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Why Does Bad News Increase Volatility and Interest Rate, and Decrease Optimism, Asset Prices and Leverage?

Why Does Bad News Increase Volatility and Interest Rate, and Decrease Optimism, Asset Prices and Leverage?. F. Albert Wang University of Dayton. The Great Recession. A joint collapse of the mortgage and the housing markets during 2007-2009

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Why Does Bad News Increase Volatility and Interest Rate, and Decrease Optimism, Asset Prices and Leverage?

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  1. Why Does Bad News Increase Volatility and Interest Rate, and Decrease Optimism, Asset Prices and Leverage? F. Albert Wang University of Dayton

  2. The Great Recession • A joint collapse of the mortgage and the housing markets during 2007-2009 • A close interlock among mortgage, housing, and credit markets • A recurrent “leverage cycle” phenomenon in American financial history (Geanakoplos 2010) • Bad news increases volatility and interest rate, and decreases optimism, asset prices and leverage

  3. Theoretical Framework • Collateral constraints on asset pricing (Geanakoplos 2003, 2010) • Mortgage (risky derivative asset) vs. house collateral (underlying asset) • Asset prices derived from a risk-neutral probability under no arbitrage • Subjective house values based on natural buyers’ heterogeneous beliefs about the housing market • The risk-neutral probability is the marginal belief

  4. u 1 1 a a a p k q 1-a d 1-a 1 1-a d Asset Prices under No Arbitrage • Three assets: house, mortgage, and risk-free bond with prices (p, q, k) and risk-neutral probability (a) House (underlying asset) Mortgage (derivative asset)

  5. Asset Prices, Margin, Leverage, and Interest Rate • Asset prices: house (p); mortgage (q) • Margin: • Leverage: 1/m • Interest Rate:

  6. u h d 1-h Agents with Heterogeneous Beliefs 0 a 1 h pessimists optimists h= a = Marginal agent belief

  7. u h h d 1-h 1-h Maximizing Expected Utility • Endowment:1 house (Y) and 1 consumption good (e) • Pessimists think house (Y) is overpriced • Optimists think house (Y) is underpriced Y

  8. Market Clearing Condition and Equilibrium 0 a 1 • Pessimists sell all their houses, consume all endowment, and lend mortgage • Optimists buy houses using their endowment and borrowing to the max from mortgage • Combing no arbitrage asset pricing with equilibrium natural buyers to obtain a unique equilibrium: (a, p, q)

  9. 1 u-1 0 e 0 d Optimal Investment and Consumption pessimists optimists consumption consumption • Optimists use mortgage to maximize their housing investment and consume none now • Pessimists lend mortgage, shun housing investment, and smooth consumption

  10. The Dynamic Model • Extend the one-shot model into a dynamic model incorporating a possible crash in the interim period • Trading takes place at time 0 and subsequently at time 1 in either good state U or bad state D • The fundamental house value is realized at time 2 • Mortgage principal links to the underlying house collateral price in each state of each time • Why bad news increases volatility and interest rate, and decreases optimism, asset prices and leverage?

  11. The Contingent House Prices: Risk-neutral probabilities = marginal beliefs

  12. The Contingent Mortgage Prices: • Mortgage principal is the current house price • Maturity misalignment between short-term mortgage and long-term house v d

  13. Marginal Agent Beliefs: pessimists optimists new new pessimists optimists new new pessimists optimists

  14. Housing Market in Bad State D • Optimists default and leave the market • Pessimists (lenders) seize the house collateral • New aggregate endowment: consumption good (e) • Existing agents trade once again among themselves to maximize expected utility • New pessimists think the house is overpriced • New optimists think the house is underpriced

  15. Market Clearing Condition in Bad State D 0 • New pessimists sell all their houses, consume all endowment, and lend mortgage • New optimists buy houses using their endowment and borrowing to the max from mortgage

  16. Housing Market in Good State U • Optimists pay off mortgage principal and keep the house • Pessimists get payment and leave the market • Net aggregate endowment after debt payment: • Existing agents trade once again among themselves to maximize expected utility • New pessimists think the house is overpriced • New optimists think the house is underpriced

  17. Market Clearing Condition in Good State U 1 • New pessimists sell all their houses, consume all endowment, and lend mortgage • New optimists buy houses using their endowment and borrowing to the max from mortgage

  18. h h 1-h 1-h Maximizing Expected Utility in Initial State 0 • Endowment:1 house (Y) and 1 consumption good (e) • Pessimists think house (Y) is overpriced • Optimists think house (Y) is underpriced Y

