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Arbitrage and Finance

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Arbitrage and Finance

Sendhil Mullainathan

Economics 2030

Fall Lecture 5

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Noise trader risk
- Arbitrageurs have limited horizon
- Agency costs

- Problem can get worse before it gets better
- Arbitrage has risk
- Non-diversifiability is key
- How to think about this?

- Arbitrageurs have limited horizon
- Notice beauty of this paper:
- No psychology

- How do we think about non-diversifiability of this risk?

- Not limits of arbitrage but dangers of arbitrage
- Suppose traders’ have positive feedback
- What should aribtrageurs do now?

- Transaction costs

- 1999: 3Com announced it would spin off Palm
- Stage 1: 3Com sold 4% of Palm in IPO
- Stage 2: remaining shares would be distributed to 3Com shareholders
- Each 3Com shareholder should get 1.5 Palm shares

- Behavioral economics:
- At end of IPO –
- 3Com selling for $82.
- Palm selling for $95 (got as high as $165).
- What’s the problem here?

- At end of IPO –

- Implementation Costs
- Commission
- Bid/Ask Spread
- Price Impact
- Short Sell Costs
- Fees
- Volume Constraints
- Legal Restraints

- Identification Cost
- Mispricing ≠> Predictability

- Noise Trader Risk
- Implementation Costs
- Fundamental Risk

- Stock Price Jumps Permanently
- 3.5% Average

- Fundamental Risk
- Poor Substitutes (best R2 < 0.25)

- Efficient prices vs no arbitrage
- Some key questions
- Best aggregator of beliefs?
- Note what short-sale constraints tells us in this context
- Note what arbitrage literature tells us in this context

- Best aggregator of beliefs?
- What would efficiency costs be?

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Limits of Arbitrage tells us why mispricings may occur
- The examples so far are somewhat generic
- Is there structure to mispricings?
- Should there be?

- Not just winners and loser but also general statement about prices

- Rational Interpretation
- Multi-factor models
- Daniel Titman test

- Two sources of this structure
- Arbitrage limits provide structure
- Psychology of individuals provide structure

- Three prominent models
- BSV
- DHW
- HS

Behavioral Models

Barberis, Shleifer and Vishny (1998)

Short-term gambler’s fallacy. Updating leads to long-term hot-hand belief.

Daniel, Hirshleifer and Subrahmanyam (1998)

A mix of biases

Confirmation(self-serving bias) leads to short-term under-reaction

Long-term over-reaction occurs because of correction

This is an odd feature of these results.

Hong-Stein

Limited attention and two types of traders: fundamentals and trend-chasers

But information diffuses slowly. So diffusion creates trends which trend-chasers over extrapolate

- Lots more to be done here.
- Think of the wealth of data.
- Simple models with testable predictions would be very high return.
- Limited attention seems to re-appear often

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Another interesting area
- A few observations:

- Another interesting area
- A few observations:
- There are a lot more bubbles than you might recognize
- Bubbles appear to have structure

- Another interesting area
- A few observations:
- There are a lot more bubbles than you might recognize
- Bubbles appear to have structure

- Yet we have very little study of them
- Are “bubbles” distinct? Or merely an arbitrary line on a continuum?
- Can we measure sentiment directly?

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Simple Euler equation
- What if there are multiple assets?
- How do we convert this to equity pricing?

- Mehra Prescott, 1890-1979
- Rate of return on equity is about .06
- Std dev of consumption growth: .036
- Std dev of stock market: .167
- Correlation: .40
- Covariance: .0024

- Implies: =25

- Mankiw Zeldes:
- 1948-1988, equity premium rises to 8%
- Covariance goes down
- Implies =91

- A of 30 implies:
- 50% chance to double wealth, 50% chance to have wealth fall by half
- Would pay 49% of wealth to avoid this gamble

- Survivorship bias
- 36 exchanges, ½ had interruptions or abolished
- But note: 1929 stock crash
- Other evidence: international equity premium

- Learning over time
- Possibly true
- Equity premium may have permanently decreased
- Won’t know for sure

- Limited Participation
- Intermediation costs?

- Original calculations
- Rate of return on equity is about .06
- Std dev of consumption growth: .036
- Std dev of stock market: .167
- Correlation: .40
- Covariance: .0024

- Which value seems low?

Basic idea

Suppose expected utility tomorrow also affects utility today

- Separate coefficient of relative risk aversion from intertemporal substitution
- Has trouble fitting all the facts
- Hasn’t generated high volatility of stock returns

- Perhaps consumption covaries too little with stock market growth
- Nearly every explanation uses this feature in some way

- Most direct
- Suppose you only adjust consumption every D quarters.
- What impact would this have to estimated equity premium?
- Show bias on estimated risk aversion is of order of 6 D

- How might you solve this problem?
- Aggregate at higher horizons
- Might here be some other benefit of higher level aggregation?

- Investors invest in stocks and bonds
- Observe performance of portfolio in time intervals
- Loss averse investors
- What is the implication of variance now?
- Does it depend on frequency of observation?

- How different is this from traditional risk?
- Notice relation to Barberis and Xiong’s point

- At around evaluation of year, stock and bond roughly equal
- At existing equity premium.

- Observe that in calibrations this is not enough
- BT is not an equilibrium model.
- Does not produce enough stock return volatility.

- How to price risk in even more?

- Standard utility function in consumption
- Utility over wealth
- Defined over current gains/losses (X)
- Impact of S, wealth, relative to lagged reference points captured in z. Allows changing reference points (mental accounting)
- Key feature: Wealth movements matter independent of consumption

- Show they can calibrate such a model to explain equity premium.

- Limits of Aribitrage
- Structure of mis-pricings
- Bubbles
- Equity Premium puzzle
- Volume

- Looks for direct evidence of prospect theory in asset markets
- In investor behavior.
- How do they buy or sell stocks?

- Genesove-Mayer examine housing markets

- Higher loss means higher selling price
- Other Facts
- Higher loss means longer time to sell
- But also higher sales price
- Interesting aside: Implied return on waiting pretty high

- Deeper question
- What generates so much volume?
- A puzzle in and itself?

- Can we better understand disagreement
- Rational models have odd features
- What would a behavioral model look like?

- Have we fully exploited the structure of loss aversion?

- Bertrand et. al., “What's Advertising Content Worth? Evidence from a Consumer Credit Marketing Field Experiment,” mimeo.
- Gabaix, X. and Laibson, D. (2006) Shrouded Attributes, Consumer Myopia, and Information Suppression in Competitive Markets, Quarterly Journal of Economics, 121 (2), 505-540
- Ellison, G. (2006) Bounded Rationality in Industrial Organization, in Blundell, Newey and Persson (eds.), Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, Cambridge University Press.
- Andrei Shleifer, The Market for News" (with S. Mullainathan), American Economic Review, September, 2005.