A macrofinance view of US sovereign CDS premiums

Mikhail Chernov joint work with Lukas Schmid (Duke) and Andres Schneider (UCLA)

Wisconsin School of Business | April 2017

This version: April 5, 2017 0 / 26

0

20

40

60

2007−04−02 The US crisis

100

2008−10−01 2010−04−01 2011−10−03 2013−04−01 2014−10−01 Brexit

Debt ceiling 2015

Fears of Greek default 2015

Debt ceiling 2013

Fears of Greek default 2011 Fiscal cliff

Debt ceiling 2011

Beginning of the Euro Crisis

80

History of US CDS premiums

2016−03−31

1 / 26

Which risks are compensated in this market? Our main objective is to establish a quantitative benchmark for thinking about this question There are a lot of reasons to think that various institutional features result in frictions that are responsible for at least some of the premium We do not disagree with this but we want to start with the first risk that comes to mind in this context: default We’d like to establish what kind of a premium default risk would command in a “standard” model I

I

Use a fundamentals-based model that is used in the literature for valuation of various assets Complement the model with features necessary to generate endogenous default 2 / 26

Outline of our model Endowment economy with Epstein-Zin rep. agent Aggregate output, consumption growth and government expenditures are exogenous Monetary policy and fiscal policy The government budget constraint (GBC) ties all of this together By assumption, an increase in the tax rate has a negative effect on long-term output growth This feature may lead to fiscal default when the GBC-based tax rate is larger than the one that leads to sustainable surplus 3 / 26

Implications

High government debt corresponds to high marginal utility states Writers of protection against the USA face payments in these states Despite losses on government debt being relatively small, they occur in the worst of all states This leads to high premiums

4 / 26

Counterfactual experiments

Inflate debt away Tax debt away Effects of QE

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Corporate CDS No payment upfront Protection buyer pays quarterly premium In case of default protection seller pays face value in exchange for a bond, or cash settles Valuation by no-arbitrage: I I

Buy corporate + protection via CDS = riskless security If Treasury is riskless, should be the same value

As a result, credit spreads (corporate bond yield minus Treasury bond yield) serve as a benchmark for CDS valuation Details I I I

Marking to market / collateralization CDS-bond basis Big/Small Bang protocols

6 / 26

Sovereign CDS

What if Treasury bond is defaultible? I I

Buy Treasury + protection via CDS = riskless security But there is no other riskless security to compare its value to

A sovereign CDS is a non-redundant contract even ignoring various institutional details Absence of replication calls for an equilibrium approach to valuation of sovereign US CDS

7 / 26

Additional risks Currency risk: US CDS are denominated in e I

$ contracts are traded since 08/2010 (ave spread is 8 bps/25%)

Recovery risk: the economic value is uncertain + the auction procedure Liquidity risk: outstanding net notional amount is $3 bn Regulatory risk: Basel III allows dealers to buy protection against their counterparties to reduce a capital charge associated with counterparty risk Legal risk: credit event determination

8 / 26

Valuing default risk: Roadmap Consider the simplest case of a one-period nominal bond Denote default time by t D , loss given default by L, and the $ nominal pricing kernel by Mt,t+1 Then the bond’s price is  h i $ (1 − 1{t D =t+1} ) + (1 − L)1{t D =t+1} Qts = Et Mt,t+1 To do list: I

I

I

Macro-based economy that delivers the real pricing kernel Mt,t+1 (Epstein-Zin/Bansal-Yaron) $ Inflation that connects Mt,t+1 and Mt,t+1 (Monetary policy/Taylor rule) What determines default time t D ? (Fiscal policy/Laffer curve) 9 / 26

The model: Endowment economy A global representative agent with recursive preferences: Ut

1/ρ

= [(1 − β)Ctρ + βµt (Ut+1 )ρ ]

α µt (Ut+1 ) = Et (Ut+1 )1/α

Consumption growth (Bansal and Yaron, 2004; Model I): ∆ct+1 = ν + xt + σc εt+1 xt+1 = ϕx xt + σx εt+1 Additional notation: I I

This setup implies the real pricing kernel Mt To value nominal securities, we’ll need inflation Πt = Pt /Pt−1

10 / 26

The model: the economy and the government

US (log) output growth: ∆yt+1 = ν + ϕy (τt − τ ) + σy εt+1 I I

τt = log Tt is the (log) tax rate deviations of the prevailing tax rate from the mean affect future growth prospects, ϕy < 0

