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When actively trading the financial markets, it is easy to overlook basic facts about the assets traded. For example, based on the time duration that a position is expected to remain open, does the trader know the asset’s average price range or whether it is a stock, futures or exchange-traded fund? To address this common oversight, a set of price-range statistical indicators was developed to gauge the measure of price ranges for the S&P 500 E-mini futures contract. This can be used to help make trading decisions.
“Flash crash volatility” (below) gives daily bars of the E-mini contract with an indicator measuring daily price range as a number of standard deviations from the contract’s average daily price range. Cyan coloring on the bottom indicator displays more than two standard deviations in daily price range (the day’s high-to-low value).
On May 6, 2010, the “flash crash,” we see a greater than five-standard-deviation price move. Also of interest is the indication of low volatility preceding the flash crash and then higher volatility aftershocks that appear to be the result of market nervousness immediately following the historic event. (The average price range indicator previously was highlighted in “Technical indicators: A statistical approach,” July 2010.)
Assuming price followed a normal distribution, a five-standard-deviation move has a probability of approximately 0.00003%, and if using a daily chart and 250 trading days per year, we should experience a five-standard-deviation flash crash event no more than once every 13,000 years. Obviously, financial markets cannot be modeled completely using normal distribution. Markets exhibit what are known as “fat tails,” which indicate more than normal activity far from the mean. Fat tails account for panics and over-exuberance, and different assumptions of distribution are required to model them.
Nonetheless, normal distribution works as a good first approximation (as long as extreme events are ensured against). For example, the Market Profile Value Area is defined as encompassing a 70% price movement beginning from a mode (most common) price. The 70% value represents a one-standard-deviation variation in price. Bollinger Bands are similarly based on standard deviation calculations and normal distribution.