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Economy & Finance

Sovereign Debt in the 21st Century, ADEMU at Toulouse School of Economics, 5/6 April 2018

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- Sovereign Default and Information Frictions Christian Hellwig, Roberto Pancrazi, and Constance de Soyres Toulouse School of Economics, University of Warwick, Toulouse School of Economics August 22, 2017
- The Sovereign Bond Spread Puzzle • Sovereign bond spreads historical default losses → high excess returns, esp. for low-rated bonds • Spreads very volatile, only loosely connected to country fundamentals • Longstaff et al.: Sovereign credit risk driven more by global than country-specific factors. Global factor driving both default risk and default risk premia. • Puzzle as large, if not larger than corporate credit spread puzzle • Challenge for main models of sovereign debt dynamics in which default risk is fairly priced and tightly linked to country fundamentals (Arellano 2008 etc.)
- This paper • Document some stylized facts supporting sovereign bond spreads puzzle • Propose a resolution based on micro-structure frictions in bond markets (noisy information aggregation) • Explore impact of market frictions on country savings and default incentives. • Key theoretical challenge: how to increase the level and volatility of spreads, and maintain or increase borrowing incentives.
- - EMPIRICS -
- Empirical Motivation Data: • Dataset with CDS spreads on sovereign bonds of 69 countries, over the period 2008-2014, at 4 maturities 2, 3, 5, and 10 years (Datastream). • History of sovereign credit ratings (Moody’s). ⇒ We construct a dataset of CDS spreads net of the US spread by rating and by maturity.
- Empirical Motivation Stylized facts: 1 Sovereign bond CDS spreads are very high relative to historical default losses. 2 The gap between CDS spreads and historical default losses is larger for lower-rating bonds. 3 The gap present also for super safe (AAA, short maturity) bond: something else than default risk per-se ⇒ Hard to explain in standard models, in which price reﬂects expected losses and risk premium ⇒ The puzzle is as big, if not bigger, than for corporate bonds [Albagli, Hellwig and Tsyvinski (2013)]
- Empirical Motivation Average CDS Spreads (bps) Annualized Loss Rates (bps) 2 yr 3 yr 5 yr 10 y 2 yr 3 yr 5 yr 10 yr Aaa 12.52 14.45 27.71 26.05 0.00 0.00 0.00 0.00 Aa 47.52 55.54 73.38 79.11 0.00 2.55 7.20 4.36 A 112.23 120.99 137.85 139.05 1.55 7.04 9.77 22.99 Baa 174.47 189.63 212.26 222.43 9.95 10.91 10.26 7.56 Ba 244.48 258.92 278.30 281.07 32.41 40.98 45.83 51.31 B 977.91 959.56 907.97 892.71 120.43 107.03 94.25 69.34 Caa-C 1752.14 1583.39 1417.06 1235.32 939.29 724.24 434.55 217.27 Excess Return Sharpe Ratio CDS Spreads 2 yr 3 yr 5 yr 10 yr 2 yr 3 yr 5 yr 10 yr Aaa 12.52 14.45 27.71 26.05 0.32 0.35 0.65 0.60 Aa 47.52 52.99 66.18 74.75 0.63 0.72 1.02 1.21 A 110.68 113.95 128.08 116.06 0.70 0.80 1.01 1.10 Baa 164.52 178.72 202.00 214.87 0.85 0.98 1.27 1.55 Ba 213.07 217.94 232.47 229.76 0.83 0.93 1.18 1.41 B 857.48 852.53 813.72 823.37 0.97 1.08 1.15 1.22 Caa-C 812.85 859.15 928.51 1018.05 0.44 0.49 0.55 0.61
- Sovereign and Corporate Excess Returns
- - THEORY -
- A Super-Simple Model: Small Open Economy, 2 periods • Preferences Uc0 EUc1 , where Uc 1 1− c1− • Date 0: Income y0 1, legacy debt b0 • Country decides whether to repay, borrows b1 at bond price q qb1 . • Date 1: Income y1 eu , where u N0,u 2 . • Default at date 1 if y1 − b1 ≤ y1 u ≤ lnb1 − ln1 − • Value of default at date 0: D default threshold for legacy debt B̄.
- Country decision problem with no default at t 0: max b1 U1 − b0 b1qb1 EUmaxy1,y1 − b1 • First-order condition for b1: qb1 b1q′ b1 1 − b0 b1qb1 − Eeu − b1 − ¦u ≥ lnb1 − ln1 − Pru ≥ lnb1 − ln1 − • Evaluate date 0 default incentives through envelope condition on country objective.
