Many assume high frequency trading (HFT) has made the markets less stable and dishonest. In reality, markets were unstable and crooked before the advent of computerized trading. A century ago, it wasn’t uncommon for indexes and individual stocks to fall several percentage points in a single day for seemingly no reason. Fast forward to today and a two percent decline is a pretty big deal. In the early days, volume was very thin, allowing a handful of individuals to impact the stock price. Sometimes stocks on the NYSE would go for days or weeks without trading and transactions, if they occurred, had to be made by appointment. This made stocks much easier manipulate than is possible today, allowing unscrupulous operators to make large profits with impunity. Stocks were expensive to own for average individuals due to the very wide bid and ask spreads and exorbitant commission fees. Furthermore, the absence of computers didn’t prevent people from dumping stocks to the tune of twenty percent in just two days during the crash of 1929. In recent years, thanks to the sensationalist media, volatility events receive much more press than in the past, but that doesn’t mean they are more prevalent. Computerized trading and high frequency traders (which could also include day traders) has made the markets more efficient, more honest, and cheaper in terms of smaller bid ask spreads and commissions. This confers with E Renshaw – 1995 that the market is more stable than it used to be.

Using the Chart to Scalar theory, we can offer a mathematical explanation for why HFT could make markets more stable. We’ll make reference to an abridged version of the theory.

If we assume discrete buy and sell orders are the propagators of price change, we can model these individual orders as a distribution and using the variance of price change.

A buy order b_o causes the stock to rise by some amount

A sell order s_o causes it to fall by the same amount

These orders exist in a right hand side (RHS) trading space with a volume v_r and a trade size a_v. There is a volume resistor on the LHS (left hand side) that has v_o. This LHS quantity is what prevents the stock from going to zero if you sell. It’s like friction.

From the paper, we have:

The first equation tells us that the number of buy and sell orders must equal the total volume (v_r) divided by the average order size (a_v). The second equation gives a relationship between discrete buy and sell orders and price displacement of a stock. The difference between buy and sells causes the stock to rise or fall.

Skipping ahead, we derive the standard deviation for price change

If the trade size a_v is small relative to v_r, then the variability of moves is smaller. (a_v=0 for example) . On the other hand, if we increase a_v, v_r,and v_o by a scaling factor it cancels out and sigma is unchanged. So in the context of this model, HFT is either stabilizing or neutral.

For example, without HFT let’s assume we have: v_o=10^6, v_r=10^6, a_v=10^3

now introduce HFT: v_o=10^7, v_r=10^7,a_v=10^3

We’ve increased the volume v_o of the stock on the LHS (left hand side) and the RHS v_r but the trade size is unchanged because we’re assuming the high frequency trades are no larger than normal trades. Because:

(10^6*10^3)^.5/10^6>(10^7*10^3)^.5/10^7

We see that the noise orders have a stabilizing effect

The limitations of this model is the assumption that HFT is the same as random trades and ignoring possible feedback effects.