Long-duration Bonds and Sovereign Defaults Juan C. Hatchondo Richmond Fed Leonardo Martinez Richmond Fed June 3, 2009 1
Business cycles in emerging economies Emerging Economies Developed Economies σ(gdp) 2.79 1.37 σ(p C)/σ(GDP) 1.30 0.92 σ(r) 2.32 1.66 ρ(r, GDP) -0.55 0.20 Source: Neumeyer and Perri (JME 05) Interest rates are also substantially higher in emerging economies. 2
Sovereign default models Interest rate = risk-free rate + default premium. Problem with the baseline model: Default premium generated by the model is too low and not volatile enough to account for the behavior of interest rates in emerging economies (Aguiar and Gopinath JIE 2006). Arellano (AER 2008): spread is close to zero most of the time and is too high in the period preceding a default. Chatterjee and Eyigungor (2009), Arellano and Ramanarayanan (2008). 3
Arellano (AER 08) 4
What do we do? We propose a tractable extension to the baseline framework of sovereign default that allows us to study long-duration bonds without expanding the state space. Macaulay definition of duration of a bond that pays a deterministic sequence of cash flows {X t } t=1 Duration t=1 t X t (1 + r ) t q where t denotes payment dates, q denotes the bond price, and r denotes the constant per-period yield delivered by the bond. 5
We compare two economies. Main findings Government issues perpetual bonds with decreasing coupons. Duration of debt = four years (sovereign bonds in emerging economies). Government issues one-period bonds (same as in previous studies). Duration of debt = one quarter. We show that in the economy with long-duration bonds the mean and the volatility of the interest rate are substantially larger than in the economy with one-period bonds. 6
The model Stochastic endowment economy. log(y t ) = (1 ρ) µ + ρlog(y t 1 ) + ε t, where ρ < 1, and ε t N (0,σ 2 ǫ ) Objective of the government: where [ ] Max E t β s u (c t+s ) s=0 u (c) = c1 σ 1 σ 7
Borrowing opportunities Risk-neutral lenders with deep pockets. Opportunity cost of lending: risk-free bonds paying r. Incomplete markets: only non-contingent bonds. Each period the government can choose any issuance amount for that period, anticipating that the issuance price is such that lenders buying bonds make zero profits in expectation. Frictionless competitive credit market with exclusive borrowing contracts. 8
Our bonds A bond promises an infinite stream of coupon payments that decreases at a rate δ. 1 1- δ (1- δ) 2 t t + 1 t + 2 t + 3 9
Advantages of this approach It allows us to study long-duration bonds without increasing the dimensionality of the state space. Law of motion for coupon payment obligations when there is no default: b = b(1 δ) ι where ι = current issuance level. One-period debt is a special case (δ = 1). Value of δ can be chosen to mimic average debt duration in the data. Duration = 1+r δ+r. 10
Debt duration in emerging markets Argentina 4.13 Brazil 4.94 China 4.56 Ecuador 5.90 Russia 5.78 Turkey 5.95 Venezuela 4.15 Average 4.77 Source: Cruces et. al. (2002) using data from J.P. Morgan 2000. 11
Defaults The government cannot commit to honor debt contracts. If the government defaults, current output is reduced by φ (y) = λy. Total defaults: The government announces that it will not pay any current or future coupon obligations contracted in the past. 12
Equilibrium concept: Markov Perfect The government cannot commit to future default and borrowing decisions: Each period the government decides whether to default and the volume of new debt issuances taking as given its future default and borrowing strategies. Strategies depend on payoff-relevant state variables. If the government could commit to future default and borrowing decisions, it would internalize the effects of period-t decisions on every period before t. 13
