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Chapter 1
Introduction — Calendar Anomalies1
Constantine S. Dzhabarov
Alpha Lake Financial Analytics Corp, Canada
William T. Ziemba
University of British Columbia, Canada
ICMA Centre, University of Reading, UK
1.1 Introduction to Seasonal Anomaly Effects
Seasonality of stock markets has a long history despite the academic research being dominated by efficient market theory as surveyed by Fama (1970, 1991). Small firm effects were popularized by University of Chicago students Banz (1981), Reinganum (1981), Blume and Stambaugh (1983), Roll (1983), and Ritter (1988) among others.
Early surveys are in Lakonishok and Smidt(1988), Thaler (1992) and Ziemba (1994). The latter references considerable regularity of various seasonal anomalies in Japan as well as in the U.S. Jacobs and Levy (1988abc) have used seasonal and fundamental factor model derived anomalies to create a multibillion dollar investment firm. Dimson (1988) and Keim and Ziemba (2000) present whole books with studies across the world. The Stock Traders Almanac discusses some such anomalies in yearly updates; see Hirsch and Hirsch (2011).
Anomalies of the seasonal variety as discussed in this chapter and those based on fundamental and other factors in the rest of this book, and in Keim and Ziemba (2000) and Zacks (2011) are not fully accepted nor believed by many strong efficient market theorists. Part of this dismissal is that the anomalies are too small to be bothered with as Ross (2005) argues. So, more or less, does Fama (1970, 1991). The great financial empiricist Roll(1994) makes the startling statement that even with considerable resources, he has never been able to find a profitable anomaly. The well-known book Malkiel (2011) even states that strong effects like the January effect do not exist. Marquering, Nisser and Valle (2006) argue that the anomalies disappear after they are published, although some reappear; see also Dimson and Marsh (1999) and Schwert (2003). Hudson, Keasey and Littler (2002) and Lucey and Pardo (2005) discuss how anomalies are affected by papers published on them.
There also is the serious issue of data mining. Indeed, many results are in-sample and true tests out-of-sample. Statistical verification of the actual existence of significant seasonal anomaly effects is studied by Sullivan, Timmerman and White (1999) who analyze 9452 calendar based trading rules. See also Hansen, Lunde and Nason (2005) who study 181 calendar effects and Lo and MacKinley (1990) who discuss data snooping biases. Also t values tend not to show statistical significance in many cases where successful trades have been made because of high standard deviations.
Rather than debate such people, Ziemba and Ziemba (2007) simply argued that there are five basic stock market camps. Each has a cut or version of certain sections of the market and makes its point for a certain subset of market participants, instruments and strategies. There may be other classifications but these provide a useful framework for discussion.
The Five Groups are:
1. Efficient markets (E)
2. Risk premium (RP)
3. Genius (G)
4. Hog wash (H)
5. Markets are beatable (A)
The first group are those who believe in efficient markets (E). They believe that current prices are fair and correct except possibly for transactions costs. These transaction costs, which include commissions, bid-ask spread, and price pressures, can be very large.2
The leader of this school which had dominated academic journals, jobs, fame, etc. in the 1960s to the 1980s was Eugene Fama of the Booth School of Business, University of Chicago. A brilliant researcher, Fama is also a tape recorder: you can turn him on or off, you can fast forward or rewind him or change his volume, but you cannot change his views no matter what evidence you provide; he will refute it forcibly. In the aggregate there is much to support his case. One such example is the $300+ million gift from former student David G. Booth to name the Chicago Graduate School of Business earned from fees from his index fund firm Dimension Fund Advisors (DFA) founded with another Chicago student Rex Sinquefield. Booth never got his Ph.D. but Fama helped him get a job and later in 1981 DFA was founded with Fama as a key advisor. Some multi-billion plus later in fees shows how low fees with simple strategies can add up with huge volume. Booth has a co-authored paper with Donald Keim on the January effect in the cash market in the Keim and Ziemba (2000) anomalies book.
This group provided many useful concepts such as the capital asset pricing model of Sharpe (1964), Lintner (1965) and Mossin (1966), which provided a theoretical justification for index funds, which are the efficient market camp's favored investment mode. They still beat about 75% of active managers. Since all the managers comprise the market, that's 50% of them beaten by the index. Transactions (commission plus market impact) such as exchange taxes, bid-ask spread and other costs eliminate another 25%. See Ziemba and Schwartz (1991:44–46) for examples of how few funds beat the index across the world. In a sample of 167 funds, only 48 (28.7%) beat the benchmark.
