Asset Float and Speculative Bubbles

HARRISON HONG, JOSE SCHEINKMAN, and WEI XIONG


The Journal of finance ,March 27, 2005 

Abstract

Model the relationship between asset float (tradeable shares) and speculative bubbles

Investors trade a stock with limited at because of insider lock-ups

have heterogeneous beliefs due to overconfidence and face short-sales constraints

A bubble arises as

price overweighs optimists' beliefs

investors anticipate the option to resell to those with even higher valuations

The bubble's size depends on

float as investors anticipate an increase in float with lock-up expirations

speculate over the degree of insider selling

On the lock-up expiration date

the bubble, turnover and volatility decrease with float and prices drop

Price Level Correlated with Turnover

• Speculation in Stock Market 
• Large Trading Volume 
• Need risk-sharing and liquidity to get trades but magnitudes seem too large

Volume, Risk and Expected Return

• Daily price-variability and volume correlated (Epps and Epps 1976, Tauchen and Pitts 1983) and volume ameliorates leverage effect (Gallant, Rossi and Tauchen 1992) 
• Abnormally high volume past 6-12 months forecasts low monthly returns in time-series and cross-section, controlling for liquidity measures (Piqueira 2006, Baker and Stein 2004, Mei, Scheinkman and Xiong 2005) 
• More momentum in high volume stocks (Lee and Swaminathan 2000) 
• Abnormally high volume and high past returns forecasts crashes or negative skewness (Chen, Hong and Stein 2003)

Different Approaches

Liquidity and asymmetric information models (Campbell, Grossman and Wang 1993, Wang 1994)

- Volume proportional to liquidity trades

Noise traders or limits of arbitrage approach (Delong, Shleifer, Summers and Waldman 1990)

- No volume without large price moves

Disagreement approach (agree to disagree about fundamentals)

Start with speculative motive which can generate large trading volume absent price moves and see price implications

Develop simple A-B model to explain above stylized facts

SET UP

• a discrete-time, multi-period model 
• investors trade a stock that initially has a limited float because of lock-up restrictions 
• but the tradeable shares of which increase over time as insiders become free to sell their positions 
• there is limited risk absorption capacity (i.e. downward sloping demand curve) 
• investors are divided into two groups and differ in two ways. 
• First, they have different prior beliefs about fundamentals (i.e. one group can in general be more optimistic than the other). 
• Second, they differ in their interpretation of these signals as each group overestimates the informativeness of a different signal. 
• Investors anticipate changes in asset supply over time due to potential insider selling.
• The price is biased upwards because of heterogeneous initial priors 

When these priors are sufficiently different, price only reflects the beliefs of the optimistic group as the pessimistic group simply sits out of the market because of short-sales constraints. 

Label this source of an upward bias an optimism effect. 

• Investors pay prices that exceed their own valuation of future dividends as they anticipate finding a buyer willing to pay even more in the future. 

Label this source of an upward bias a resale option effect.

• Our model generates a number of implications absent from standard models of asset pricing with downward sloping demand curves. 

the magnitude of the decrease in price associated with greater asset supply is highly nonlinear—it is much bigger when the ratio of float to risk bearing capacity is small than when it is large. 

this decrease in price is accompanied by lower turnover and return volatility since these two quantities are tied to the amount of speculative trading. 

• Each group of investors thinks that the insiders are “smart” like them. 

Overconfidence 

• As a result, each group of investors expects the other group to be more aggressive in taking positions in the future since each group expects that the insiders will eventually come in and share the risk of their positions with them. 
• Since agents are more aggressive in taking on speculative positions, the resale option and hence the bubble is larger. 
• The insiders’ belief is rational and some investors are more optimistic than insiders, there will be more selling on the part of insiders on the date of lock-up expiration than is anticipated by outside investors. 
• Hence, the stock price tends to fall on this date.
• Our model can also rationalize why the internet bubble bursted in the Winter of 2000 when the float of the internet sector dramatically increased and why trading volume and return volatility also dried up in the process. 
• A key determinant of the size of the bubble in our model is the ratio of the float to risk absorption capacity. 
• The first is the optimism effect due to initial heterogeneous priors. 

As float increases, the chances of optimists dominating the market becomes smaller and hence the smaller is the bubble. 

• Second, the larger is the float, the smaller is the resale option and hence the smaller is the bubble. 

After the expiration of lock-up restrictions, speculation regarding the degree of insider selling also diminished, again leading to a smaller internet bubble.

