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Dan diBartolomeo. Emilian Belev. A Structural Model Of Sovereign Credit Risk. January, 2013. Presentation Outline. Motivation Review of Contingent Claims Analysis for Corporations Key Literature: Bodie , Gray Merton (2005) Northfield “spin” on BGM Some “Real” Political Illustrations.

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presentation outline
Presentation Outline


Review of Contingent Claims Analysis for Corporations

Key Literature: Bodie, Gray Merton (2005)

Northfield “spin” on BGM

Some “Real” Political Illustrations

Slide 2

structural model for sovereign credit risk
Structural Model for Sovereign Credit Risk

“A Crisis is a Terrible Thing to Waste”, Paul Romer

Slide 3

sovereign debt and the financial system
Sovereign Debt and the Financial System

The Global Financial Crisis of 2007-2009 and the ongoing problems of the European financial system leave little doubt about the current state of affairs

National governments have no choice but to keep major banks and financial institutions intact: TBTFIRR

One of the largest investments by banks and other financial institutions is sovereign bonds

  • If a sovereign nation defaults on their debts, the banks are the big losers so there are more bailouts: a death spiral
  • The allocation to sovereign debt increases in crises

Investment theory is left searching for a risk free asset

  • The S&P downgrade of US Treasury debt

Slide 5

review of cca for corporations
Review of CCA for Corporations

Merton (1974) poses the equity of a firm as a European call option on the firm’s assets, with a strike price equal to the face value of the firm’s debt

  • Alternatively, lenders are short a put on the firm assets
  • Default can occur only at debt maturity

Black and Cox (1976) provide a “first passage” model

  • Default can occur before debt maturity
  • Firm extinction is assumed if asset values hit a boundary value (i.e. specified by bond covenants)

Leland (1994) and Leland and Toft (1996)

  • Account for the tax deductibility of interest payments and costs of bankruptcy
  • Estimate boundary value as where equity value is maximized subject to bankruptcy

Slide 6

analogy with corporate debt
Analogy with Corporate Debt

Probability Density

Asset Return

Inputs to Credit Model: σ Debt Asset Level

Model States: βbond = βstock * -(Pstock / Pbond) * (Δput/ Δcall)

Corollaries: ① LGD = Pbond* scalar; ② LGD & OAS  Prob. Default

Slide 7

practical outcomes of the cca framework
Practical Outcomes of the CCA Framework

The value of a corporate bond is split into two pieces

A portion of the value is a risk free bond

The remainder of the value is equity in the firm

The equity portion goes to zero during bankruptcy so you know your “expected loss given default” (LGD)

Conditional on an estimate of the risk aversion of bond investors, you can derive the “probability of default” (PD) from the LGD and the credit yield spread (OAS)

Slide 8

key literature for our model
Key Literature for our Model

Bolster, Paul, Ronald Johnson and VenkatSrinivasan,“Sovereign Debt Ratings: A Judgmental Model Based on the Analytic Hierarchy Process”, Journal of International Business Studies, 1990.

Bodie, Zvie, Dale Gray and Robert Merton, “A New Framework for Analyzing and Managing Macrofinancial Risks of an Economy”, National Bureau of Economic Research, 2005.

Slide 9

more on bodie gray merton 2005
More on Bodie, Gray, Merton (2005)

The paper provides a complex system of theoretical balance sheet relationships among three types of entities: the Corporate Sector, the Financial Sector including Central Banks, and Sovereign Governments

The interrelationships between sectors are modeled as a set of put and call options among the players

The government has a call on corporate assets (taxes)

The banks have a call on the government (bailouts)

A key attribute (asset) of some but not all governments is a monopoly authority on the printing of money

Slide 10

pragmatic options for governments
Pragmatic Options for Governments

Under CCA, corporate shareholders have the option to pay off the firm’s debts and own the assets outright. Sovereign governments have the option to impose fiscal austerity measures (higher taxes, cut spending) as in Italy and Spain today.

As we’ll see in a minute, this can be counterproductive

Under CCA, corporate shareholders can use their limited liability put option to walk away and give the assets of the firm to the bondholder. Only some sovereign governments have the option to print money to inflate their way out of debt (think of Zimbabwe).

