How Market Makers Manage Delta-Neutral Positions

While market makers are not position traders per se, they are expert position managers. For the most part, market makers make their living by buying the bid and selling the offer. In general, they don’t act; they react. Most of their
trades are initiated by taking the other side of what other people want to do and then managing the risk of the positions they accumulate.The business of a market maker is much like that of a casino.

A casino takes the other side of people’s bets and, in the long run, has a statistical (theoretical) edge. For market makers, because theoretical value resides in the middle of the bid and the ask, these accommodating trades lead to a theoretical profit—that is, the market maker buys below theoretical value and sells above. Actual profit—cold, hard cash you can take to the bank—is, however,dependent on sound management of the positions that are accumulated.

My career as a market maker was on the floor of the Chicago Board Options Exchange (CBOE) from 1998 to 2005. Because, over all, the trades I made had a theoretical edge, I hoped to trade as many contracts as possible on my markets without getting too long or too short in any option series or any of my greeks.As a result of reacting to order flow, market makers can accumulate a large number of open option series for each class they trade, resulting in a single position.

For example, Exhibit 16.7 shows a position I had in Ford Motor Co. (F) options as a market maker.With all the open strikes, this position is seemingly complex.The position was accumulated over a long period of time by initiating trades via other traders selling options to me at prices I wanted to buy them—my bid—and buying options from me at prices I wanted to sell them—my offer. Upon making an option trade, I needed to hedge directional risk immediately.

I usually did so by offsetting my option trades by taking the opposite delta position in the stock—especially on big-delta trades. Through this process of providing liquidity to the market, I built up option-centric risk.To manage this risk I needed to watch my other greeks. To be sure,trying to draw a P&L diagram of this position would be a fruitless endeavor.Exhibit 16.8 shows the risk of this trade in its most distilled form.

The 11,075 delta shows comparatively small directional risk relative to the 210,191 gamma. Much of the daily task of position management would be to carefully guard against movement by delta hedging when necessary to earn the $1,708 per day theta.Much of the negative gamma/positive theta comes from the combined 1,006 short January 15 calls and puts. (Note that because this position is traded delta neutral, the net long or short options at each strike is what matters, not whether the options are calls or puts.

Remember that in deltaneutral trading, a put is a call, and a call is a put.) The positive vega stems from the fact that the position is long 1,927 January 2003 20-strike options.Although this position has a lot going on, it can be broken down many ways. Having long LEAPS options and short front-month options gives this position the feel of a time spread. One way to think of where most of the gamma risk is coming from is to bear in mind that the 15 strike is synthetically short 503 straddles (1,006 options 4 two).

But this position overall is not like a straddle. There are more strikes involved—a lot more.There is more short gamma to the downside if the price of Ford falls toward $12.50. To the upside, the 17.50 strike is long a combined total of 439 options. Looking at just the 15 and 17.50 strikes, we can see something that looks more like a ratio spread: 1,006:439. If the stock were at $17.50, the gamma would be around 15,000.

With the stock at $15.72, there is realized volatility risk of F rallying,but with gamma changing from negative to positive as the stock rallies, the risk of movement decreases quickly. The 20 strike is short 871 options which brings the position back to negative-gamma territory. Having alternating long and short strikes, sometimes called a butterflied position, is a handy way for market makers to reduce risk.

A position is perfectly butterflied if it has alternating long and short strikes with the same number of contracts.Through Your Longs to Your Shorts:With market-maker-type positions consisting of many strikes, the greatest profit is gained if the underlying security moves through the longs to the shorts. This provides kind of a win-win scenario for greeks traders. In this situation, traders get the benefit of long gamma as the stock moves higher or lower through the long strike. They also reap the benefits of theta when the stock sits at the short strike.