  19. Market Clearing Condition in Initial State 0 0 1 • Pessimists sell all their houses, consume all endowment, and lend mortgage • Optimists buy houses using their endowment and borrowing to the max from mortgage

  20. The Equilibrium of the Dynamic Model • There exists a unique equilibrium of the model: • Extend Geanakoplos (2003, 2010) under risk-free mortgage to a general model under risky mortgage • Yield pro-cyclical mortgage credit, consistent with Schularick and Taylor (2012) • Provide endogenous leverage cycle and interest rate dynamics

  21. A Special Case under Risk-free Mortgage(Foster and Geanakoplos 2012) • Agents choose between Extreme Bad Volatility (EBV) and Extreme Good Volatility (EGV) projects • EBV or EGV: payoffs only volatile in bad or good times • Agents prefer EBV projects because they offer higher initial price and leverage • So, bad news increases volatility and decreases leverage • Re-examine this issue with two restricted assumptions: (1) extreme payoff structure and (2) risk-free mortgage

  22. Extreme Payoff Structure: • E. bad volatility (EBV) project: (u,v,d)=(1,1,0.2) • E. good volatility (EGV) project: (u,v,d)=(1,0.2,0.2)

  23. Risk-free Mortgage: • Mortgage principal is the low value of house next period, i.e., the recovery value v d

  24. Equilibrium Results: EBV Project vs. EGVProjectEBV project gives higher initial price and leverage

  25. Summary of Findings: EBV vs. EGV • Agents prefer EBV projects because they offer higher initial price and leverage • Flat interest rates dynamics • EBV project: extreme optimism and infinite leverage in good times • EGV project: extreme optimism and infinite leverage in bad times • Replicate results of Foster and Geanakoplos(2012)

  26. The Dynamic Model under Risky Mortgage • Relax the two restricted assumptions: (1) extreme payoff structure and (2) risk-free mortgage • Agents choose between bad volatility (BV) and good volatility (GV) projects under a general payoff structure • BV project: • GV project: • Examine the general properties of the dynamic model under risky mortgage, assuming

  27. Equilibrium Results: BV Project vs. GV ProjectBV project gives higher initial leverage, but lower initial price

  28. General Properties of the Dynamic Model • Agents still prefer BV projects because they offer higher initial leverage, though not higher price • Pro-cyclical optimism and asset prices • BV project: pro-cyclical leverage; counter-cyclical volatility and interest rate • Give a unified explanation: why bad news increases volatility and interest rate, and decreases optimism, asset prices and leverage

  29. Double Leverage Cycle (Geanakoplos 2010) • The Great Recession is particularly bad because it suffers from a “double leverage cycle” problem • One primary cycle in the housing market and one secondary cycle in the mortgage securities market • The same collateral (house) backs the mortgage payment first and the mortgage securities again • The two cycles reinforce each other in a positive feedback loop, resulting in greater volatility, more severe leverage cycle, and worse financial crises

  30. The Extended Model with Double Leverage Cycle • Add a secondary cycle in the mortgage securities • Let mortgage principal be a weighted average of the current house price and the recovery value • The “funding margin” (n) of the secondary cycle

  31. The Extended Model (Cont.) • Mortgage prices under double leverage cycle • The market clearing condition in good state U • BV (u,v,d) = (1.2,1,0.4) vs. GV (u,v,d) = (1.6,1,0.8) • Loose funding (n=0) vs. tight funding (n=0.2) • The marginal effect of tightening the funding margin in the secondary cycle on the primary cycle

  32. Equilibrium ResultsBV Project vs. GV ProjectLoose Funding (n=0) vs. Tight Funding (n=0.2)

  33. Main Findings of the Extended Model • Agents still prefer BV projects because they offer higher initial leverage, though not higher price • BV project: pro-cyclical optimism, asset prices and leverage; counter-cyclical volatility and interest rate • Bad news increases volatility and interest rate, and decreases optimism, asset prices and leverage • Tightening funding margin magnifies the leverage cycle and volatility • Double leverage cycle leads to more severe leverage cycle, thus resulting in worse financial crises

  34. Conclusion • Combine no arbitrage asset pricing with equilibrium natural buyers to obtain a dynamic model of leverage cycle and interest rate • Extend Geanakoplos (2003, 2010) under risk-free mortgage to a general model under risky mortgage • Explain why bad news raises volatility and interest rate, and reduces optimism, asset prices and leverage • Yield new testable implications: the marginal effect of funding margin on the leverage cycle • Double leverage cycle leads to more severe leverage cycle and worse financial crises

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