Are HFTs responsible for low market volatility?

I received a number of thoughtful responses from last post about falling equity volatility (see Will the quants blow up the markets again?). One of the themes that was repeated several times in the comments pointed to HFT algos as a possible culprit for the low volatility regime.

On the surface, the HFT explanation does make sense. HFTs are supposed to provide liquidity to the market during "normal" markets (and the current market regime is "normal"). Bloomberg reported that a study on HFT behavior based on Norway`s SWF trading activity and found that, in aggregate, HFT algos were providing liquidity to orders and not front-running them (emphasis added):

High-frequency traders are more prone to first go against the flow of orders by large institutions, according to a study based on trade data provided by investors including Norway’s $890 billion wealth fund.

The study found that HFTs “lean against the order” in the first hour and then turn around and go with the flow in the case of multi-hour trades, the study by University of Amsterdam professors Vincent van Kervel and Albert J. Menkveld released Thursday showed. Trading costs are 39 percent lower when the HFTs lean against the order, “by one standard deviation,” and 64 percent higher when they go with it, they said.

“The results are inconsistent with ‘front-running’ in the sense of HFTs who detect a large, long-lasting order right from the start and trade along with it,” van Kervel and Menkveld said. “We speculate that HFTs eventually feel the imbalance caused by it. In response, they trade out of their position as they understand that leaning against such order as a market maker requires a long-lasting inventory position. HFTs prefer to be flat at the end of the day.”

How fat are the tails?
Another way of thinking about market volatility is to see if stock returns have fat-tails. One statistical measure is kurtosis, which is explained this way:

Having discussed the shape of a normal distribution, we can talk about kurtosis and what it means to have fat tails and peakedness. The total area under a curve is by definition equal to one.

With that in mind, think about what having fatter tails might mean. If you were to think of a curve having three parts (all imaginary) – the peak, the shoulder (or the middle part), and the tails, you can imagine what happens if you stretch the peak up. That reduces variance, and probably sucks in ‘mass’ from the shoulders. But in order to keep the variance the same, the tails rise higher, increasing variance and also providing fatter tails.

Fat tails would imply there is more area under the tails, which means something else has to reduce elsewhere – which means that the ‘shoulders’ shrink making the peak taller. In order to compare kurtosis between two curves, both must have the same variance. At the risk of being repetitive, note that the variance has an impact on the shape of a curve, in that the greater the variance the more spread out the curve is. When we say that kurtosis is relevant only when comparing to another curve with identical variance, it means that kurtosis measures something other than variance.

For the non-geeks, here is how you interpret kurtosis. A standard normal distribution has a kurtosis of 0 and fat-tailed distributions have positive kurtosis.

Here is a chart of the rolling one-year kurtosis of daily SPX returns going back to 1990. First, the median kurtosis is 1.34, indicating that stock returns have fatter tails than a typical normal distribution (and option traders using the Black-Scholes model, which is based on a normal distribution, know that fact well). As well, kurtosis has been falling since 2011, indicating that the tails are getting thinner. This is not unusual as there has been episodes in the past when kurtosis has been even lower than they are today.

If HFTs are coming into the market and providing liquidity by buying the dips and selling the rips at a micro level, then we should expect kurtosis to fall.


An HFT Bataan death march?
The hypothesis that HFT algos were the cause of the low volatility environment is intuitively attractive from a data standpoint, but illogical from a business viewpoint. That's because HFT profitability has been tanking for the last several years. This Bloomberg story from 2013 (two years ago) show how HFT industry profitability has cratered over the years:

According to Rosenblatt, in 2009 the entire HFT industry made around $5 billion trading stocks. Last year it made closer to $1 billion. By comparison, JPMorgan Chase (JPM) earned more than six times that in the first quarter of this year. The “profits have collapsed,” says Mark Gorton, the founder of Tower Research Capital, one of the largest and fastest high-frequency trading firms. “The easy money’s gone. We’re doing more things better than ever before and making less money doing it.”

“The margins on trades have gotten to the point where it’s not even paying the bills for a lot of firms,” says Raj Fernando, chief executive officer and founder of Chopper Trading, a large firm in Chicago that uses high-frequency strategies. “No one’s laughing while running to the bank now, that’s for sure.” A number of high-frequency shops have shut down in the past year. According to Fernando, many asked Chopper to buy them before going out of business. He declined in every instance.

This slide from an HFT presentation in 2014 tells the same story (annotations in purple are mine):

Given how industry margins has fallen over the years and the reports of diminishing HFT profitability came out in 2013, it would be illogical for the industry to engage in a further arms race to drive down volatility further. Such an act would amount to a Bataan death march for HFT.

Based on this analysis, HFT algos may have contributed to the decline in equity volatility since 2011, but I cannot conclude that they were the main culprits. The mystery of equity market volatility compression still remains a mystery.