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Arbitrage and Finance. Sendhil Mullainathan Economics 2030 Fall Lecture 5. Overview. Limits of Aribitrage Structure of mis -pricings Bubbles Equity Premium puzzle Volume . Overview. Limits of Aribitrage Structure of mis -pricings Bubbles Equity Premium puzzle Volume .

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arbitrage and finance

Arbitrage and Finance

Sendhil Mullainathan

Economics 2030

Fall Lecture 5

overview
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
overview1
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
limits of arbitrage
Limits of Arbitrage
  • 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?
  • Notice beauty of this paper:
    • No psychology
limits of arbitrage1
Limits of Arbitrage
  • Not limits of arbitrage but dangers of arbitrage
  • Suppose traders’ have positive feedback
  • What should aribtrageurs do now?
limits of arbitrage2
Limits of Arbitrage
  • Transaction costs
palm 3 com
Palm-3 Com
  • 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?
implementation costs
Implementation Costs
  • Implementation Costs
    • Commission
    • Bid/Ask Spread
    • Price Impact
    • Short Sell Costs
      • Fees
      • Volume Constraints
      • Legal Restraints
    • Identification Cost
      • Mispricing ≠> Predictability
limits of arbitrage3
Limits of Arbitrage
  • Noise Trader Risk
  • Implementation Costs
  • Fundamental Risk
index inclusions
Index Inclusions
  • Stock Price Jumps Permanently
    • 3.5% Average
  • Fundamental Risk
    • Poor Substitutes (best R2 < 0.25)
limits of arbitrage4
Limits of arbitrage
  • 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
  • What would efficiency costs be?
overview2
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
structure of mispricings
Structure of Mispricings
  • Limits of Arbitrage tells us why mispricings may occur
  • The examples so far are somewhat generic
  • Is there structure to mispricings?
      • Should there be?
broader effect
Broader effect
  • Not just winners and loser but also general statement about prices
structure of mispricings1
Structure of Mispricings
  • Rational Interpretation
    • Multi-factor models
    • Daniel Titman test
structure of mispricings2
Structure of Mispricings
  • Two sources of this structure
    • Arbitrage limits provide structure
    • Psychology of individuals provide structure
  • Three prominent models
    • BSV
    • DHW
    • HS
behavioral models

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

behavioral models1
Behavioral Models
  • 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
overview3
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
bubbles
Bubbles
  • Another interesting area
  • A few observations:
bubbles1
Bubbles
  • Another interesting area
  • A few observations:
    • There are a lot more bubbles than you might recognize
    • Bubbles appear to have structure
bubbles2
Bubbles
  • 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?
overview4
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
consumption model
Consumption Model
  • Simple Euler equation
  • What if there are multiple assets?
  • How do we convert this to equity pricing?
calibrating this model
Calibrating this model
  • 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
other estimates
Other estimates
  • 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
potential explanations
Potential Explanations
  • 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?
observation
Observation
  • 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?
epstein zin preferences
Basic idea

Suppose expected utility tomorrow also affects utility today

Epstein-Zin preferences
implications
Implications
  • Separate coefficient of relative risk aversion from intertemporal substitution
  • Has trouble fitting all the facts
    • Hasn’t generated high volatility of stock returns
potential explanation
Potential explanation
  • Perhaps consumption covaries too little with stock market growth
    • Nearly every explanation uses this feature in some way
gabaix laibson
Gabaix-Laibson
  • 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?
benartzi thaler
Benartzi Thaler
  • 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
interesting findings
Interesting findings
  • At around evaluation of year, stock and bond roughly equal
    • At existing equity premium.
barberis huang santos
Barberis-Huang-Santos
  • 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?
barberis huang santos1
Barberis Huang Santos
  • 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.
overview5
Overview
  • Limits of Aribitrage
  • Structure of mis-pricings
  • Bubbles
  • Equity Premium puzzle
  • Volume
odean
Odean
  • Looks for direct evidence of prospect theory in asset markets
  • In investor behavior.
  • How do they buy or sell stocks?
other asset markets
Other asset markets
  • Genesove-Mayer examine housing markets
interpretation
Interpretation
  • 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
volume
Volume
  • 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?
to read for next week
To Read for Next Week
  • 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.
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