Empirical Financial Economics

1. Empirical Financial Economics Ex post conditioning issues

2. Fama Fisher Jensen and Roll

3. FFJR Redux

4. FFJR Redux

5. Overview • A simple example • Brief review of ex post conditioning issues • Implications for tests of Efficient Markets Hypothesis

6. Performance measurement Style: Index Arbitrage, 100% in cash at close of trading

7. Frequency distribution of monthly returns

8. Percentage in cash (monthly)

9. Examples of riskless index arbitrage …

10. Percentage in cash (daily)

11. Is doubling low risk? $1 $0 $-1 1 p = 2

12. Is doubling low risk? $1 $0 $-3 1 p = 4

13. Is doubling low risk? $1 $0 $-7 1 p = 8

14. Is doubling low risk? $1 $0 $-15 1 p = 16

15. Is doubling low risk? $1 $0 $-31 1 p = 32

16. Is doubling low risk? $1 $0 $-63 1 p = 64

17. Is doubling low risk? $1 $0 $-127 1 p = 128

18. Is doubling low risk? • Only two possible outcomes • Will win game if play “long enough” • Bad outcome event extremely unlikely • Sharpe ratio infinite for managers who survive periodic audit

19. Apologia of Nick Leeson “I felt no elation at this success. I was determined to win back the losses. And as the spring wore on, I traded harder and harder, risking more and more. I was well down, but increasingly sure that my doubling up and doubling up would pay off ... I redoubled my exposure. The risk was that the market could crumble down, but on this occasion it carried on upwards ... As the market soared in July [1993] my position translated from a £6 million loss back into glorious profit. I was so happy that night I didn’t think I’d ever go through that kind of tension again. I’d pulled back a large position simply by holding my nerve ... but first thing on Monday morning I found that I had to use the 88888 account again ... it became an addiction” Nick LeesonRogue Trader pp.63-64

20. The case of the Repeated Doubler • Bernoulli game: • Leave game on a win • Must win if play long enough • Repeated doubler • Reestablish position on a win • Must lose if play long enough

21. The challenge of risk management • Performance and risk inferred from logarithm of fund value:

22. The challenge of risk management • Performance and risk inferred from logarithm of fund value: • is expected return of manager • Lower bound on with probability is Value at Risk (VaR)

23. The challenge of risk management • Performance and risk inferred from logarithm of fund value: • But what the manager observes is A = {set of price paths where doubler has not embezzled}

24. The challenge of risk management • Performance and risk inferred from logarithm of fund value: • But what the manager observes is yet A = {set of price paths where doubler has not embezzled}

25. National Australia Bank

26. Ex post conditioning • Ex post conditioning leads to problems • When inclusion in sample depends on price path • Examples • Equity premium puzzle • Variance ratio analysis • Performance measurement • Post earnings drift • Event studies • “Anomalies”

27. Effect of conditioning on observed value paths • The logarithm of value follows a simple absolute diffusion on

28. Unconditional price paths

29. Effect of conditioning on observed value paths • The logarithm of value follows a simple absolute diffusion on • What can we say about values we observe? A = {set of price paths observed on }

30. Absorbing barrier at zero

31. Conditional price paths

32. Effect of conditioning on observed value paths • Define • Observed values follow an absolute diffusion on Stephen Brown, William Goetzmann and Stephen Ross “Survival” Journal of Finance 50 1995 853-873.

33. Example: Absorbing barrier at zero AsTgoes to infinity, conditional diffusion is Expected return is positive, increasing in volatility and decreasing in ex ante probability of failure

34. Expected value path

35. Emerging market price paths

36. Important result • Ex post conditioning a problem whenever inclusion in the sample depends on value path • Effect exacerbated by volatility • Induces a spurious correlation between return and correlates of volatility

37. Important result • Ex post conditioning a problem whenever inclusion in the sample depends on value path • Effect exacerbated by volatility • Induces a spurious correlation between return and correlates of volatility • A much misunderstood issue in empirical Finance!

38. Important result • Ex post conditioning a problem whenever inclusion in the sample depends on value path • Effect exacerbated by volatility • Induces a spurious correlation between return and correlates of volatility • A much misunderstood issue in empirical Finance!

39. Equity premium puzzle • With nonzero drift, as T goes to infinity • If true equity premium is zero, an observed equity premium of 6% ( ) implies 2/3 ex ante probability that the market will survive in the very long term given the current level of prices ( )

40. Unconditional price path p0 pT

41. Conditional price paths pT * p0

42. Properties of survivors • High return • Low risk • Apparent mean reversion: • Variance ratio =

43. Variance of long holding period returns 0.0172

44. ‘Hot Hands’ in mutual funds

45. ‘Hot Hands’ in mutual funds Cross section regression of sequential performance

46. Survivorship, returns and volatility • Index distributions by a spread parameter • Selection by performance selects by volatility Stephen Brown, William Goetzmann, Roger Ibbotson, Stephen Ross “Survivorship bias in performance studies” Review of Financial Studies, December 1992 553-580.

47. Managers differ in volatility Manager y Manager x a 0%

48. Performance persists among survivors • Conditional on x, y surviving both periods: Stephen Brown, William Goetzmann, Roger Ibbotson, Stephen Ross “Survivorship bias in performance studies” Review of Financial Studies, December 1992 553-580.

49. Summary of simulations with different percent cutoffs

50. Prices of ten art works Korteweg, Arthur G. and Kräussl, Roman and Verwijmeren, Patrick, Does it Pay to Invest in Art? (October 15, 2013). Available at : http://ssrn.com/abstract=2280099