Over time the hard efficient market line has softened into a Risk Premium (RP) camp. They feel that markets are basically efficient but one can realize extra return by bearing additional risk. They strongly argue that, if returns are above average, the risk must be there somewhere; you simply cannot get higher returns without bearing additional risk. For example, beating the market index S&P500 is possible but not risk adjusted by the capital asset pricing model (CAPM). They measure risk by Beta, which must be greater than one to receive higher than market returns. That is, the portfolio risk is higher than the market risk. But they allow other risk factors such as small cap and low book to price. But they do not believe in full blown 20–30 factor models such as used by Jacobs and Levy (1988) for the U.S. and Schwartz and Ziemba (2000) for Japan. Rather they prefer to use just a few factors and small cap and price to book value are favorites. Ziemba recalls Barr Rosenberg focusing on small cap and low price to book as the key factors in 1967, see Rosenberg, Reid and Lanstein (1985). Later, Fama and French (1992) took the credit for these ideas with a more complete study. Fama and his many disciples moved to this camp in the 1990s. This camp now dominates the top U.S. academic journals and the jobs in academic finance departments at the most famous business schools in the U.S. and Europe.
The third camp is called Genius (G). These are superior investors who are brilliant or geniuses but you cannot determine in advance who they are. The late MIT economist Paul Samuelson championed this argument. Samuelson felt that these superior investors do exist but it is useless to try to find them as in the search for them you will find 19 duds for every star. Surprisingly, Samuelson was an early investor in the very successful futures trading operation Commodity Corporation run, partly, by one of his MIT students. This view is very close to the Merton– Samuelson criticism of the Kelly criterion: that is, even with an advantage, it is possible to lose a lot of your wealth. See MacLean et al. (2011) for simulations discussing this point and Thorp and Ziemba's (2012) response to private letters received from Samuelson. The evidence though is that you can determine some superior investors ex ante and to some extent they have persistent superior performance, see Fung et al. (2006), Jagannathan et al. (2006), Ziemba (2005) and Gergaud and Ziemba (2012). Soros did this with futures with superior picking of commodities and currencies to bet on; this is the traders are made not born philosophy. This camp will isolate members of other camps such as in (A) or (H).
The forth camp is as strict in its views as camps (E) and (RP). This group feels that efficient markets that originated in and is perpetuated by the academic world is hogwash (H). In fact the leading proponent of this view, and one with whom it is hard to argue as he tops the lists of richest people and greatest investors, is Warren Buffett, who wants to give university chairs in efficient markets to further improve his own very successful trading. An early member of this group, the great economist John Maynard Keynes was an academic. We see also that although they may never have heard of the Kelly criterion, this camp does seem to use it implicitly with large bets on favorable investments. See MacLean, Thorp and Ziemba (2011). Ziemba and MacLean (2011) present a table of actual asset positions in a George Soros fund where about half the portfolio is invested in one position and equity weights near 10% for several positions are in Warren Buffett's Berkshire Hathaway. They do not care about monthly losses, and have many, but they focus instead on high long term wealth growth. So they resemble Kelly bettors.
This group feels that by evaluating companies and buying them when their value is greater than their price, you can easily beat the market by taking a long-term view. They find these stocks and hold them forever. They find a few such stocks that they understand well and get involved in managing them or they simply buy them and make them subsidiaries with the previous owners running the business. They forget about diversification because they try to buy only winners. They also bet on insurance when the odds are greatly in their favor. They well understand tail risk which they only take at huge advantages to themselves when the bet is small relative to their wealth levels. Indeed Buffett's long-term approximately 15– 18 year bet shorting S&P500 over-the-counter puts, for which he received much incorrect criticism, sure looks good now with the S&P500 closing 2011 at 1257.60 and in the 1400 area in April 2012. The odds favor him not to have to pay back the $4.6 billion premium he is now using for trades like the 10% loans to GE and Goldman Sachs. Calculations indicate that Buffett collected about twice the fair value of these American put options that cannot be exercised until expiry many years in the future.
The last group are those who think that markets are beatable (A) through behavioral biases, security market anomalies and other research using computerized superior betting techniques. They construct risk arbitrage situations with positive expectation. They research the strategy well and follow it for long periods of time repeatin...
