Investment XYZ

Thursday, May 04, 2006

Is Option a Zero-Sum Game?

Is option trading a zero-sum game? That sounds strange to ask such question. All option textbooks say that: option trade is like betting: an option contract has two sides: if you buy a call and win, the other side who sold you the call would lose. Isn't it obvious?

The Fear of Trading Against MM

If option trades are zero-sum, investors seems to be in a wrong crowd: they are usually betting against the other crowd who are professional option market makers (if you want to buy, they create the contract and sell it to you; if you want to sell, they buy it from you), and this crowd usually win. So if it is zero-sum, the investors must be on the losing side -- at least statistically speaking. No wonder people love to guess which side MM (market makers) is at and trying the stand on the same side.

Such belief is totally untrue. In many cases, the so-called MM (in the option market) are actually bogie-man that people create to scare themselves. It is a useless effort trying to stand on the same side as MM, because they have no side. They stand on both sides and make money on the bid/offer spreads.

Here is how the option market works: when an investor opens an option contract (for example, buy a call), the investor is speculating on the direction (wish the market to go up), while the other side, the market maker, has no view (up or down), but has the obligation to write the contract (the investor is on the long side, the MM is on the short side). After the contract is opened, the investor would sit on it and hope his speculation is correct (wish the stock to rise for calls), while the market maker would immediately hedge the position. In this example, the MM short call, so he buys stock to neutralize the delta. Furthermore, he has to "dynamic hedge" this position when the stock moves up and down.

It is easy to figure out whether the investor has a good trade or not: if his call option rises, he makes money; if drops, he loses. For MM, it is less obvious, because the total profit/loss of the position has to accumulate the entire path of hedging, including both the stock and option positions. However, statistically, MM would make money on the two factors: 1) bid/ask spread; 2) option volatility.

Thus the unhedged option trades by investors will earn the profit/loss from the speculation of direction, while the hedged MM opposite side of the contracts will earn it from bid/ask and volatility. Of course, some MM would also speculate on the direction, thus that may justify the fear of betting against some big guy who knows more than you. But in the option market (both the public exchanges and OTC), all MM hedge.

Thus option trading is absolutely not zero-sum. To the contrary, stock trading is absolutely zero-sum. If you buy stock, someone else in the market has to sell that stock to you (there is no equivalence to the option market that you can create a contract out of blue -- that's the so-called fungibility of options and futures).

A Win-Win Example

Let me illustrate a case that would show you how an option trade can be win-win for both sides: you (the investor) bet the stock would rise at earning release (ER), so you buy 10 contracts of at-the-money call at $1.5 (total cost = $1500). The MM now short 10 contracts of call, and buy 500 shares of stock to hedge. The earning release comes and your speculation is right, stock jumps up $2.5, now the call becomes $2.5, you make $1000. Does the MM loss $1000? His option part loses $1000, his hedging stock gains $1250, thus his net gain is $250! How nice, you win, the MM wins too. The ending seems better than a classical fairytale.

The scenario for the profit/loss for the MM in the above case is much more complicate than the investor. For you, if the stock drops after ER, say down $1, option drop to $0.75, you loss $750, the MM would has a gain of $750 - $500 = $250 -- magically he would still make money. For investors, this trade is 50/50 chance of making it out (just as the stock has 50/50 chance of going up and down). For MM, it is a non-linear surface: he would make money if the stock price change (up or down) is within a certain range, but would lose -- and can loss big -- if the change (up or down) is huge.

That's the end of the "option is zero-sum game" myth. Welcome to the myth of "risk transfer".

If the stock speculators still like to play the game of "standing in the same side with MM", they'd better pick the stock MM, not the option MM. However, with the electronic markets and the huge liquidity in stock trading, it is hard to pin point who are the professional MM and who is the speculators. In contrast, MM in option market is a special class of traders.

So don't try to guess the mind of MM in the option market. They are a bunch of "delta neutral" guys, believe in nothing except liquidity.

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