A-B Model

• Single traded asset, interest rate is zero, and t = 0; 1; 2 
• Investors A and B: E[W] - 1/2ηVar[W] 
• Perceived payoff at t = 2 is f ~ N( f0 , 1/τ0) 
• Q shares outstanding, symmetric endowments at t = 0 
• At t = 1, public signals 

SA = f + εA ; SB = f + εB 

where εA and εB are i.i.d. N(0; 1/τε)

• Group A (B) over-weights signal A (B) as Φτε (Φ>=1) 
• Beliefs at t = 1 are N( f1A ; 1/τ) and N( f1B ; 1/τ) 

• τ= τ0 + (1+Φ)τε 

f1A = f0 + Φτε/τ(SA - f0) + τε/τ(SB - f0) 

f1B = f0 + τε/τ(SA - f0) + Φτε/τ(SB - f0) 

• Let l1 = f1A - f1B 
• At t = 0, 

l1 is normal with mean zero and a variance σl2

Sources of Disagreement

• Overconfidence 

- why so many unprofitable restaurants and so many unprofitable trades 

• Heterogeneous priors or different models (and slow learning) 
• Bounded rationality 
• Limited attention and delegate to advisors 
• Key: no inference from prices 
• Agreeing to disagree 

- private valuations or disagreement in face of public information 

- Investors with subset of information act as if they have all the information 

- act as if their model is the true model

• Asset demand at t = 1 equal 

Q1A = max[ητ( f1A - p1) , 0] 

Q1B = max[ητ( f1B - p1) , 0] 

• Asset demand at t = 0 equal 

Q0A = max[η( E0A [p1] - p0)/ΣA , 0] 

Q0B = max[η( E0B [p1] - p0)/ΣB , 0] 

• Assume same priors 

E0A [p1] = E0B [p1] and ΣA = ΣB = Σ

Importance of Short-Sales Constraints

• Not literally physical cost of shorting but rather institutional 
• Many institutional and individual investors (e.g. mutual funds) do not short or use derivatives (Almazan et.al. 2001, Koski and Pontiff 1999) 
• Dot-com stocks difficult to short due to low float 
• Homes difficult to short 
• Subprime securities difficult to short for a while before synthetics

Equilibrium without Short-Sales Constraints

• Equilibrium holdings and prices 

p1 = (f1A + f1B )/2 - Q/2ητ 

p0 = f0 - ΣQ/2η - Q/2ητ 

Q1A = ητ(l1 /2 + Q/2ητ) 

Q1B = ητ(-l1 /2 + Q/2ητ) 

• Expected turnover proportional to E[|Q1A - Q/2|] increases with Φ 
• High turnover on no price change (Kandel and Pearson 1995)

Equilibrium with Short-Sales Constraints

• Case 1 

If l1 > Q/ητ , 

Q1A = Q , Q1B = 0 , 

p1 = f1A - Q/ητ 

• Case 2 

If |l1| <= Q/ητ , same equilibrium as without short-sales constraint 

• Case 3 

If l1 < -Q/ητ , 

Q1A = 0 , Q1B = Q , 

p1 = f1B - Q/ητ

• Overpricing due to disagreement and short-sales constraints, more likely with lower supply to risk absorption (Miller 1977,Chen, Hong and Stein 2002) 
• For stocks, high dispersion of opinion (Diether et.al. 2002,) and low breadth of ownership (Chen, Hong and Stein 2002)forecasts low returns 
• Highest home prices in low supply elasticity states (Glaeser, Gyourko and Saiz 2008) 
• Dynamic implications for volume and returns 
• Correlation between absolute value of price changes and trading - crossing of valuations (Harris and Raviv 1993) 
• Higher Φ means higher turnover and higher returns with news

Resale Option and Bubble

• p0 = f0 - ΣQ/2η - Q/2ητ + B(Q)

• l1 underlying asset and Q/ητ the strike price for an option 
• Harrison and Kreps 1978 and Scheinkman and Xiong 2003 in risk-neutral setting, B(Q = 0)

• The higher is Φ, the higher is σl and B(Q)
• Also higher is turnover and price volatility (vol. of max belief is higher than vol.of average beliefs)
• Smith, Mill, Wicksell and Fischer, overtrading
• Euphoric investors purchase shares solely in anticipation of future capital gains
• Keynes Greater Fools

• B(Q), expected turnover and return volatility falls with Q 
• |B’(Q)| peaks at Q = 0 and decreases with Q 
• Collapse of internet stock prices, turnover and volatility coincided with expiration of IPO lock-ups in spring 2000 (Ofek and Richardson 2003) 
• Collapse of CDO subprime securities with synthetic shorting (John Paulson-Goldman Sachs scandal) 
• Short-sales not the villain? 
• Lack of shorting or supply led to bubble and lots of excessive investments