Arbitrage and finance
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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


Royal dutch shell

Royal Dutch/Shell


Arbitrage and finance

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


Closed end fund discount

Closed End Fund Discount


Limits of arbitrage1

Limits of Arbitrage

  • Not limits of arbitrage but dangers of arbitrage

  • Suppose traders’ have positive feedback

  • What should aribtrageurs do now?


Hedge funds and internet

Hedge Funds and Internet


Hedge fund performance

Hedge Fund Performance


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?


Price 3com 1 5 price palm

Price3Com – 1.5 PricePalm


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?


Prediction markets

Prediction Markets


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?


Winners and losers

Winners and Losers


Broader effect

Broader effect

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


A very different effect

A very different effect


Earnings drift

Earnings Drift


When it s realized

When it’s realized?


Broader version

Broader Version


Momentum

Momentum


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?


Equity pricing model

Equity pricing model


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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