- Eaton-Gersovitz (1981)/Arellano (2008): • Competitive bond-prices equal to repayment probabilities: qb1 Pru ≥ lnb1 − ln1 − 1 − lnb1 − ln1 − u • From FOC: qb1 b1q′ b1 qb1 Default option lowers marginal benefit of borrowing • Eeu − b1 − ¦u ≥ lnb1 − ln1 − Eeu − b1 − Default option lowers marginal cost of borrowing • Ambiguous effect of borrowing option on debt level (negative if is low, positive if high) • Idea: alter bond price formation to explore effect on savings incentives...
- Eaton-Gersovitz with public signal of y1: • Bond market has access to public signal z Nu,z 2 qb1,z Pru ≥ lnb1 − ln1 − ¦z 1 − 1 − lnb1 − ln1 − − z u where 1/z 2 1/u 21/z 2 . • Average bond price Eqb1,z Pru ≥ lnb1 − ln1 − doesn’t change (Martingale property of information) • Expected output, borrowing b1 and date 0 default threshold B̄ are all increasing in z. • Information adds to volatility (but not level) of spreads, volatility is tightly linked to informativeness of spreads about future default risk!
- Noisy information aggregation: • Unit measure of risk-neutral, informed foreign bond traders, decide whether to buy up to b1 units of bonds • Private Information: signals xi Nu,x 2 iid across bond traders • Demand by uninformed bond traders: b1s, where s N,s 2 , stochastic, inelastic • Noisy Rational expectations equilibrium: demand function dx,q ∈ 0,b1 , bond price function qu,s, such that: i bond traders’ demand is optimal, given information x,q, and ii markets clear for all u,s.
- Equilibrium Characterization: • Equilibrium characterized by threshold rule: buy if xi ≥ x̂P • Demand of bonds by informed traders: b1 1 − x̂P − u • Market-clearing: b1 b1 1 − x̂P − u b1s x̂P z u xs • Price qb1,z determined from indifference condition for trader with signal x̂P z: qb1,z Pru ≥ lnb1 − ln1 − ¦x z,z 1 − 1 − lnb1 − ln1 − − z u where 1/x 21/z 2 1/u 21/x 21/z 2 . • Market overweighs z: extra adjustment in marginal trader expectations to absorb shocks
- Implications for Borrowing: • qb1,z b1 q′ b1,z qb1,z b1q′ b1,z for most z: cheaper credit, higher b1 except if initial b1 very high or z very low. • Note: marginal costs (marginal disutility of repayment) is unchanged from before (since based on undistorted expectations) • Spreads loose disciplinary role (flatter in b1, less correlated with actual defaults) • z only loosely connected to u country credit conditions disconnected from fundamentals, borrowing driven by noise trader shock • Date 0 default incentives: lower for most realizations of z, but exposure to defaults driven by noise trader shocks (low z realizations)
- Implications for Default: • higher default incidence at t 1: due to higher b1 • Ambiguous at date 0: higher for low initial b0 because of exposure to low z shocks... • but lower for high initial b0 ("gambling for ressurrection") • Conclusion: Noisy information aggregation model can jointly account for: higher, more volatile spreads higher debt levels higher default incidence
- Theoretical model: Main Ingredients • Sovereign debt model a la Arellano (2008) • Simplifying assumptions: CRRA utility + random walk income growth • New ingredient: Information frictions between the traders who buy the sovereign bonds
- Theoretical model: Main Ingredients • Sovereign debt model a la Arellano (2008) • Simplifying assumptions: CRRA utility + random walk income growth • New ingredient: Information frictions between the traders who buy the sovereign bonds There are 2 types of traders: • Informed traders: receive a private signal about future income growth • Noise traders: buy a random fraction of the bonds In an environment with dispersed information, the market-clearing price is an endogenous public signal.
