And here comes Hurst, they think it’s all over! It is now! July 14, 2010 at 6:06 am

There has been some comment recently about a paper by Reginald Smith on the impact of high frequency trading (HFT) on market dynamics. I want to spend a little timing explaining what the paper says, roughly, and why it matters.

We can clearly demonstrate that HFT is having an increasingly large impact on the microstructure of equity trading dynamics… the Hurst exponent H of traded value in short time scales (15 minutes or less) is increasing over time from its previous Gaussian white noise values of 0.5. Second, this increase becomes most marked, especially in the NYSE stocks, following the implementation of Reg NMS by the SEC which led to the boom in HFT. Finally, H > 0.5 traded value activity is clearly linked with small share trades which are the trades dominated by HFT traffic. In addition, this small share trade activity has grown rapidly as a proportion of all trades.

So first, what is a Hurst exponent?

Roughly speaking, Hurst exponents measure autocorrelation or, even more loosely, predictability. If H is close to 0.5, the series is a random walk, or what we were told equity prices did in Finance 101. In particular, if H = 0.5, the idea of volatility makes sense, and we can quantify risk using volatility.

If H is bigger than 0.5, though, the series shows positive autocorrelation: roughly, it has very busy periods when volatility is high, and quieter low volatility periods. It switches regimes between these with no warning. Thus we might try to calibrate a simple risk model but if we are unlucky we will calibrate it to a low vol period and then when the high vol hits, our risk estimates are wrong.

So, what the paper seems to have proved (and I have not checked all the details) is that HFT has changed the nature of stock price returns from being a random walk (H = 0.5) to having significant positive autocorrelation. Increasingly we see quiet periods when not much happens followed by periods of intense volatility, and the change between these is unpredictable. Now notice the time period cited, 15 minutes or less. What is happening, then, is that HFT appears to be creating islands of high volatility amid an ocean of more stable prices. Something sets off a price change, which creates a flurry of HFT activity, exacerbating volatility; this then dies away over a period of minutes or hours.

Why does this matter to the ordinary investor? Simply that their trading might hit one of those flurries of activity, and they might well get a significantly worse price than average if it does. Moreover of course simple risk models such as VAR will be less and less accurate risk gauges the higher the autocorrelation. I suspect on the typical VAR one day holding period this does not matter much, but it might.

Finally, there is the issue that HFT might be increasing the risk of flash crashes. If autocorrelation is too high then the probability of very large deviations from the mean over short timescales increases dramatically. I have no idea if this research supports the idea that we have got to that point yet. But I do think that someone should find out.

2 Responses to “And here comes Hurst, they think it’s all over! It is now!”

  1. […] of equity market trading (more bots, more ETFs) has affected the dynamics of the market. (See here for a previous item.) Specifically, according to FT alphaville (who cite Barclays research) equity […]

  2. […] know – or at least strongly suspect – that HFT activity has changed the nature of US equity markets, and likely others. Similarly, bots seem if not the culprit, at least one of the culprits in the […]