Note this is not the same as a government using the printing of money to stimulate the economy in a Keynesian framework

Slide 11

inputs to sovereign credit model
Inputs to Sovereign Credit Model

Asset Level is the sum of:

  • Domestic and foreign currency reserves, deposits in banks and receivables, commodities reserves, and others
  • The projected long term stream of taxes, fees, tariffs, exploration rights, all discounted to present value
  • Given appropriate projections of GDP and its components – individual income, corporate income, and international trade, as well as established tax rates - we can find the second component

Liability Level is the sum of:

  • Notional debt in local currency held domestically
  • Notional debt in local currency held by foreign entities
  • Foreign currency debt
  • Reserves for bank bailouts
  • Reserves for unfunded pensions and entitlements

Slide 12

inputs to sovereign credit model cont d1
Inputs to Sovereign Credit Model (cont’d)

Sovereign Asset Volatility is upper bounded by Stock Market Volatility

On one side

  • As net groups, companies are a relatively smaller number of providers and individuals are relatively larger number of price takers
  • Productivity growth gains (synonymous with GDP growth) accrue to capital owners while, when economy shrinks, wages are rigid in downward direction, and brunt of the business loss is taken by capital owners
  • So, when economy booms, corporations accrue gains faster than individuals; when economy slumps, corporations accrue losses faster than individuals

On the other side

  • Market capitalization is the future corporate profit stream discounted to the present moment. A fixed tax rate applied to corporate profits results in the same volatility number for the corporation and the corporate tax stream

Slide 14

gdp projections and demographics
GDP Projections and Demographics

GDP discounted cash-flow model is the baseline for the sovereign asset level estimation

Arnott and Chaves (2012) find a strong relationship between demographic variables (age group shares) and GDP growth

Demographic trends are predictable out in the future with great degree of certainty. Today’s 40 yr olds are next year’s 41 yr olds.

Demographics affect one more important input for the option default model– the strike price, or the level of debt

  • An aging population increases the dis-saving and divestment in “safe” assets, pushing down financial asset prices and increasing borrowing costs to the government, making debt service more onerous

Slide 15

inputs to sovereign credit model cont d2
Inputs to Sovereign Credit Model (cont’d)

Sovereign Asset Volatility continued:

  • In the US, personal Income tax corresponds to approx. 80% of federal tax revenue
  • Return on Personal Income is dependent on the same economic drivers as the stock market, but is exposed in a muted and lagged way for the reasons mentioned.
  • A lagged equation can link return on personal income to the risk model factors
  • Personal Income Tax stream then becomes just another “position” in the sovereign asset portfolio with known risk factor exposures
  • We can estimate σ for our default “option” model

Slide 16

governments are short the bailout put
Governments are Short the Bailout Put

The “systemic” banks and most pension funds (ie.g. PBGC) have a call option on government bailout funds

  • If you assume banks need 8% equity capital you just need to know how big the “big banks” balance sheets (total assets) are relative to GDP
  • US, 65%, UK 337%, France 249%, Switzerland 550%

Underfunding of public (state and local) pensions in the US is a big issue. The gap is between $2 and $5 Trillion depending on what accounting standard you like

Slide 17

government and a single bank
Government and A Single Bank

Joint Distribution of Sovereign and Bank Assets

Bank Asset Return

Bank Asset Return

Sovereign Asset Return

Sovereign Asset Return


Multinomial Model

Slide 18

distress zone
Distress zone

The correlated expected tail loss on the bank side accumulates to the sovereign asset loss side at each density level, fattening the tail of the sovereign distribution

Slide 19

types of sovereign credits
Types of Sovereign Credits

Three ways in which Sovereigns can react to a crisis in the real / banking / government finance sector:

Respond via fiscal means – increase taxation / divert tax revenues to prop banking capital and infrastructure investment (Fiscally Responsive Sovereigns)

React “responsibly” with monetary means – increase supply of credit to support banking liquidity and assure sovereign financing (Monetarily Responsive Sovereigns)

Engage in irresponsible money creation or ruthless default (Rogue Sovereigns)

Slide 20

fiscally responsive
Fiscally Responsive
  • Governments are elected by taxpayers, not bondholders
  • Consequently their priority is to save economy
  • Credit outlook is supported in the long run, but shorter term credit quality takes back stage
  • Action plans span a wide spectrum – from austerity support to “fiscal cliff” prevention

