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StuartReid On September 15, Hackers would make great traders. At a meta level, hackers and traders do the same thing: This article is broken up into three sections. The first section will present background information about the random walk hypothesis and compares the statistical definition of randomness to the algorithmic definition. The third and final section will subject a number of financial markets to these tests and end off by concluding whether or not the market are random and, if they are random, comment on the nature of that randomness.
Depending on your familiarity with the subject matter and time constraints, you may wish to skip some sections. This section introduces the random walk hypothesis and it's importance to quantitative finance. It also discusses the two definitions of randomness namely, statistical and algorithmic. It very succinctly describes the test that Professor Malkiel performed and the conclusions he drew from this test.
The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day.
Cycles or trends were determined from the tests. The chartist told Malkiel that they needed to immediately buy the stock. Since the coin flips were random, the fictitious stock had no overall trend. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin. Have a go with the following three images. Either image may either be a real market return series, or just the output from a calibrated Heston stochastic volatility model.
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We often speak implicitly of different types of randomness but neglect to name or categorize them. Consider this post to be a kind of white paper or rough draft on the division of randomness into five categories.
If you start using these distinctions explicitly, even if only in your own head, I think you will find them highly useful, as I have. Type 0 randomness is the special case of randomness where the data are already known. Any known outcome, regardless of the process that generated it, is Type 0 randomness. Once known, it has become a constant.
In terms of information conveyed, all Type 0 randomness has zero informational entropy a measure of uncertainty , and all messages with zero entropy are examples of Type 0 randomness. Most computers generate random numbers by a deterministic process.
These algorithms can be very good, in terms of producing sequences of numbers that have desirable qualities. Yet, if you know that the sequence comes from some variation of, say, the Mersenne Twister , then a single number or short sub-sequence might be enough to predict all the subsequent numbers.
Card shuffling machines, if sufficiently precise in their operation, map each unique ordering of playing cards to a single final ordering.
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