Magic Numbers in the Dow

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Magic numbers in the Dow Roy Batchelor and Richard Ramyar Cass Business School, City of London September 2006 Abstract There is a widespread belief in financial markets that trends in prices are arrested at support and resistance levels that are to some degree predictable from the past behaviour of the price series. Here we examine whether ratios of the length and duration of successive price trends in the Dow Jones Industrial Average cluster around round fractions or Fibonacci ratios. We iden
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  1 Magic numbers in the Dow Roy Batchelor   and Richard Ramyar Cass Business School, City of LondonSeptember 2006  Abstract There is a widespread belief in financial markets that trends in prices are arrested at support andresistance levels that are to some degree predictable from the past behaviour of the price series. Herewe examine whether ratios of the length and duration of successive price trends in the Dow JonesIndustrial Average cluster around round fractions or Fibonacci ratios. We identify turning points byheuristics similar to those used in business cycle analysis, and test for clustering using a block bootstrap procedure. A few significant ratios appear, but no more than would be expected by chancegiven the large number of tests we conduct.  Keywords : Technical Analysis, Stock Market, Forecasting, Anchoring, Stationary Bootstrap  JEL Classification : C15, C53, G10 Roy Batchelor, HSBC Professor of Banking and Finance, Sir John Cass Business School, City of London, 106 Bunhill Row, London EC1Y 8TZ, United Kingdom. Telephone: +44 207 040 8733, fax+44 207 040 8881 E-mail:    Richard Ramyar, PhD Researcher (2002-2006), Sir John Cass Business School, currently of RamyarIntegrated Consulting. Telephone: +44 207 870 3185   2 1.   INTRODUCTION This paper tests a popular but previously untested proposition about the behaviour of the stock market. The proposition is that when the market changes direction after aperiod of trending prices, the magnitude and duration of the next trend is not random,but depends on the magnitude and duration of the previous trend. Specifically we areinterested in whether the ratios of successive trends cluster around Fibonacci ratios or“round numbers”.The idea that price trends may be arrested at predictable support and resistance levelsis one of many tools used by technical analysts. Technical analysis – the prediction of turning points in financial markets by chart-based methods - has long been popularamong practitioners, but viewed with suspicion by academics. Burton Malkiel, in hisclassic book writes, among many similarly cutting remarks - “Technical strategies areusually amusing, often comforting, but of no real value” (Malkiel, 1996, p161).The root of the problem is the failure of technical analysts to specify their tradingrules and report trading results in a scientifically acceptable way. Too often, rules areso vague or complex as to make replication impossible. Too often popular textscontain dramatic examples of successful predictions of turning points, with no countof misses or false alarms. Recently, however, academics have begun to look systematically at some of the more easily replicable technical trading rules. Park andIrwin (2004) provide a comprehensive review of these studies. Of 92 studiespublished in the period 1988-2004, 58 reported positive excess profits from atechnical rule, 10 yielded mixed results, and 24 reported losses. Even allowing for abias towards publishing positive results, and the possibility that not all studies  3 properly accounted for transactions costs and risk, this does suggest that not all of technical analysis can be dismissed prima facie.The paper falls into four sections. Section 2 below introduces our hypothesis andreviews relevant research findings. Section 3 introduces our data – high/low/openclose prices for the Dow Jones Industrial Average in the years 1914-2002 - anddevelops a method for identifying turning points in range data based on Pagan andSoussonov (2003). Section 4 reports the resulting distributions of price and time ratiosfor successive trends, and compares them to distributions that would be expected tooccur by chance using the Politis and Romano (1994) stationary block bootstrapmethodology, again modified for the special features of our data. 2.   SUPPORT, RESISTANCE AND FIBONACCI NUMBERS The popularity of technical analysis among market practitioners is evident from anycasual reading of the financial press and the many web-based financial informationservices, and has been widely documented. Allen and Taylor (1992) and Lui andMole (1998) find that technical analysis is used as a primary or secondary method of forecasting market trends by ninety per cent of players in the foreign exchangemarket. A third of currency traders rely on technical techniques exclusively (Cheungand Chinn, 1999 and Cheung and Wong, 1999).Technical analysis itself is an umbrella term for a heterogeneous set of techniques,some relying on visual recognition of chart patterns, others on values of statisticalindicators calculated from recent price or volume data. Many practitioner booksdescribe these techniques, most prominently Achelis (2000), Murphy (2000), Edwardsand Magee (2001), and Pring (1998). Neely (1997) provides a readable academic  4 summary. Academic research has focussed on the profitability of trading onmechanical technical indicators. Many early studies investigate filter rules that requirea trader to go long if price rises more than k% above the most recent low price, andvice versa. Examples are the classic stock market studies of stock market efficiencyby Alexander (1961) and Fama and Blume (1966), and the contrary finding of profitable filter rules in currency markets by Sweeney (1986) and Levich and Thomas(1993). More recent studies investigate moving average rules that require the trader togo long or short if the current price (or short term moving average of price) is aboveor below a long term moving average. LeBaron (1999) finds evidence that thisgenerates profits in currency markets. Brock, Lakonishok and LeBaron (1992) claimto find profits from applying moving average rules to the Dow Jones IndustrialAverage, though this is disputed by Sullivan, Timmerman and White (1999). Asmaller number of studies evaluate pattern-based trades. Some look at trendlinebreaking rules that require the trader to buy or sell if the price breaks above someoverhead resistance level, or falls through some lower support level (see for exampleCurcio, Guillaume, Goodhart and Payne, 1997). Others look at reversal pattern tradesthat require the trader to sell if some sequence of prices characteristic of the end of anupward trend appeared – the well-known “head-and-shoulders” or “double top”patterns for example. Lo, Mamaysky and Wang (2000) use local smoothing process toidentify ten patterns often cited in technical analysis texts in a large sample of USstocks. They show that the statistical characteristics of the time series of price changesafter the occurrence of familiar chart patterns, but stop short of claiming that thisleads to profitable trading rules. Zhou and Dong (2004) use fuzzy logic to identifythese patterns, but find no excess profits from trading. The study of the head andshoulders pattern in currencies by Chang and Osler (1999) does find some excess
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