Arbitrage and Finance

1. Arbitrage and Finance Sendhil Mullainathan Economics 2030 Fall Lecture 5

2. Overview • Limits of Aribitrage • Structure of mis-pricings • Bubbles • Equity Premium puzzle • Volume

3. Overview • Limits of Aribitrage • Structure of mis-pricings • Bubbles • Equity Premium puzzle • Volume

4. 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

5. Royal Dutch/Shell

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

7. Closed End Fund Discount

8. Limits of Arbitrage • Not limits of arbitrage but dangers of arbitrage • Suppose traders’ have positive feedback • What should aribtrageurs do now?

9. Hedge Funds and Internet

10. Hedge Fund Performance

11. Limits of Arbitrage • Transaction costs

12. 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?

13. Price3Com – 1.5 PricePalm

15. Implementation Costs • Implementation Costs • Commission • Bid/Ask Spread • Price Impact • Short Sell Costs • Fees • Volume Constraints • Legal Restraints • Identification Cost • Mispricing ≠> Predictability

16. Limits of Arbitrage • Noise Trader Risk • Implementation Costs • Fundamental Risk

17. Index Inclusions • Stock Price Jumps Permanently • 3.5% Average • Fundamental Risk • Poor Substitutes (best R2 < 0.25)

19. 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?

20. Prediction Markets

21. Overview • Limits of Aribitrage • Structure of mis-pricings • Bubbles • Equity Premium puzzle • Volume

22. 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?

23. Winners and Losers

24. Broader effect • Not just winners and loser but also general statement about prices

26. A very different effect

27. Earnings Drift

28. When it’s realized?

29. Broader Version

30. Momentum

33. Structure of Mispricings • Rational Interpretation • Multi-factor models • Daniel Titman test

34. Structure of Mispricings • Two sources of this structure • Arbitrage limits provide structure • Psychology of individuals provide structure • Three prominent models • BSV • DHW • HS

35. 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

36. 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

37. Overview • Limits of Aribitrage • Structure of mis-pricings • Bubbles • Equity Premium puzzle • Volume

38. Bubbles • Another interesting area • A few observations:

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

43. 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?

44. Overview • Limits of Aribitrage • Structure of mis-pricings • Bubbles • Equity Premium puzzle • Volume

45. Consumption Model • Simple Euler equation • What if there are multiple assets? • How do we convert this to equity pricing?

46. Equity pricing model

47. 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

48. 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

49. 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?

50. 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?