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Stock market anomalies and asset management

S.P. Kothari & Jon Lewellen

Sloan Innovation Period, Spring 2004

MIT SLOAN SCHOOL OF MANAGEMENT SIP Session 1

2

Today Stock market anomalies

Overview Definition, evidence, perspective

Behavioral finance Why do anomalies exist? What types of systematic errors do investors make?

Applications Study several anomalies in detail

Practical issues and limitations How should the evidence affect investment decisions? What can go wrong?


3

Background What is an ‘anomaly’?


4

Predictable price changes $

20

30

40

50

60

70

80

Jul-99

Sep-99

Nov-99

Jan-00

Mar-00

May-00

Jul-00

Sep-00

Nov-00

Jan-01

Mar-01

May-01


5

Random walk (with drift) $

50

55

60

65

70

75

80

0 10 20 30 40 50 60 70 80 90 100


6

Background Market efficiency

Return = 1-t

1-tttt P

P )P~ D~( R~ −+= =

1-t

1-tt

1-t

t

PP P~

PD~ −

+

Returns should be unpredictable:

tt

~ r R~ ε+=

r is the risk-adjusted required return from holding the stock εt is unpredictable


7

The CAPM Capital Asset Pricing Model

Measuring risk Risk is measured by a stock’s β, which tells you how sensitive the stock is to overall market movements

Required returns Investors are compensated for bearing beta risk. The required return is:

r = rf + β (rM – rf)

Risk-adjusted returns Risk-adjusted returns are measured by α, the difference between the actual return and the return predicted by the CAPM


8

Gillette vs. Total U.S. market return

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Monthly returns β = 0.81


9

NASDAQ vs. Total U.S. market return

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

-20% -15% -10% -5% 0% 5% 10% 15% 20%

Monthly returns β = 1.57


10

Required return vs. risk

0%

5%

10%

15%

20%

25%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Stock's beta

Req

uire

d re

turn

Slope = rM – rf

β = 1.5

β = 0.5

β = 0

Market index (β = 1)


11

Anomalies Are returns predictable? Is there evidence of regular patterns in returns? Do some trading strategies earn positive risk-adjusted returns?


12

Anomalies Cross sectional Size (stock picking) Value Momentum Post-earnings announcement drift Accruals New-issues puzzle Short-horizon reversals Miscellaneous Time series January effect Lead-lag patterns in returns Market timing (maybe) Excess volatility and market crashes Internet bubble Discounts on closed-end stock funds


13

Takeover announcements Stock price of target firm


14

Size effect, 1964 – 2001

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

Small 2 3 4 5 6 7 8 9 Big

Firms sorted by MARKET CAP

Avg

retu

rns

(% m

onth

ly)


15

Value premium, 1964 – 2001

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

Low 2 3 4 5 6 7 8 9 High

Firms sorted by MKT CAP / BOOK EQUITY

Avg

retu

rns

(% m

onth

ly)


16

Value premium, 1964 – 1993

Low 2 3 4 5 6 7 8 9 High M/B P/E P/C SR

0.0%0.2%0.4%0.6%0.8%1.0%1.2%1.4%


17

Momentum, 1964 – 2001

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

Low 2 3 4 5 6 7 8 9 High

Firms sorted by PAST 12-MONTH RETURN

Avg

retu

rns

(% m

onth

ly)


18

Momentum profits at short- and long-horizons


19

Accrual* effect, 1964 – 2001

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

Low 2 3 4 5 6 7 8 9 High

Firms sorted by last year's OPERATING ACCRUALS *Operating income minus operating cashflows

Avg

retu

rns

(% m

onth

ly)


20

Portfolio returns Size, B/M, momentum, and accrual portfolios, 1964 – 2001 Monthly returns (%)

Avg. returns Alphas Portfolio Size M/B R-12 Acc Size M/B R-12 AccLow 1.37 1.45 0.58 1.25 0.35 0.47 -0.49 0.252 1.19 1.30 0.96 1.27 0.13 0.38 0.01 0.353 1.19 1.01 0.82 1.10 0.15 0.10 -0.10 0.264 1.10 0.88 1.07 1.02 0.08 -0.08 0.14 0.09High 0.97 0.93 1.36 0.74 -0.01 -0.08 0.35 -0.36Long–short 0.40 0.52 0.78 0.51 0.36 0.55 0.84 0.61t-statistic 1.75 2.60 3.11 4.43 1.58 2.75 3.37 4.73


21

Short-horizon reversals, 1964 – 2001

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

Low 2 3 4 High

Firms sorted by LAST MONTH'S RETURN

Avg

retu

rns

(% m

onth

ly)


22

Post-earnings announcement drift

Low2

34

High

+1 +2 +3 +4

0%

1%

2%

3%

4%

5%

6%

Ret

urns

Firms sorted by earnings growth Quarter after

announcement


23

January effect by size decile, 1964 – 2001

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Small 2 3 4 5 6 7 8 9 Big

Firms sorted by MARKET CAP

Avg

retu

rns

(% m

onth

ly)

January

All months


24

IPO returns, 1970 – 1990 Average annual returns, 1 – 5 years after IPO


25

SEO returns, 1970 – 1990 Average annual returns, 1 – 5 years after SEO


26

Weekly lead-lag effects, 1964 – 2001

-1.0%

-0.5%

0.0%

0.5%

1.0%

1.5%

Small 2 3 4 Big

Firms sorted by market cap (quintiles)

Return after a good week

Return after a bad week


27

Miscellaneous Spin-offs (Palm / 3Com) Closed-end funds MCI / MCIC Internet name changes (‘A Rose.com by any other name’)


28

Internet stock prices, 1999 – 2000

40

70

100

130

160

190

220

250

280

Jun-99 Sep-99 Dec-99 Mar-00 Jun-00 Sep-00 Dec-00

ISDEX

Sample


29

Price-to-sales ratios

0%

5%

10%

15%

20%

25%

30%

35%

Perc

ent o

f firm

s

10 40 70 100 130 160 190 220 250 280 More

Price-to-sales ratio


30

Rational? Market cap of sample = $529 billion Hypothetical value

r = 10%, long-term growth = 6%, profit margin = 5% If short-run growth is … Then value is … 20% growth for 10 years → $42 billion

15 years → $68 billion

30% growth for 10 years → $89 billion 15 years → $209 billion

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