The Market Maker’s Edge

When it comes to Roulette, the casino’s edge is the green square. This is what allows them to consistently make money playing the game. When it comes to trading, you need your own green squares.

What are your green squares?

I think it’s easy to understand what an edge is in the abstract and purely mathematical sense but it can be hard to understand what it may look like in the real world for a lot of people. Something that really helped me understand just one of the forms it may take was understanding how option dealers actually make markets.

I always knew what they were (market makers), but what they did was always a gray area. I understood that they are posting bids and offers but never really knew how they actually make money doing that.

For example, an option market maker’s edge is in “making the market” using something like the black-scholes model to give a theoretical value for a market they are trying to make.

They use the model to calculate an option’s theoretical price. So say for example the market maker was looking at EUR/USD and was going to price a call option for some strike price 60 days out. He would plug the current price, volatility, risk-free rate, etc into the model which also makes the assumption that prices are normally distributed, and outcomes a theoretical price for this option. Let’s say $6.75.

He would then go make the market AROUND this price. So he would offer a bid of $6.50 and an ask of $7.00, creating the spread that you’d see in the brokerage account when looking at the contract.

Then someone either hits his ask or bid. Let’s say the hit his bid, so he has now purchased this option for $6.50. He knows he needs to instantly sell this contract for higher than he bought it for because he is not taking a directional play, he is only making the market and collecting a spread.

The closest asking price is still $7.00 (his ask), and the current bid is still only $6.50. If he sold his contract at the market price he would make no money, and if he waited to see if someone will hit his asking price of $7.00, he could be exposed directionally if the bids started dropping from $6.50. And remember, he is only trying to collect a spread, so this would mean a ton of risk for a tiny reward.

So what does he do?

The answer was really kind of profound when I first heard it. He synthetically sells the contract for $6.75 immediately after he buys it in order to collect his $0.25 spread over the life of the option.

This spread, between what he bought the option for and what he is going to synthetically sell it for, is the market maker’s green zero. It’s important to understand though, this doesn’t mean his trade is 100% risk-free. Remember he is using a model to synthetically sell the option, which can sometimes have errors or create issues if used incorrectly because models make assumptions.

One of the assumptions of the black-scholes model is it assumes volatility will remain constant through the life of the option, which we know does not happen in actuality.

In order to synthetically sell the option for $6.75, he needs to remain delta neutral with the option he sold. What this means is, he has completely removed any direction risk from the option he holds, by actually shorting EUR/USD directly. So say the option had a delta of .50 and the option was for the right to buy 100,000 units of EUR/USD at the option’s strike price. This means he would need to sell 50,000 units of EUR/USD in order to remove his directional risk so that regardless of where the market goes, he gets to collect his spread.

If the price of EUR/USD moves lower and the delta is now .20, he would need to buy back 30,000 units, which would result in a small profit from the price change. Then if the market moved again and the delta went back up to .75, he would need to short an additional 55,000 shares in order to get delta neutral again.

He will continuously hedge his delta until the call option he purchased for $6.50 has expired. At the end of it, if everything, especially volatility, remained constant throughout the life of the option, the profits generated from delta hedging would produce the exact same result as if he really sold his call option for $6.75, allowing him to actually buy the option for $6.50 and instantly “sell it” for $6.75. It just took him till the option’s expiration to fully collect the proceeds of the sale.

See what’s really interesting about the black-scholes model is, the price given by the model, is the exact amount it estimates he will make delta hedging the call option contract he bought throughout its life. So if the model is right, his trading of EUR/USD directly, synthetically produces the outcome of selling his contract for its “fair price”, allowing him to capture his edge of buying below the “true or fair” market price.

Again though, because it’s a model it’s not 100% risk-free. Chances are volatility is not going to remain constant over the next 60 days, and if he wrongly assumes volatility will be higher than it actually was, the result of synthetically selling the option could end up that he really sold it for $6.35, losing $0.15 on the trade. On the flip side though, if volatility is even higher than he estimated, the result of his delta hedging could be that he synthetically sold the option for $7.25, even more than he initially expected.

So even though the delta hedging eliminates the market maker’s directional risk, he still has exposure to volatility and can lose money if he wrongly estimates what it will do. But market makers continue to stay in business while traders continue to blow up regularly because volatility is a lot easier to estimate than direction.

So now that you know what a real edge looks like, what its risks are, and how they can play out, I think it’s important to determine if you can explain/understand your edge as clearly as the one above. If you can’t, there is a good chance whatever one you think you have is not really there.

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