

6. Our 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 SH’s 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).

7. Modeling 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 fund’s 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 firm’s 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.

8. Modeling 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 (β) 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 PACICC’s 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 < 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.

9. Optimality Criteria for TCFP • Decision rule for government: • Maximize expected utility of future tax revenues.

10. Model 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.

11. Model Implementation

12. Numerical Results and their Interpretation • In Table 1 and Figure 1 (varying the firm’s 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 (β) be.

15. Numerical Results and their Interpretation • In Table 2 and Figure 2 (varying the firm’s debt and the guaranty fund’s ex-post assessment), we find that: • Again, there is a downward shift in value of the firm’s 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 government’s claims (G) but it does have a mixed impact on the value of the insurer’s equity claim (E): • E increases (decreases) when the assessment is low (high) • Same effect on E when the insurer’s 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.

18. Numerical Results and their Interpretation • In Figure 3, we find that: • The optimal tax deferral rate is highly sensitive to the tax authority’s degree of risk aversion: • W/r to the insurer’s 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 government’s claim due to TCFP: • is not very sensitive to the tax authority’s degree of risk aversion • largely depends on the amount of assessment charged by the guaranty fund and, to a lesser extent, also upon the insurer’s dividend payout.

19. Figure 3: The Optimal Tax-Deferral Rate

20. Figure 4: The Appreciation Rate of the Government’s Claim Due to the TCFP

21. Conclusions • Overall, our results suggest that: • TCFP does effectively reduce the contagion effect; • TCFP does systematically increase the value of the government’s prior claim; • TCFP does not always verify the incentive compatibility condition w/r to equityholders as shown in eq.4.14