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Good Ponzi schemes and the price of debt

Good Ponzi schemes and the price of debt. Bernardo Guimarães CEP Annual Conference 2005. The story of Carlo Ponzi An unprofitable business, A creative borrowing strategy, borrowing from Peter to pay Paul, And a few months of glory. National debts

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Good Ponzi schemes and the price of debt

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  1. Good Ponzi schemes and the price of debt Bernardo Guimarães CEP Annual Conference 2005

  2. The story of Carlo Ponzi • An unprofitable business, • A creative borrowing strategy, • borrowing from Peter to pay Paul, • And a few months of glory.

  3. National debts • Average maturity of OECD countries’ debts: 4.5-6 years. • Size of debt: 60%, 80%, 100% of their GDP. • Debt maturing in 1 year or less: 10-20% of countries’ GDPs. • How can a country pay that? • Emerging markets: shorter maturities. • Brazil in 2000: maturity of 50% of internal debt < 1 year. • It did manage to roll over the whole amount… • Short run: borrowing from Peter to pay Paul.

  4. Purpose of this paper • Framework for studying debt roll-over. • Focus on the price of debt. • Related Literature • Coordination and the price of debt (Morris and Shin, 2004). • static model, expectations, coordination. • The deficit gamble (Bohn, 1995 and Ball et al, 1998). • sustainability of deficits (long run question).

  5. Some results • Heterogeneity among (timing of) lenders makes a big difference, • Role of reserves, • Expectations about debtor’s policy, • Effects of maturity.

  6. Benchmark model • The debtor: • Stochastic cash flow ( Dq ~ N(mq,sq) ). • Stock of cash: q --- also affected by interest payments. • May issue debt (D): • Goes bankrupt and defaults when there is not enough money. • Lenders are paid pro-rata if there is some money. • Objective: • Survive as long as it can.

  7. Benchmark model with synchronized lenders • The lenders: • Continuum of lenders (measure 1, they have limited money). • They all come at the same time and stay for exactly DT. Then, they leave the economy and another set of lenders come in. • Assumption: lenders perfectly coordinate.

  8. Benchmark model with synchronized lenders • Equilibrium: • Lenders get 0 expected return. • Debtor may choose to borrow: • from a small fraction of lenders. • only when q is not too bad. • Ponzi scheme may provide a little help to survive (if mq > 0). • little or no long run effects.

  9. Benchmark model with synchronized lenders

  10. Adding heterogeneity in the model • Lenders: • At every period (Dt, small), l.Dt lenders arrive. • Lenders’ time in the economy: geometric distribution: • (l.Dt).(l.Dt) stay for 1 period, • (l.Dt).(l.Dt).(1 – l.Dt) stay for 2 periods, • (l.Dt).(l.Dt).(1 – l.Dt)2 stay for 3 periods, • and so on. • One state variable (D) tells me all about maturity of debt (no memory, no need to keep track of history).

  11. Adding heterogeneity in the model • Results: • I can’t calculate the optimal borrowing scheme for the debtor… • … but numerical examples show a much larger impact in the odds of surviving. • Key reason: externality provided by former lenders (they are stuck in their position).

  12. Good Ponzi schemes

  13. The price of debt

  14. Maturity

  15. Forward looking behavior of the interest rate. • Results: • interest rate paid today may be lower if debtor is expected to borrow even with worse values of q in the future. • however, the optimal scheme may be not borrow in the case of so bad values of q. • short-run biased debtor may be willing to tie its hands, but that may not be optimal…

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