Recursive formulation V (b,y) = max {dṽ dǫ{0,1} (1,b,y) + (1 d)ṽ (0,b,y)} Ṽ (d,b,y) = max b 0 { u (c) + β } V (b,y )F (dy y), c = y dφ (y) + (1 d)b q(b,y) (b (1 d)(1 δ)b) 14
Zero-profit bond price With long-term debt, bond price depend on all future borrowing and default decisions, not only on next period borrowing and default decisions. q ZP (b,y) = 1 1 + r 1 δ 1 + r (1 d ) F (dy y) + }{{} Expected coupon payment in the next period (1 d ) q ZP (b,y )F (dy y), }{{} Expected value of current debt in the next period where d = h(b,y ), and b = g(h(b,y ),b,y ). 15
Markov perfect equilibrium 1. a set of value functions Ṽ (d,b,y) and V (b,y), 2. a default decision rule h (b,y) and a borrowing rule g(d,b,y), 3. and a bond price function q ZP (b,y), such that: (a) given h (b,y) and g(d,b,y), V (b,y) and Ṽ (d,b,y) satisfy the functional equations presented before, when the government can trade bonds at q ZP (b,y); (b) given h (b,y) and g(d,b,y), q ZP (b,y) satisfies the lenders zero-profit condition; (c) h (b,y) and g(d,b,y) solve the dynamic programming problems presented before when the government can trade bonds at q ZP (b,y). 16
Parameterization We solve the model numerically. φ(y) = λy. λ {0.083, 0.2, 0.5}. Risk aversion σ 2 Interest rate r 1% Output autocorrelation coefficient ρ 0.9 Standard deviation of innovations σ ǫ 2.7% Mean log output µ (-1/2)σǫ 2 Discount factor β 0.95 We present results for δ = 1 and δ = 0.045. 17
Simulations Moments: averages over 500 samples of 32 periods before a default episode. λ =0.1 λ =0.2 λ =0.5 data 1Q 4Y 1Q 4y 1Q 4Y σ (R s ) 2.51 0.03 0.27 0.04 0.29 0.06 0.33 E(R s ) 7.44 0.12 3.01 0.11 2.93 0.12 2.73 debt/output 9.0 10.0 18 21 44 51 18
Mechanism 1. With long-duration bonds, equilibrium spreads depend on the default probability in every future period spreads depend on borrowing decisions in every future period (debt dilution). 2. The government cannot commit to future borrowing levels. Consequence: 1) borrowing decisions in every period do not internalize the effects of those decisions on the price of past debt issuances; 2) Lenders anticipate future borrowing behavior and charge a discount on current bond prices accordingly. 3. With one-period bonds this effect is not present. 19
Borrowing opportunities and choices 4 y low y high 4 y low y high 3 3 Annual spread (%) 2 Annual spread (%) 2 1 1 0.6 0 0.5 0.4 0.3 0.2 0.1 0 Debt (a) Duration = one quarter 0.6 0 0.5 0.4 0.3 0.2 0.1 0 Debt (b) Duration = four years 20
Borrowing opportunities q ZP (b, y) = 1 1 + r (1 d ) F (dy y) + 1 δ 1 + r (1 d ) q ZP (b, y )F (dy y) where d = h (b, y ), and b = g(h(b, y ), b, y ). 21
Borrowing choices Let b (1 d)(1 δ)b. u 1 (c) q(b,y) }{{} Current benefit = β u 1 (c ) (1 d ) [1 + q(b,y )(1 δ)]f(dy y) } {{ } Future cost ( ) u 1 (c) q 1 (b,y) b b }{{} Current cost 22
Arellano (AER 08) 23
The economy is better off with shorter bonds 2 x 10 4 1 Consumption compensation 0 1 2 3 4 Low income Mean income High income 5 0.65 0.7 0.75 0.8 δ 0.85 0.9 0.95 1 24
Conclusions We presented an extended version of the baseline model of sovereign default that allows us to study long-duration bonds. We showed that with four-year bonds, the mean and the volatility of the interest rate are substantially larger than with one-quarter bonds. This indicates that the extended model could be a useful tool for future research about emerging economies. 25