Modeling%20Contagion%20Risk%20and%20a%20Tax-Carry-Forward%20Program%20in%20an%20Insurance%20Guaranty%20Fund:%20The%20Case%20of%20PACICC%20in%20Canada - PowerPoint PPT Presentation

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Title: Modeling%20Contagion%20Risk%20and%20a%20Tax-Carry-Forward%20Program%20in%20an%20Insurance%20Guaranty%20Fund:%20The%20Case%20of%20PACICC%20in%20Canada

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

  • Purpose and Research Question.
  • Literature Review on Contagion Risk in the
    Financial Services Industry.
  • Description of the Basic Model of the Insurance
  • 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.

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

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 LH sector
  • Angbazo Narayanan (1996) also found contagion
    effects in the PC sector due to catastrophic and
    regulatory events.

Our Basic Model of the Insurance Firm
  • EBIT-based default risk model of an insurance
    firm that allows for stochastic CFs and interest
  • 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)

Our Basic Model of the Insurance Firm (cont)
  • Main features
  • The insurer pays dividends out of its cash
    reserves which includes all other marketable
  • 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

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 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.

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 (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.

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

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.

Model Implementation
Numerical 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
  • 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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Numerical 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
  • 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 increases (decreases) when the assessment is
    low (high)
  • Same effect on E when the insurers debt level is
  • 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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Numerical 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.

Figure 3 The Optimal Tax-Deferral Rate
Figure 4 The Appreciation Rate of the
Governments Claim Due to the TCFP
  • Overall, our results suggest that
  • TCFP does effectively reduce the contagion
  • 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