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Evaluating the Implicit Guarantee to Fannie Mae and Freddie Mac

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					Evaluating the Implicit Guarantee to Fannie Mae
   and Freddie Mac Using Contingent Claims

                    Michael Gapen
    Board of Governors of the Federal Reserve System


                       June 2009
A Framework for Risk Management


  Entities in the economy are linked since liabilities of one entity are
  assets of another
    I   Changes in the value of assets induce changes in the value of
        liabilities backed by those assets
    I   These valuation linkages are crucial in the macroeconomy,
        especially when default on liabilities is a possibility
    I   However, most current macro models, especially those that
        underlie policy analysis, ignore valuation linkages and default
        probabilities
What is macro missing?




          "Study of …nancial fragility has not been well served
      by macroeconomic theory. Financial fragility is intimately
      related to probability of default. Default is hard to handle
      analytically being a discontinuous, nonlinear event so
      most macro models abstract from default and …nancial
      intermediaries such as banks." - Charles Goodhart, 2005
      IMF Conference
The Risk Management Process
Outline



   Purpose: to provide an example of how contingent claims analysis
   can be applied to the macro risk management process
     I   The Black-Scholes-Merton Model
     I   Measure and Estimate Risk Exposure with Contingent Claims
     I   Case study: Fannie Mae and Freddie Mac
     I   Illustrates the provision of implicit government guarantees and
         risk transfer
Preview of Main Results



    1. Accurate signals of building risk exposure in Fannie Mae and
       Freddie Mac, as early as November 2007
    2. An average of the VaRs showed 95% VaR of US$100bn
    3. Approximately the size of the Treasury Preferred Stock
       Purchase Program
    4. The Program covers weakness from a VaR perspective
    5. Losses senstivie to assumptions
The BSM Model and MKMV
  Black and Scholes (1973) and Merton (1974) use options
  relationships to price debt and equity
    I   MKMV uses a variant of the framework to derive an
        "expected default frequency" or EDF
    I   Uses market information, not judgemental ratings or historical
        transition frequencies
  EDF is a function of
    I           s
        the …rm’ capital structure
    I   implied asset value and uncertainty of asset return
  EDF is calculated in a three-step process
    I   Estimate the value and volatility of …rm assets
    I   Calculate "distance to default"
    I   Scale distance to default into pr(default)
The BSM Model and MKMV



  Improved predictive power
    I           s
        Moody’ KMV shows the framework to be more e¤ective at
        default prediction
    I   Power comes from nonlinear option pricing
    I   The value of the option is most sensitive to changes in the
        underlying in the neighborhood of the default barrier
    I   Option price sensitivities lead to greater predictive power over
        linear methods
Contingent Claims Analysis: Beyond Corporate Credit Risk



    I   Can be applied to banks (Chan-Lau and Sy, 2006)
    I   Used to estimate sovereign risk (Gapen et al., 2008)
    I   Economywide risk (Gray and Malone, 2008; Gray et. al.,
        2007, Gapen et al., 2004)
    I   This paper highlights its application to assessing guarantees
        and risk transfer (see Merton 1998)
    I   Fannie Mae and Freddie Mac provide a timely example
Contingent Claims Analysis with Multiple Layers of
Liabilities
   Essential insight from BSM: equity is a call option on assets
     I   Strike is based on level of liabilities
Contingent Claims Analysis with Multiple Layers of
Liabilities

   Applying BSM to Fannie Mae and Freddie Mac
    I   The GSEs have transparent balance sheets
    I   Liability structure comprised mainly of senior debt and
        common equity
    I   Smaller quantities of subordinated debt and preferred equity
        act as capital bu¤ers, similar to traditional …nancial
        institutions
    I   Assets comprised of diversi…ed pools of mortgages
    I   In addition, the asset side includes an implicit government
        guarantee, which is a contingent liability of the federal
        government
Contingent Claims Analysis with Multiple Layers of
Liabilities

   Equity as a call option on GSE assets
                                               rτ
             VE = VA N (d1 (DB3 ))     DB3 e        N (d2 (DB3 ))

     I   where DB3 is the distress barrier on senior, subordinated and
         preferred equity
   Use this with the following

                           σE VE = σA VA N (d1 )

     I   two equations in two unknowns to solve for VA and σA
Some Discussion on Model Calibration


   Equity Volatility
     I   12-month ahead implied equity volatility from at-the-money
         option
     I   Exponentially weighted realized volatility (Carlson et al. 2008)
   Distress Barrier
     I                            s
         For corporates, Moody’ KMV uses all short-term, half
         long-term, plus interest
     I                          s
         For …nancials, Moody’ KMV uses somewhere between 70 and
         90 percent of total liabilities
Some Discussion on Model Calibration


