Quote from jz3384:
I am wondering how do liquidity providing traders hedge their risk? Let's us they post both a bid and/or ask, and the bid gets hit. Now what if the stock price keeps going down? Is he not losing money now? How does he manage this directional risk? If he does fully hedge when his bid is hit, then by definition he can not make a profit since he is now fully hedged and not to mention he will be losing the bid-ask spread by using a market order to hedge. Appreciate any insights into this.
I had this exact same question and posted a question about how the liquidity provider GETCO (use the search feature) makes its money. Someone answered, and I pieced the system together. There are papers written about this that are freely available on the web. Read that thread!!
I've always subscribed to the theory that the greater the first-order (lag 1) auto-correlation [for small time-scale returns] is on a normalized time-scale, the more likely the MM is recovering the spread. This is mentioned loosely in the book "An Introduction to High Frequency Finance", by Olsen I think. (Chapter 5.)
So in other words, if there's a spread of 5 cents, e.g., 1.35 x 1.40, and the stock's real fair price is 1.375, the MM can quote at 1.35. If he gets hit, he can temporarily come back in at 1.37 or 1.38 and collect a spread. MM will always quote at a level that envelopes the theoretical-value [perhaps constructed with intraday factor models, or relative valuation, or what have you].
If he doesn't get hit at 1.37, he can remove liquidity at a loss back on the bad -- he cannot hedge with options because the option spread is going to be too wide. He -can- hedge with a synthesized portfolio of other stocks [stat-arb technique]; however, note that the MM is betting that the opportunity to collect the spread is statistically more likely than not collecting the spread.
MMs can create an effective "guess" as to what his expected value for his trade. Let's use a simple model, where the spread collected is a fixed constant and the loss-cutting is also a fixed constant, instead of random variables themselves:
Let X have two outcomes:
A: collecting the spread, or
B: cutting losses.
Let alpha = profit from collecting spread
Let beta = loss from cutting losses
[Note, alpha and beta are just arbitrary constants here and do not have their usual meaning when referring to stocks]
E[X] = alpha * p( A ) + beta * p( B )
if( E[X] - transaction costs > 0 ), the MM is going to play this game all day long.
The real world doesn't have a fixed alpha or beta in that above expectation. The MM probably has proprietary algorithms to estimate those parameters so he can make profits in the markets that he wants to make profits on. I suggest you record the level-2 depth and level-2 quote for a day, homogenize the time-series, and go back and analyze the individual transactions -- then assign guesses to when MMs were involved. It's enlightening.