Log of government expenditures (as a fraction of output): gt+1 = (1 − ϕg )g + ϕg gt − σg εt+1

11 / 26

Financing expenditures The government raises taxes and issues nominal debt to finance expenditures I I

Tax receipts are Tt Yt The nominal face value of debt is Nt

Two types of nominal debt: I

I

I

One-period bond with a price Qts – instrument of the conventional MP Long-term bond with a price Qt` , coupon γ and repayment fraction λ ST and LT debt is issued in constant proportion: Nts = ωNt and Nt` = (1 − ω)Nt

The real face value of debt as a fraction of output is Bt = (Nt /Pt )/Yt

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The Government Budget Constraint The properties of debt and taxes are connected via the government budget constraint (GBC): ` Tt Yt + Qt` (Nt` − (1 − λ)Nt−1 )/Pt + Qts Nts /Pt ` s = (γ + λ)Nt−1 /Pt + Nt−1 /Pt + Gt Yt

I I I I

Tax receipts Government expenditures Debt repayment Raising new debt

13 / 26

The Government Budget Constraint The properties of debt and taxes are connected via the government budget constraint (GBC): ` Tt Yt + Qt` (Nt` − (1 − λ)Nt−1 )/Pt + Qts Nts /Pt ` s = (γ + λ)Nt−1 /Pt + Nt−1 /Pt + Gt Yt

I I I I

Tax receipts Government expenditures Debt repayment Raising new debt

The implied tax rate is: −1 Tt = Gt − Qt Bt + CFt · Bt−1 Π−1 t (Yt /Yt−1 ) I I

Qt ≡ ωQts + (1 − ω)Qt` is the market value of debt CFt ≡ ω + (1 − ω)(γ + λ + (1 − λ)Qt` ) is the promised cash flow 13 / 26

Policies Monetary policy −qts I I I

= δ0 + δπ πt + δy ∆yt + ξtq

Taylor rule Determines πt when combined with the pricing kernel Normally, has no real impact in an endowment economy; here affects the real value of debt via the GBC

Fiscal policy bt = ρ0 + ρb bt−1 + ρx xt + ξtb I

I

New debt issuance is determined by debt outstanding and global economic conditions The tax rate is then determined via the GBC 14 / 26

Default Fiscal default in the spirit of Laffer curves At some point further tax increases lowers tax revenues Our model captures this with ϕy < 0 The expected surplus is ∞ X St = Et Mt,t+j (Tt+j − Gt+j )Yt+j /Yt j=1

The fiscal limit Tt∗ is related the maximum sustainable surplus St∗ = Et

∞ X j=1

I

∗ Mt,t+j (Tt+j ∧ Tt∗ − Gt+j )Yt+j /Yt∗

Tt∗ solves St = St∗

Default when Tt ≥ Tt∗

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Calibration: exogenous variables Valuation: Bansal and Yaron (2004) Macro: I I

Expenditures: fit an AR(1) to the 2000 - 2014 period Output: ϕy = −0.024 (Croce, Kung, Nguyen, and Schmid, 2012)

Debt: I I I I

Share of short term debt ω = 0.2 Repayment rate λ = 0.04 Coupon γ = 0.05 Loss given default L = 0.2

Policy: I I

the Taylor principle is satisfied ρx < 0, so negative shock to expected consumption growth leads to increase in debt

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Calibration: endogenous variables

Market value of debt (Qt Bt ) Taxes (Tt ) Annual gross inflation (Πt )

Debt limit (St∗ ) Tax limit (Tt∗ ) Default probability (PtD )

Data Mean Std

Model Mean Std

0.916 0.326 1.011

0.903 0.354 1.012

0.112 0.124 0.027

1.414 0.829 0.002

0.119 0.068 0.001

0.086 0.031 0.012

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CHAPTER ONE CBO estimate of B as of 07/12/2016

THE 2016 LONG-TERM BUDGET OUTLOOK

Figure 1-1.

Federal Debt Held by the Public Percentage of Gross Domestic Product

150

Actual

Extended Baseline Projection

125 World War II

100 75 Great Depression

50 Civil War

World War I

25 0 1790

1810

1830

1850

1870

1890

1910

1930

1950

1970

1990

2010

High and rising federal debt would reduce national saving and income in the long term; increase the government’s interest payments, thereby putting more pressure on the rest of the budget; limit lawmakers’ ability to respond to unforeseen events; and increase the likelihood of a fiscal crisis.

