Shane Whelan

1
Seasonality in Equity Markets Half-Yearly and
other Apparent Anomalies

• Shane Whelan
• (Most of this research was done with Brian Lucey,
  TCD)
• 18th October 2007

2
A Promising Timing Strategy in Equity Markets

• Bouman Jacobsen (AER Dec 2002) investigate
• Sell in May and go away but buy back by St.
  Leger Day
• Adjusted slightly
• They report it works
• halves the risk of equity markets but leaving
  return largely unchanged
• In 36 out of 37 markets investigated over last
  decade and three decades

3
Returns on 19 Major Stock Markets, 1970-1998
16
14
12
10
8
6
4
2
0
UK
US
Italy
Japan
Spain
Austria
Canada
France
Belgium
Norway
Sweden
Australia
Denmark
Germany
Singapore
-2
Hong Kong
Switzerland
Netherlands
South Africa
-4
Average November-April
Average May-October
Source MSCI Total Return Indices, data kindly
supplied by Bouman Jacobsen
4
Returns on 16 Minor Stock Markets, 1988-1998
60
50
40
30
20
10
0
Chile
Korea
Ireland
Jordan
Finland
Greece
Mexico
Taiwan
Turkey
Portugal
Malaysia
Thailand
Argentina
Indonesia
Philipines
New Zealand
-10
-20
Average November-April
Average May-October
Source MSCI Total Return Indices, data kindly
supplied by Bouman Jacobsen
5
A Promising Timing Strategy

• It works almost everytime
• In small markets and large markets.
• In 10 out of 11 markets as far back as records
  allow
• In particular, UK market as far back as 1694
• Results statistically significant

6
Doubts

• Number of markets largely irrelevant
• we could be merely identifying the same global
  equity pattern in its many manifestations, not
  different instances of the same pattern.
• So it relies on the statistical evidence
  pattern is so strong within markets.
• However, even that evidence can be doubted
• Data-mining.

7
Data-mining

• Sullivan, Timmerman White (2001)
• We find that although nominal p-values of
  individual calendar rules are extremely
  significant, once evaluated in the context of the
  full universe from which such rules were drawn,
  calendar effects no longer remain significant.
  (Abstract)

8
Virgin Data Set CSO Price Index

• Monthly capital index of Irish Stock Market,
  commenced January 1934
• Described in Geary (1944) as a capitalisation-weig
  hted arithmetic average, with complete coverage
• Some technical changes through its history
  Murray (1960), Kirwan McGilvray (1983)
• Superceded in mid-1980s by ISEQ Indices
• Hence complete coverage of capital movements in
  Irish equity market from January 1934
• Irish market had unique features

9
CSO Price Index Compared to UK US Indices
10
Monthly Capital Returns on Irish Market, Jan.
1934-Dec. 2000
11
Evolution of Returns on Irish Market Compared to
UK US, 1934-2000
12
Returns on Irish Market Independent of Other
Markets
Irish v- UK market, 1934-69
Irish v- US market, 1934-69
13
3 Statistical Tests

• Test 1 Simple randomisation
• make 10,000 random drawing of 216 monthly
  returns (out of the 432 over period 1934-69) and
  see how many exceed the return in 6-months ending
  April each year
• Result 6 p-value.
• Test 2 A Binomial type-test
• pair returns in one half-year ending April
  with immediately preceding (and following)
  six-month return and score 1 if higher, 0
  otherwise. Observed score 21 (respectively 20)
  out of total possible 35
• Result 16-25 p-value.

14
3 Statistical Tests

• Test 3 Simple randomisation on
  risk-standardised returns
• - attempt an explicit adjustment of the return
  series to equalise risk and then do test 1 on the
  risk-standardised returns

15
Risk measures - Irish Equity Market, 1934-2000
Lagging Volatility
16
3 Statistical Tests

• Test 3 Simple randomisation on
  risk-standardised returns
• - attempt an explicit adjustment of the return
  series to equalise risk and then do test 1 on the
  risk-standardised returns
• Result 12 p-value

17
Conclusion on Sell in May

• It Works!

18
Quote from Lucey Whelan (2001), SSISI Paper
19
Updated, MSCI World Total Return, each half year
ending
20
Updated, from 31st October 2001 to 10th October
2007 (6 years)
Source MSCI Total Return Indices, (local
currency)
21
Re-interpretating Literature on Monthly
Seasonality

• January effect documented since 1942.
• So strong that January, as an explanatory
  variable, accounts for more cross-sectional
  return variations than CAPM.
• Sometimes February, December, and April reported
  as highest monthly return.
• We investigate with our novel data set

22
Monthly Seasonality in Irish Equity Market,
1934-2000
23
Monthly Seasonality in Irish Equity Market,
1934-1969
24
Results on Monthly Seasonality

• Yes, January return abnormally high in Ireland
  stochastically dominating most other months
• But, December, February, and April also
  stochastically dominate most other months
• Probability of observing January returns as high
  as this is about 12, given the half-yearly
  effect identified by Bouman Jacobsen
• Is monthly seasonality better ascribed to the
  (now demonstrated) half-yearly effect?

25
For More, Visit my Website www.ucd.ie/statdept/st
aff/swhelan.htmlIn particular, see A Promising
Timing Strategy in Equity Markets. (with Brian
Lucey of Trinity College Dublin). Journal of the
Statistical and Social Inquiry Society of
Ireland, Vol. XXXI, 2001/2002     Monthly and
semi-annual seasonality in the Irish Equity
market 1934-2000(with Brian Lucey).  Applied
Financial Economics, Vol. 14, No. 3/1, 203-208,
(February 2004). Bull and Bear or Simply All
Bull? Risk Rewards, Society of Actuaries (US),
48, August 2006, 22-30. Econophysics Making
Money before Doomsday. Risks and Rewards, 46,
Cover Story 1  4-6, February 2005, Society of
Actuaries (US). Actuaries' Evaluation of the
Utility of Financial Economics. Forthcoming as
Chapter in Fabozzi, F. (Ed.) (2008) Handbook of
Finance, John Wiley Sons, New York. A Primer
in Financial Economics (with David Bowie and John
Hibbert), British Actuarial Journal, Vol. 8,
Part I, (2001/2002).      
26
Seasonality in Equity Markets Half-Yearly and
other Apparent Anomalies

• Shane Whelan
• (Most of this research was done with Brian Lucey,
  TCD)
• 18th October 2007