   Dynamic Leverage
     I   liabilities are non-static. May want to adjust distress barrier
         based on historical relationship between assets and liabilities.
         Useful in simulations.
   Dividends
     I   Not taking them into account here. Could do that.
   Lack of absorbing barrier in BSM (European option).
     I   Can this be altered to allow for an absorbing default barrier?
Modeling Risk Transfer with Contingent Claims

   After decisions on calibration, solve the model and produce
   indicators of risk exposure
   Distance to Minimum Capital
                                                  1 2
                             ln VA exp       r    2 σA   τ    (ln DB3 )
      D2MC = d2 (DB3 ) =                           p
                                                 σA τ

   Could also think of this as
     I   Distance to prompt corrective action (Chan-Lau and Sy, 2006;
         Kupiec, 2005, 2007)
   Distance to Default on Senior Debt:
                                                 1 2
                             ln VA exp   r       2 σA    τ   (ln DB1 )
         D2D = d2 (DB1 ) =                        p
                                                 σA τ
From Risk Neutral to Actual Probability of Default


   Risk-neutral pricing results from BSM and riskless hedge portfolio

         RNPMC = N ( d2 (DB3 )),           RNDPSL = N ( d2 (DB1 ))

     I                                t
         Advantage: option value doesn’ depend on risk preferences
     I   Disadvantage: real world risk indicators depend on preferences
     I   Market practitioners often adjust risk-neutral into "actual"
         risk indicators
           I   Use market price of risk and Sharpe ratio to proxy for risk
               aversion
           I   Bohn (2000)
           I   Gray and Malone (2007) and Gray, Merton, Bodie (2007)
Fannie Mae


       Market Capitalization and Equity                  Distance to Default and Minimum Capital
       Volatility                                        (in standard deviations of asset value)
 350                                           80   6                                              6

 300                      12-mo. Ahead         70   5                                              5
                              Implied
                         Equity Volatility     60   4                                              4
 250
                         (In percent, left)                              Senior Debt
                                               50   3                                              3
 200     Market Cap.
        (US$bn, right)                         40   2                                              2
 150
                                               30   1                                              1
 100
                                               20   0                                              0
  50                                                       Preferred Equity
                                               10   -1                                             -1

  0                                            0    -2                                             -2
   Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08        Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08


       Estimated Actual Probabilities                    Estimated Implied CDS spreads:
       (in percent)                                      Senior Debt (in basis points)
Freddie Mac


       Market Capitalization and Equity                  Distance to Default and Minimum Capital
       Volatility                                        (in standard deviations of asset value)
 350                                           50   6                                              6

                          12-mo. Ahead         45   5                                              5
 300
                              Implied          40
                         Equity Volatility          4                                              4
 250                                           35
                         (In percent, left)                              Senior Debt
                                                    3                                              3
         Market Cap.                           30
 200
        (US$bn, right)                         25   2                                              2
 150
                                               20   1                                              1
 100                                           15
                                                    0                                              0
                                               10
  50                                                       Preferred Equity
                                                    -1                                             -1
                                               5
  0                                            0    -2                                             -2
   Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08        Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08


       Estimated Actual Probabilities                    Estimated Implied CDS spreads:
       (in percent)                                      Senior Debt (in basis points)
Implied Actual Default Probability

     I   RN distance-to-default has asset drift of r and RN default
         probability of N ( d2 )
     I   "Actual" distance-to-default has asset drift of µA and default
         probability of N   d2,µ
     I   These are related by the market price of risk, λ
                                                   p
                         N    d2,µ = N      d2 λ τ

     I   where the market price of risk is estimated by
                      µA r
                           = λ,       µA = r + ρA,M SRσA
                        σA
         and SR is the market Sharpe ratio, ρA,M is the correlation
         between implied asset return and the market
Fannie Mae (left) and Freddie Mac (right)


      Estimated Actual Probabilities               Estimated Actual Probabilities
      (in percent)                                 (in percent)
 70                                           70
                                                            Pr(default on senior debt)
                 Pr(default on senior debt)                 Pr(breach min. capital)
 60                                           60
                 Pr(breach min. capital)
 50                                           50

 40                                           40

 30                                           30

 20                                           20

 10                                           10

  0                                           0
  Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08    Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08
The Implicit Government Guarantee


           s
   Now let’ think about how to use this framework to value the
   guarantee
Estimating the Market Value of the Guarantee


   Senior liabilities derive their value from two sources
     I   Pure-default free value
     I   Bearing of default risk of the issuer
   Any guarantee against default must o¤set total expected loss on
   senior debt