- Model: Timing • Sovereign: default decision, choose debt and consumption • Traders: observe public/private signal and price the bond t (at, yt) Default Decision yt+1 realizes (unobserved) Sovereign forms expectations on q(at+1, yt , ζt ) and chooses at+1 public signal ζt reveals private signal xt realizes traders submit bids market clear bond price emerges t + 1 (at+1, yt+1) • If Default, permanent exclusion from ﬁnancial market
- Model environment: Sovereign • Preferences: Et ∞ s=0 ρs U(ct+s) where 0 < ρ < 1 is the discount factor, c is consumption, and U(·) is increasing and strictly concave • Income growth process: ln (yt+1/yt) = ln t+1 ∼ N 0, σ2
- Model environment: Assets and default Sovereign • has access to perpetuities paying {λ, λ (1 − λ) , λ (1 − λ) 2 , ...} • can decide to default on its debt at any time • after a default, all the sovereign’s debt is erased, it is excluded permanently from ﬁnancial markets, and it incurs direct output costs
- Model environment: Sovereign’s value function V (at, yt) = max V (yt), max ct ,at+1 E {U (ct) + ρV (at+1, yt+1)} under the budget constraint ct + q (at+1, yt, yt+1, ζt) (at+1 − (1 − λ)at) = yt + λat • V (at, yt): sovereign’s value function at time t • V (yt): default value at time t
- Model environment: Sovereign’s value function V (at, yt) = max V (yt), max ct ,at+1 E {U (ct) + ρV (at+1, yt+1)} under the budget constraint ct + q (at+1, yt, yt+1, ζt) (at+1 − (1 − λ)at) = yt + λat • V (at, yt): sovereign’s value function at time t • V (yt): default value at time t The Sovereign’s Repayment set R(at+1): R(at+1) = {yt+1 : V (yt+1) ≤ max ct ,at+2 E {U (ct) + ρV (at+2, yt+2)}
- Model environment: Assets and default Traders • Large number, competitive, risk neutral • Have access to an international credit market where they can borrow/lend at rate r • Recover a fraction q ∈ (0, 1) of their initial investment if the country defaults • Face limits to their asset positions
- Model environment: Assets and default Traders • Informed traders (unit measure) receive a noisy private signal xt ∼ N ln yt+1 yt , β−1 • Noise traders buy a random fraction of the bonds Φ(ut) where ut ∼ N 0, 1 δ2 . • They all observe the endogenous public signal ζt coming from the price as they submit their bids on the market.
- Signal threshold condition Informed trader submits an order of −a , whenever; ˜q (α + µ, ζ) ≤ 1 1 + r q + ∞ ln α+µ α λ + (1 − λ) ˜q ˜α α − q d ˜f ln | x, ζ ⇔ x ≥ x(α + µ, ˜q) ˜f (·)= cdf of the future income growth conditional on the public signal ζ and the private signal x
- Market Clearing and equilibrium bond price The market clearing condition is: a 1 − Φ β (x(α + µ, ˜q) − ln ) + a Φ(u) = a Hence, the indiﬀerence condition for the signal threshold deﬁnes the traders’ bond price: ˜q (α + µ, ζ) = 1 1 + r q + ∞ ln (α+µ) α λ + (1 − λ) ˜q ˜α α − q d˜h ln | ζ, x = ζ where ˜h(· | ζ, x = ζ) is the conditional distribution of ln such that: ln ( | ζ, x = ζ) ∼ N β(1 + δ) 1 σ2 + β(1 + δ) ζ, 1 1 σ2 + β(1 + δ) = N γpζ, (1 − γp)σ2
- Recursive equilibrium A Recursive Bayesian Equilibrium consists of a bond price function ˜qt, a value function ˜V (·), a policy rule ˜α(·), a repayment set R(at+1), a schedule for the informed traders ai (at+1, yt, ˜qt, ζt, xt) ∈ [0, −at+1], and informed traders’ beliefs H(· | at+1, yt, ˜qt, ζt, xt) such that: (i) given the repayment set, ˜qt satisﬁes the bond price equation (ii) the value function and the policy rule, combined with the repayment set, solve the Bellman equation (iii) the schedule for the traders is optimal given their beliefs (iv) traders’ beliefs are consistent with Bayes’ rule (v) the bond price function clears the market for all (at+1, yt, yt+1, ζt, ut).
- Simplifying assumptions Proposition Let us assume that U(c) = c1−ψ /1 − ψ and V (y) = Dy1−ψ where D is a constant, and ψ the CRRA parameter. With the income growth process following a random walk, we can re-write the model using a single state variable, the Asset/Debt-to-GDP ratio α = a/y. Then: ˜V (a, y) = y1−ψ ˜v(α) ˜q(a , y, ζ) = ˜q(a /y, ζ) ˜α(a, y) = ˜α(α)y with: • ˜α(α) = α + µ = a /y • µ = (a − a)/y
- Simplifying Assumption: Sovereign’s value function ˜v(α) = max D, max c,µ E U c y + ρ (α + µ) 1−ψ (α ) ψ−1 ˜v (α ) subject to: c y = 1 + λα (1 − ˜q(α + µ, ζ)) − µ˜q(α + µ, ζ) ⇒ The sovereign decides to default whenever α ≤ α = ˜v−1 (D).