2030

Source: Congressional Budget Office. For details about the sources of data used for past debt held by the public, see Congressional Budget Office, Historical Data on Federal Debt Held by the Public (July 2010), www.cbo.gov/publication/21728. The extended baseline generally reflects current law, following CBO’s 10-year baseline budget projections through 2026 and then extending most of the concepts underlying those baseline projections for the rest of the long-term projection period.

Later in the 10-year baseline period, CBO projects, deficits would be notably larger, approaching 5 percent of GDP if current laws generally remain unchanged.

Meanwhile, rising revenues would keep pace with the economy and remain close to 18 percent of GDP over the next 10 years, largely reflecting offsetting movements

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Basic implications via impulse responses −3

x 10

x

g

0.1

−0.33

0.066

0.066

−0.66

0.033

0.033

−1

0 0

50

100

τ

0.1

0 0

50

100

∆y

0

0

−0.006

0.0066

0.033

−0.013

0.003

0

−0.02 50

100

τ∗

0

50

P

0.00025

100

0

D

0.00016

0.266

0.00008

0.13

−0.02

0 100

50

100

m

0.4

−0.013 50

100

0 0

−0.006

0

50

π

0.01

0.066

0

b

0.1

0 0

50

100

0

50

100

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Term structure of US interest rates

Maturity, years 1 3 5 10

Real yields

Model Pseudo risk-free yields

Yields

Data Yields

0.52 0.46 0.38 0.21

1.90 2.27 2.59 3.41

2.09 2.48 2.83 3.68

2.01 2.53 3.03 3.76

20 / 26

0

20

40

60

2007−04−02 The US crisis

100

2008−10−01 2010−04−01 2011−10−03 2013−04−01 2014−10−01 Brexit

Debt ceiling 2015

Fears of Greek default 2015

Debt ceiling 2013

Fears of Greek default 2011 Fiscal cliff

Debt ceiling 2011

Beginning of the Euro Crisis

80

US CDS premiums / FX

2016−03−31

21 / 26

0

20

40

60

2007−04−02 The US crisis

100

2008−10−01 2010−04−01 2011−10−03 2013−04−01 2014−10−01 Brexit

Debt ceiling 2015

Fears of Greek default 2015

Debt ceiling 2013

Fears of Greek default 2011 Fiscal cliff

Debt ceiling 2011

Beginning of the Euro Crisis

80

US CDS premiums / FX

2016−03−31

21 / 26

Term structure of US CDS spreads

Maturity, years

Data e 2007 –

Data e 2010 –

Data $ 2010 –

Model

L·Mean(PtD )

1 3 5 10

16.13 22.18 29.34 40.79

15.61 21.66 31.29 46.86

13.29 17.32 23.11 34.92

11.42 15.94 20.72 33.91

3.97 5.62 7.30 12.16

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Changes in monetary stance

δπ 1.50 1.35 1.20

Mean CDSt (5)

Qt Bt

PtD

0.9034 0.8829 0.8538

0.0024 0.0022 0.0019

21 23 24

Πt

Std Πt

1.0123 1.0181 1.0236

0.0274 0.0315 0.0382

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Changes in fiscal stance

ρb 0.96 0.94 0.92

Mean CDSt (5)

Qt Bt

PtD

0.9034 0.8729 0.8515

0.0024 0.0021 0.0019

21 23 25

Tt

Std Tt

0.3540 0.3817 0.4022

0.1237 0.1365 0.1443

24 / 26

Changes in debt duration

λ 0.01 0.04 0.16

PtD

Mean CDSt (5)

0.0021 0.0024 0.0032

18 21 27

Std Tt

Qt Bt

0.1190 0.1237 0.1436

0.1081 0.1124 0.1317

25 / 26

Summary CDS premiums on US Govt are high Understanding this phenomenon calls for an equilibrium approach as basic replication is not feasible We use off-the-shelf elements to construct a macro-finance model featuring: I I I I

A rep. agent with recursive preferences Output that declines with increase in taxes Monetary and fiscal policies GBC

The model leads to endogenous debt, taxes, and inflation Laffer-curve-style effect leads to fiscal default High debt and default probability episodes endogenously correspond to high marginal utility states in the model This feature leads to quantitatively realistic magnitudes of CDS premiums 26 / 26