             Implicit guarantee = defaul-free debt - risky debt

            Risky debt = default-free debt - implicit guarantee
                  rτ             rτ
   VSL = DB1 e           DB1 e        N ( d2 (DB1 ))   VA N ( d1 (DB1 ))
Estimating the Market Value of Expected Capital Losses
   Under the assumption that subordinated debt and preferred equity
   re‡ect a capital bu¤er
     I   summing over the expected loss on subordinated and preferred
         debt is a measure of the present value of expected capital
         losses
     I   a "top down" approach to measuring capital adequacy


                      rτ                 rτ
   VSUB = DB2 e               DB2 e           N ( d2 (DB2 ))   VA N ( d1 (DB2 ))
                 rτ                rτ
         DB1 e             DB1 e        N ( d2 (DB1 ))     VA N ( d1 (DB1 ))


                      rτ                 rτ
   VPRE = DB3 e               DB3 e           N ( d2 (DB3 ))   VA N ( d1 (DB3 ))
                 rτ                rτ
         DB2 e             DB2 e        N ( d2 (DB2 ))     VA N ( d1 (DB2 ))
Estimating the Market Value of the Guarantee and
Expected Capital Losses
Fannie Mae

      Expected Loss: Subordinated Debt and          Expected Loss: Senior Debt
      Preferred Equity (in US$ billions)            (in US$ billions)
                                              120
 12               Subordinated Debt
                  Preferred Equity            100
 10

 8                                             80


 6                                             60


 4                                             40

 2                                             20

 0                                              0
  Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08     Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08
Freddie Mac


      Expected Loss: Subordinated Debt and          Expected Loss: Senior Debt
      Preferred Equity (in US$ billions)            (in US$ billions)
 10
                                              140
 9                Subordinated Debt
 8                Preferred Equity            120
 7
                                              100
 6
                                               80
 5
 4                                             60
 3
                                               40
 2
                                               20
 1
 0                                              0
  Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08     Jun-07 Aug-07 Nov-07 Feb-08 May-08 Aug-08
Estimating the Share of the Total Expected Loss Covered
by the Guarantee
   Will the guarantee provider cover all of the loss?
     I    The model produces a CDS spread on risky debt.
     I    This is from the point of view of equityholders, who receive
          nothing in the event of default
     I    Given an expected loss, we can derive a model implied CDS,


                   ln(DB1 e   rf τ /V )           1         ELSL
                                     SL
      y     rf =                           rf =     ln 1
                              τ                   τ        DB1 e r τ

     I    Given a market CDS, we can derive an expected loss, ELCDS
   The portion of the loss covered by the guarantee

                              ELCDS = (1     η ) ELSL
      Share of Total Expected Loss Covered              Share of Total Expected Loss Covered
      by the Guarantee: Fannie Mae                      by the Guarantee: Freddie Mac
1.0                                               1.0
0.9                                               0.9
0.8                                               0.8
0.7                                               0.7
0.6                                               0.6
0.5                                               0.5
0.4                                               0.4
0.3                                               0.3
0.2                                               0.2
0.1                                               0.1
0.0                                               0.0
  Jun-07   Aug-07 Nov-07   Feb-08 May-08 Aug-08     Jun-07   Aug-07   Nov-07 Feb-08 May-08 Aug-08

Source: Author's calculations and Markit.
Monte Carlo Simulations
   Distribution of the Value of the Implicit Government Guarantee for
            s
   the GSE’ on Sept 5, 2008


                            Fannie Mae                                               Freddie Mac
        0.025                                                  0.025


        0.020                                                 . 0.020
    .
                                                              y
                                                              t
                                                              i
    y
    t                                                         l
                                                              i 0.015
    i 0.015
    l
    i                             95% <= 95                   b                                 95% <= 90
    b                                                         a
    a                                                         b
    b                                                         o
                                                              r
    o
    r 0.010                                                   P0.010
    P

        0.005                                                  0.005


        0.000                                                  0.000
                0   50      100     150    200    250   300             0   50     100    150     200     250   300
                         Value (in US$ billion)                                  Value (in US$ billion)
Conclusions: The Case Study



    1. Accurate signals of building risk exposure in Fannie Mae and
       Freddie Mac, as early as November 2007
    2. An average of the VaRs showed 95% VaR of US$95bn for
       Fannie Mae and US$90bn for Freddie Mac
    3. Approximately the size of the Treasury Preferred Stock
       Purchase Program
    4. The Program covers weakness from a VaR perspective
    5. Losses sensitive to model assumptions
Conclusions: BSM-CCA and Macro Risk Analysis



    1. BSM-CCA framework yields a structural model of risk
    2. Forward-looking, market-based estimates of risk exposure
    3. Flexible enough to handle complicated balance sheet
       structures
    4. Translates default risk into expected loss and risk transfer
    5. Can yield estimates of the value of a guarantee, and the share
       of this loss expected to be covered by the government

				
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posted:11/2/2012
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