Slide 21

fiscally responsive cont d
Fiscally Responsive (cont’d)

Put Value =

R* = r + β RM+ RS

R* - “risk-neutral” return; RM – return on factor; RS – asset specific return

In the case of a Sovereign and a Single Bank bailout:

P =

In the case of a Sovereign and n – bank bailout:


Slide 22

monetarily responsive
Monetarily Responsive
  • Some governments are effectively able to control the amount of the national currency in circulation
  • In times of crisis central banks have a similar objective and align their action with governments
  • The “print” option is more subtle than tax hikes and does not require political approval

Slide 23

monetarily responsive cont d
Monetarily Responsive (cont’d)
  • The “print” scenario is also more advantageous to debt-holders as it spreads the credit loss with all users of the currency
  • PSov = (1 / MS ) * PSov_FISC
  • MS - Money Supply in its narrowest definition - currency in circulation and cash equivalents.

Slide 24

rogue sovereigns
Rogue Sovereigns
  • Rogue governments have little concern for taxpayers or the long term economic outlook
  • As long as government revenues fall under the debt threshold, the print route is imminent
  • Money is printed to meet ongoing government spending and current debt, not to pursue any real Keynesian effects to improve the economy
  • As soon as price level increases, meeting the ongoing spending becomes a moving target. Inflation rate becomes exponentially related to time.

Slide 25

rogue sovereigns cont d1
Rogue Sovereigns (cont’d)

PSov = {D - [D / H(t)]} + [ (1 / MS )

  • H(t) is the projected level of hyperinflation process.
  • D is the Sovereign Debt level
  • A is the Sovereign Asset level
  • What about asset volatility ?
    • Rogue sovereign domiciles often don’t have a liquid and transparent stock market which is an input to the credit model.

Slide 27

rogue sovereigns cont d2
Rogue Sovereigns (cont’d)

Sovereign asset volatility can be inferred:

  • Foreign currency debt is politically sensitive, prompting rogue government to grant it seniority
  • Foreign currency debt, hedged into local currency, is a portfolio of two call options:
    • A long call on sovereign assets with a strike = local currency debt value
    • A short call on sovereign assets with a strike = foreign currency debt value translated into local currency
  • We can use this portfolio to infer market implied sovereign asset volatility

Slide 28

a simplified summary
A Simplified Summary

Sovereign debt can be broken into two value portions. The first is “transcendentally riskless” the way we used to think of risk free assets. The second is equity in the banking system that holds the government’s debt and also has a call on bailout funding.

Governments have some options about what they do to manage their economies. The relative attractiveness of the options depends on the nature of the liability mix, the volatility of the tax revenue stream and whether the option to print money in still in place.

Slide 29


A model that captures the dynamics of sovereign credit risk in an economically justified way

The methodology is comprehensive regarding the customary types of government responses to a credit crisis

This model limits the use of implied inputs, which is dominant in other models

It is computationally tractable and does not pose insurmountable data requirements

Slide 30


Slide 31


DiBartolomeo, Dan, “Equity Risk, Credit Risk, Default Correlation, and Corporate Sustainability”, The Journal of Investing, Winter 2010, Vol. 19, No. 4: pp. 128-133

Merton, R.C., “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates”, Journal of Finance, 29 (1974), pp. 449-470

Leland, Hayne, and Klaus BjerreToft, “Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads”, Journal of Finance, 51 (1996), pp 987-1019

Zeng, B., and J. Zhang, “An Empirical Assessment of Asset Correlation Models.”, Moody’s KMV Working Paper, 2001.

Gray, Dale F., Robert C. Merton and ZviBodie, "Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk", July 3, 2007

Belev, Emilian, "The Euro Zone Debt Crisis vs. Northfield's Near Horizon Adaptive EE Risk Model - A Reality Check", Northfield working papers, http://www.northinfo.com/Documents/496.pdf, December 2011

Bolster, Paul, Ronald Johnson and VenkatSrinivasan,“Sovereign Debt Ratings: A Judgmental Model Based on the Analytic Hierarchy Process”, Journal of International Business Studies, 1990.

Slide 32