- - NUMERICAL ANALYSIS -
- Calibration Parameter Value Explanation ρ 0.82 Discount factor ψ 2 Coeﬃcient of relative risk aversion σ 0.025 Standard deviation of output growth λ 0.9 Maturity structure r 0.02 Constant risk-free interest rate κ 0.985 Share of output remaining after a default q 0.6 Recovery value of lenders Strategy: • Vary the precisions of the signals (β, δ), • (β, δ) → 0 = frictionless model; bond price reﬂects fundamental default risk
- Bond Price Schedule -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 Debt-GDP ratio 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Traderbondprice Low Public Signal Average Public Signal High Public Signal Frictionless (a) Higher Precision -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 Debt-GDP ratio 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Traderbondprice Low Public Signal Average Public Signal High Public Signal Frictionless (b) Lower Precision Figure: Bond Price Schedule
- Spreads and information frictions Information frictions increase average spreads due to overreaction of traders under bad signals Info Precisions Frictionless Friction Model δ = β std priv. std pub. ¯α Average ¯α Average Good Signal Bad Signal 0.75 2.6% 3.1% -0.43 0.24 -0.42 0.35 0.23 0.58 0.5 2.9% 4.2% -0.43 0.24 -0.37 0.43 0.24 0.74 0.25 3.5% 7.0% -0.43 0.24 -0.36 0.67 0.27 1.38 Table: Spreads
- Info frictions and fundamental default risk Information frictions are larger when default risk is higher Info Precisions Frictionless Friction Model ρ = 0.82 δ = β ¯α Average ¯α Average Good Signal Bad Signal 0.75 -0.43 0.24 -0.42 0.35 0.23 0.58 0.5 -0.43 0.24 -0.37 0.43 0.24 0.74 0.25 -0.43 0.24 -0.36 0.67 0.27 1.38 ρ = 0.875 δ = β ¯α Average ¯α Average Good Signal Bad Signal 0.75 -0.47 0.24 -0.45 0.35 0.23 0.58 0.5 -0.47 0.24 -0.44 0.40 0.23 0.64 0.25 -0.47 0.24 -0.40 0.53 0.23 0.99 Table: Information Frictions and Default Risk (i)
- WHAT ARE INFORMATION FRICTIONS?
- Spreads, Rating, Transparency Cross-section 0 1 2 3 4 5 6 Rating -500 0 500 1000 1500 2000 2500 Spread Rating and Spread ARG AUSAUT BHR BEL BRA BGR CHLCHN COL CRI HRV CYP CZE DNK DOM EGY EST FINFRADEU GRC GTM HUN ISL IDN IRL ISR ITA JAM JPN KAZ KOR LVA LTU MYS MLT MAR NLDNOR PAK PANPER PHLPOL PRT QAT ROU RUS SLV SAU SRB SGP SVK SVN ESP SWECHE THA TUR UKR GBR URY VEN
- Spreads, Rating, Transparency -500 1 0 500 0.8 6 1000 Spread 50.6 1500 BCI 4 2000 Rating 0.4 3 2500 20.2 1 0 0 (a) Rating, Transparency and Spreads
- Spreads, Transparency, and Rating Si = β0 + βf fundami + βj Xj + βT Transpi + βT,f fundami Transpi + εi . (a) (b) (c) (d) (e) (f) (g) (h) fundamental, βf 121.5*** 113.9*** 92.0* -98.1 -88.2 -58.7 -27.7 -3.8 (0.00) (0.00) (0.09) (0.24) (0.30) (0.50) (0.75) (0.54) transparency, βT 155.9 -214.3 -458.1 -444.9 -553.4 -362.3 (0.63) (0.56) (0.24) (0.29) (0.20) (0.25) Interaction, βT,f 301.2** 324.5** 286.4** 268.6** 24.24** (0.01) (0.01) (0.02) (0.03) (0.01) Constant, β0 -43.6 -719.7 -723.4 111.8 424.4 312.2 262.2 -12.6 (0.62) (0.49) (0.49) (0.39) (0.69) (0.78) (0.81) (0.98) controls NO YES YES NO YES YES YES YES dependent 2y 2y 2y 2y 2y 2y 2y 2y transparency BCI BCI BCI BCI BCI CPI WGI BCI fundamental rating rating rating rating rating rating rating FF Table: Regressions - 2 year Spreads
- Spreads, Transparency, and Rating Main take-away: Non-linear eﬀect of Transparency on Sovereign Spreads • Transparency does not aﬀect spreads when default risk is low • Transparency signiﬁcantly aﬀects spreads when default risk is high • Robust to diﬀerent maturity • Robust to diﬀerent measure of transparency
- Conclusion 1 Sovereign bond Excess Return Puzzle: • CDS spreads >> historical default losses. 2 Endogenous default model with information frictions: • Bad signals on future income aﬀects equilibrium spreads • Eﬀects larger when high fundamental default risk 3 Transparency, Ratings, and Spreads: • Lack of Transparency contributes to increase spreads in higher default risk country
- Conclusion 1 Sovereign bond Excess Return Puzzle: • CDS spreads >> historical default losses. 2 Endogenous default model with information frictions: • Bad signals on future income aﬀects equilibrium spreads • Eﬀects larger when high fundamental default risk 3 Transparency, Ratings, and Spreads: • Lack of Transparency contributes to increase spreads in higher default risk country Next Steps: • Work on reﬁned calibration of the model • Tighten the link between Transparency and Information frictions

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