##
### 04

#### May, 2012

### 04

#### May, 2012

# New Academic Paper Says HFT Does Increase Volatility

It seems like every day now that we find a new academic paper that refutes many of the high frequency traders claims that they are helping the market. This time we present to you a paper titled “A Multiscale Model of High Frequency Trading” written by Andrei Kirilenko of the CFTC and Xiangqian Meng and Richard Sowers of the University of Illinois. The paper states:

“*The main issue to which we address our model is volatility. An important question is how volatility is affected by HFT. In our stylized model, we show how HFT increases volatility, and can quantify this effect as a function of the parameters in our model and the separation of scales…While high frequency traders (HFT-ers) claim that they provide liquidity, the volume they trade and the algorithmic nature of HFT can cause significant impact. The pre-eminent example of this, of course, is the Flash Crash of May 6th of 2011.”*

Now, we warn you, this paper is not intended for those who don’t like squiggly math symbols and Greek letters of the alphabet. For example, the paper states:

*“Adding the HFT approximation of (27) to the fluid approximation (7) of the liquidity traders, we get that (28) Qδ,ε ≈qδι −δν◦−γ◦lt+εςσ ̄V ̄d,ε”*

Lots of funny looking letters there, so what do they mean?

The authors created a model of an order book “*which is populated by a community of HFT-ers and a community of (*slow)* liquidity traders. The HFT-ers operate at a much faster scale than the liquidity providers. They also place and cancel a large number of orders (which is indeed what happens; HFT can account for over half of the trades on a typical day).”*

The authors then questioned what would happen to this order book in certain situations. They theorized, “*if the order queues empty earlier due to high-frequency trading, the price will have faster variations, and volatility should increase. If the order queues empty later, volatility should decrease*.” The answer to this question can be found in Theorem 7.7 of the paper (which we won’t reprint here for fear of too many squiggly lines).

The bottom line here is that this paper is mathematical evidence that **HFT does indeed increase volatility. **

And this is not the only paper that has come to this conclusion. In December 2010, Professor Frank Zhang of Yale University, wrote a paper titled “High-Frequency Trading, Stock Volatility, and Price Discovery” where he concluded that “*high-frequency trading is positively correlated with stock price volatility and stock prices tend to overreact to fundamental news when high-frequency trading is at a high volume.”*

Next week, we will be in Chicago for the CFA Institute where we will be on a panel discussing HFT with Manoj Narang. Maybe we’ll bring a copy of this new academic paper for him to read.