Benoit Mandelbrot, world renowned mathematician from Harvard and Yale, passed away last week at the age of 85.
He coined the term “fractal” (a shape comprised of smaller similar shapes). He determined that derivative pricing in financial markets follows this self-similar characteristic, which leads to infinite variance (e.g., black swan, fat-tail events)
Mandelbrot used the Hurst exponent (H) to describe the relative tendency for a time series to strongly regress to the mean or cluster in a particular direction (e.g., index of dependence or "fractalization").
The Hurst exponent identifies the manifestations associated with high frequency trading (HFT). The range for the exponent is zero to 1: zero suggests 0 percent correlation, while 1 represents 100 percent correlation. Unbiased trading activity centers near the mean of 0.5.
Correlation indicates multiple events co-exist simultaneously (doesn't imply a causal relationship). The term “herd mentality” is a manifestation of this phenomenon, whereby demand is generated by previous demand, leading many participants to make a similar decision. The result is high volatility and a large H exponent (near 1).
Reginald Smith, of the Bouche-Franklin Institute, recently examined the high frequency time series from 2002 through 2009. Starting in 2005, when high frequency trading was most prominent, nearly all of the 14 most heavily traded stocks on the New York Stock Exchange (NYSE) demonstrated a significant increase in the Hurst exponent. He noted average trade size declined during this period, which increased the magnitude closer to 1.
This suggests a self-similar correlation and it is associated with high volatility. This phenomenon occurred on May 6, which is now termed the “flash crash.”
Ironically, this high volatility caused many high frequency traders to exit the market, thereby reducing the liquidity in the system. This further exacerbated volatility within a negative feedback loop.
The SEC recently published the fee schedule for high frequency traders to obtain early access to market orders via co-location (e.g., the traders’ computer servers remain in close proximity to those of the exchange).
These fees can approach seven figures annually. With this information, the high frequency trader can identify and capture the excess demand in the system to optimize revenue and profit.
For instance, the trader may receive a market order to sell 1 million shares of Company XYZ at $10 per share. The trading system may elect to purchase all the shares at this price. It then attempts to sell these shares at a higher amount to maximize profit. It places small sell orders to assess the strength of demand by measuring the time required to fill the small order. If the time required is small, it suggests there may be stronger demand. It then places another small sell order at a slightly higher price. It continues this process until all the shares are sold. This can take less than a second with the use of high speed algorithmic trading.
Typically, most of the orders placed by the trading system (estimated near 90 percent) are to assess the market demand and are subsequently canceled. This mechanism is termed “order stuffing.”
Recently, participants with a high frequency trading firm were prosecuted for this activity, and some were fined and banned from trading for a specified amount of time.
In addition, the algorithmic nature of the system lends itself to systematic dysfunction if there is human error during the initiation phase.
High frequency traders represent 2 percent of traders, conduct more than 50 percent of trading volume, and generate annual profit of nearly $20 billion. A further consolidation of trading activity will intensify the underlying dynamics of volatility and liquidity risk in times of crisis.
The retail and institutional investor has determined the market may not be functioning in a fair, effective and efficient manner.
Recently, “60 Minutes” on CBS reported that mutual funds recently withdrew nearly $70 billion from the market. In addition, volume on the exchange has decreased. Professionals indicate this low volume environment may last a year or more as financial deleveraging continues.
Since May 6, there have been more instances of the flash crash dynamic, and professionals are explicit in saying another serious market condition can happen unless the process is reformed.
In fact, one high profile investment professional appeared on CNBC just hours following the flash crash to strongly advocate for a more responsible system that preserves market integrity.
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