1. Behavioral Finance
Economics 437

2. Ross Lecture on Anomalies
Two Criteria
Are They True?
Are They Important?
Ross Concludes
Anomalies are not usually both true and important
Anomalies covered
Closed end funds
Small stocks
January effect

3. Meanwhile

4. General Theme: Predictability
Fama French: “Cross Section” Article
Book/Market and Size => Stock Returns
“Value Investing” or “Contrarian Investing”
DeBondt Thaler: “Over Reaction”
Buy past losers; Sell past winners
Value? Investing; Contrarian Investing
Jegadeesh Titman: “Price Momentum”
Possibly “Earnings Momentum”

5. The Counter Attack Comes Swiftly
Conrad and Kaul 1993
Data Problems with all three articles
Small Stocks mainly the issue
Impact of “January”
Ball, Kothari, Shanken 1995
Small stock measurement problems
Mostly December, very low priced stocks
Priced at the bid, 1/8 error makes huge difference
Changing the months, changes the results

6. Single Period Return Calculations
(Pt+1 – Pt)/Pt is rate of return for single period, ignoring dividends
But that is not what is observed
What is observed is either bid side or offer side of the market
The arithmetic biases the calculation upward (see pages of Burton Shah)

7. Now think of a holding period of two periods
Calculate average returns over two periods:
Imagine up 50%, down 50%
Start with $ 100
$ 100 goes to $ 150, falls to $ 75
Yet average return is zero
Imagine down 50%, up 50%
$ 100 goes to $ 50, rises to $ 75
Again, average return is zero

8. Another Example Calculate average returns over two periods:
Imagine up 10%, up 20%
Start with $ 100
$ 100 goes to $ 110, rises to $ 132
Average return is 15 %, which would mean $100 goes to $ 115, then to $
Imagine up 20%, up 10%
$ 100 goes to $ 120, then to $ 132
Again, average return is 15 %, but again 15% return would get to $132.25

9. Conclusion
Averaging single period returns biases the reported returns upward. Actual returns that would be achieved are lower.

10. So, how are these papers calculating returns
Monthly returns, averaged
But cumulative returns actually would be much lower
But, there is also no rebalancing

11. What is rebalancing
At the end of the month, some stocks have gone up more than others
In a real world portfolio that changes the “weights” as stocks that have gone up more carry more “weight” in the portfolio
But, that is assumed away in these articles
There is an implicit assumption on monthly rebalancing

12. The End