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• Superceded in mid-1980s by ISEQ Indices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
Updated, from 31st October 2001 to 10th October
2007 (6 years)
Source MSCI Total Return Indices, (local
currency)
19
Updated, MSCI World Total Return, each half year
ending
20
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

21
Monthly Seasonality in Irish Equity Market,
1934-2000
22
Monthly Seasonality in Irish Equity Market,
1934-1969
23
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?

24
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).      
25
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