Shane Whelan (Most of this research was done with Brian Lucey, TCD) 18 th October 2007 Seasonality in Equity Markets: Half-Yearly and other Apparent Anomalies

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

Returns on 19 Major Stock Markets, % -2% 0% 2% 4% 6% 8% 10% 12% 14% 16% Australia Austria Belgium Canada Denmark France Germany Hong Kong Italy Japan Netherlands Norway Singapore South Africa* Spain Sweden Switzerland UK US Average November-AprilAverage May-October Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen

Returns on 16 Minor Stock Markets, % -10% 0% 10% 20% 30% 40% 50% 60% Argentina Chile Finland Greece Indonesia Ireland Jordan Korea Malaysia Mexico New Zealand Philipines Portugal Taiwan Thailand Turkey Average November-AprilAverage May-October Source: MSCI Total Return Indices, data kindly supplied by Bouman & Jacobsen

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

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.

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)

Virgin Data Set: CSO Price Index  Monthly capital index of Irish Stock Market, commenced January 1934  Described in Geary (1944) as a capitalisation- weighted 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with complete coverage  Some technical changes through its history [Murray (1960), Kirwan & McGilvray (1983)]  Superceded in mid-1980s by ISEQ Indices  Hence complete coverage of capital movements in Irish equity market from January 1934  Irish market had unique features…

CSO Price Index – Compared to UK & US Indices

Monthly Capital Returns on Irish Market, Jan Dec. 2000

Evolution of Returns on Irish Market Compared to UK & US,

Returns on Irish Market Independent of Other Markets Irish –v- UK market, Irish –v- US market,

3 Statistical Tests Test 1: Simple randomisation  – make 10,000 random drawing of 216 monthly returns (out of the 432 over period ) 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.

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…

Risk measures - Irish Equity Market, : Lagging Volatility

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

Conclusion on ‘Sell in May’ It Works!

Updated, from 31 st October 2001 to 10 th October 2007 (6 years)… Source: MSCI Total Return Indices, (local currency)

Updated, MSCI World Total Return, each half year ending…

Re-interpretating Literature on Monthly Seasonality  January effect documented since  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…

Monthly Seasonality in Irish Equity Market,

Monthly Seasonality in Irish Equity Market,

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?

For More, Visit my Website In 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 (with Brian Lucey). Applied Financial Economics, Vol. 14, No. 3/1, , (February 2004). Bull and Bear or Simply All Bull? Risk & Rewards, Society of Actuaries (US), 48, August 2006, 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).

Shane Whelan (Most of this research was done with Brian Lucey, TCD) 18 th October 2007 Seasonality in Equity Markets: Half-Yearly and other Apparent Anomalies