Practical traders, who believe themselves to be quite exempt from any intellectual influences, are usually slaves of some defunct mathematician. That is what Keynes might have said had he considered the faith placed by some investors in the work of Leonardo of Pisa, a 12th and 13th century number cruncher. Better known as Fibonacci, Leonardo produced the sequence formed by adding consecutive number components of a given series - 1,1,2,3,5,8,13 and so on. Numbers in this series crop up frequently in nature and the relationship between components tends towards 1.618, a figure known as the golden rule in architecture and design. If it works for plants (and appears in The Da Vinci Code), why shouldnt it work for financial markets? Some traders believe that markets will change trend when they reach, say, 61.8% of the previous high, or are 61.8% above their low. Believers in Fibonacci numbers are part of the school known as technical analysis, or Chartism, which believes the future movement of asset prices can be divined from past data. But there is bad news for the numerologists. A new study No Magic in the Dow by Professor Roy Batchelor and Richard Ramyar of the Cass Business School, finds no evidence that Fibonacci numbers work in American stock markets. This research may well fall on stony ground. Experience suggests that chartists defend their territory with an almost religious zeal. But their arguments are often anecdotal: If technical analysis doesnt work, how come so-and-so is a multi-millionaire? This survivorship bias ignores the many traders whose losses from using charts drive them out of the market. Furthermore, the recommendations of technical analysts can be so hedged about with qualifications that they can validate almost any market outcome. If the efficient market theory is correct, technical analysis should not work at all; the prevailing market price should reflect all information, including past price movements. However, academic fashion has moved in favor of behavioral finance, which suggests that investors may not be completely rational and that their psychological biases could cause prices to deviate from their correct level. Technical analysts also make the perfectly fair argument that those who analyze markets on the basis of fundamentals such as economic statistics or corporate profits are no more successful. All that talk of long waves is distinctly mystical and seems to take the deterministic view of history that human activity is subject to some pre-ordained pattern. Chartists fall prey to their own behavioral flaw, finding confirmation of patterns everywhere, as if they were reading clouds in their coffee futures. Besides, technical analysis tends to increase trading activity, creating extra costs. Hedge funds may be able to rise above these costs; small investors will not. As illusionists often proclaim, dont try this at home.

Now answer the following questions:

(a) Technical analysis is the search for recurring and predictable patterns in stock prices. It is based on the premise that prices only gradually close in on intrinsic value. As fundamentals shift, astute traders can exploit the adjustment to a new equilibrium. Critically explain this statement using an example.[5 marks]