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
Leeson
Investment
Management
Market
(S&P 500)
Benchmark
Short-term
Government
Average Return
.0065
.0050
.0036
Std. Deviation
.0106
.0359
.0015
Beta
.0640
1.0 .0
Alpha
.0025
(1.92)
Sharpe Ratio
.2484
.0318
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 account again ... it became an addiction”
Nick Leeson Rogue 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 Examples
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

33. Example: Absorbing barrier at zero
As T goes 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 A much misunderstood issue in empirical Finance!
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 A much misunderstood issue in empirical Finance!
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 pathpT

41. Conditional price pathspT * 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
Growth fund performance relative to alpha of median manager
winners
losers
Totals
winners 58 33 91 57 90
181
Chi-square (0.00%)
Cross Product ratio 3.04(0.02%)

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

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

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

49. Summary of simulations with different percent cutoffs
Panel 1: No Cutoff (N = 600)
Panel 2: 5% Cutoff (N = 494)
2nd time winner
2nd time loser
1st time winner
150.09
149.91
127.49
119.51
1st time loser
Average Cross Product Ratio 1.014
Average Cross Product Ratio 1.164
Average Cross Section t -.004
Average Cross Section t 2.046
Risk adjusted return 0.00%
Risk adjusted return 0.44%

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 :

51. Values of ten art works

52. Why does price depart from value?

53. Selection equation

54. Conclusion Can only examine trading records of survivors
High risk associated with return ex post
Biased inferences about performance and risk
Be careful about what you can infer!