QUIET BUBBLES

Harrison Hong  

Princeton University 

David Sraer  

Princeton University

First Draft: November 1, 2010 

This Draft: February 21, 2011

LOUD VERSUS QUIET BUBBLES

• Credit bubble in AAA/AA tranches of subprime mortgage CDOs cause of financial crisis. 
• Lacked many features that characterize classic speculative episodes. Classic bubbles loud: high price, high price volatility and high turnover. 
• Over-trading as investors buy in anticipation of capital gains. 
• Internet stocks during 1996-2000: price volatility excess of100% and more than 20% of stock market turnover. 
• Credit bubble quiet: high price but low price volatility and low turnover.

THIS PAPER


A theory (taxonomy) of loud and quiet bubbles. Build on disagreement and short-sales constraint literature.

- Over-pricing in a static setting (Miller '77, Chen-Hong-Stein '02). - Resale option in a dynamic setting (Harrison-Kreps '78, Scheinkman-Xiong '03). 

- Excessive turnover and volatility as previous pessimists' valuations exceed today's optimists. 

Leverage and skewed heterogeneous priors - quiet bubbles! - Applies to any instrument that have weakly concave pay-offs.

IMPLICATIONS OF ANALYSIS
A unified approach that can explain both dot-com and the so-called "housing bubble". 

- Bubble not in homes per se so much as in the mortgages or "credits" traded by institutions. 

Our theory offers a rationale for why smart investment banks and regulators failed to see the bubble THIS TIME?

- Low price volatility made these instruments appear safer versus high price volatility of dot-com stocks. 

- Quietness of the bubble would have made it difficult to detect even for regulators without a shadow banking economy. 

A model of Hyman Minsky's dangers of bubbles fueled by credit. • A first taxonomy of bubbles.

- Word "bubble" is too coarse, need to distinguish between different types of bubbles.

MODEL

• Three dates t = 0, 1, and 2 with risk-free asset equals zero. Risky debt w/ face value of D and pay-offs at t = 1; 2: 
• mt = Min[0 , Max(D , Ft)] ; Ft =F+εt ; and εt's are iid: normal ɸ(.). 
• 
  
• Any t = 1 (interim) cash-flow occurs on the terminal date and accrues to holders of the asset at t = 0. 
• Initial supply Q of this risky asset.
• Competitive agents hold heterogenous priors (t = 0) relative to the mean of the underlying asset: 

Vt =V+εt; 

• where V has the following distribution function across the population of agents:

At t = 1, only the agents withV = σ will receive a binomial shock to their belief given by

The expected payoff an agent with belief v regarding mt is given by

where π can be any (weakly) concave expected pay-off function.

Agents are endowed with zero wealth.
Access to a credit market that is imperfectly competitive.
The discount rate is 0 but banks charge a positive interest rate,which we call 1/λ and let

which is increasing with the efficiency of the credit market.

Quadratic trading costs given by

where nt isthesharesheldbyanagentattimetandn-1 =0for all agents.

Let P1 bethepriceoftheassetatt=1.Att=1, for an investor with belief V1, prior V , and n0(V ):

Let J(n0;V) be the value function - option to re-sale of the asset bought at t = 0 at a higher price to the

σ-agents that get a draw on their belief at t = 1

Let P0 bethepriceoftheassetatt=0.Thenatt= 0, agents with prior V have the following optimization program:

The equilibrium prices in both periods will be determined by the usual market clearing conditions.

SKETCH OF DYNAMIC EQUILIBRIUM

Construct a dynamic equilibrium with the following features that match a quiet bubble:

High price (high P0 and P1 relative to the fundamental F).

A sufficient condition is by having only the x-agents, the most optimistic, be long at t = 0. 

Low price volatility between t = 0 and t = 1. Price volatility is defined simply by

σP = |P1(-η) - P1(η)| . 

Price only varies at t = 1 due to the shock to the σ-agents' belief.

Low share turnover. Since the x-agents long all the shares at t = 0, expected turnover is

T = E|n1(x) - n0(x)|; 

where the x-agents' holding at t = 1 depend on the shock to the belief of the σ-agents.

Shocks to beliefs η's will not impact price volatility and turnover the bigger is x assuming sufficient leverage.

Proposition 1

The asset’s equilibrium price can be larger than under a symmetric distribution of priors. A decrease in the cost of leverage leads to (1) higher prices (more over-pricing) overall and (2) prices that increase over a wider range of skewness.

Debt more concave than equity in V, so leverage even more important to get high prices.

Theorem 2
Assume μγ is sufficiently large. The following three cases characterize an equilibrium in which only the x-agents are long at t=0.

Proposition 2

Assuming leverage is sufficiently cheap (i.e. μγ is large enough), then at t = 0, only the skewed x-investors are long the asset. 

Price volatility between t = 0 and t = 1 is decreasing as x increases, 

i.e. σP (Case 1) < σP (Case 2) < σP (Case 3). Expected turnover between t = 0 and t = 1 is decreasing as x increases, i.e. T (Case 1) < T (Case 2) < T (Case 3).

Conclusion
Alternative narratives of the financial crisis
(1) Financial Innovation and tail risks (Geniaoli, Shleifer and Vishny ’10).

— Dot com was a new innovation, why didn’t banks and regu- lators get caught during dot-com? 

(2) Agency and risk-shifting (see, e.g., Allen-Gale ’00).

— Agency problems also severe during dot com, but banks and regulators didn’t get caught then. 

The challenge of a unified theory to explain why this time (i.e. to explain both dot-com and credit/housing bubble)

The ”unified” narrative offers an answer and a different take on the crisis.

— Leverage led to low price volatility and turnover which made the credit bubble harder to detect. 

— Not a perfect storm that caused the crisis, but tranquility!