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Ambiguous Statistics and Esoteric Quant Analysis

The bulk of market  statistics in financial blogs and social media are ambiguous due to lack of sufficient samples and stochastic nature of price series. Here is a recent example.

I saw a tweet yesterday about the fact that in the last 25 days there have been three days when the S&P 500 rose more than 1% from previous close but then reversed and closed lower. Below is a chart of the rolling count of days with larger than 1% rise from previous close and negative daily return:

The rolling count in the above chart stays low usually during smooth uptrending markets, as should be expected, but rises during corrections and bear markets. Note that during the 1998 Ruble crisis the count rose to 3 but then the market rebounded and made new highs in 2000. Then the count rose to 3 again during 2001 but the market did not bottom until late 2002.

We cannot know how high this particular count will rise. There are no sufficient samples in the above chart. We would probably need thousands of years of data to get a sufficient sample. Any attempt to infer the parameters of the population from this limited sample will result in a large error. For this reason, these statistics can only be used to denote facts that have no forecasting value. In other words, the count of those up-down days is a random variable with unknown distribution. If we knew the distribution we could say with some statistical confidence that at this point the probability of a bottom is p, for example. However, we do not know the distribution and in fact it may not even exist at all.

Most people that talk about these “facts” know little about what they mean, in terms of both price action and statistics. Finding patterns based on these facts is not trivial task and few quants can do it. This is one reason quant trading will always remain an esoteric subject no matter how many programming languages and libraries in GitHub emerge to facilitate it. Quant trading is an art and a science. Anyone who thinks that people can learn quant analysis in universities is probably seriously misguided.

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