In quant terms, professionals bet on the "risk neutral measure" and the retailers use the "physical measure". Ajacobson's example is an example. You can equate "physical measure" with "stock direction" and "risk neutral measure" with "volatility". Two problems: 1) Stock direction is way more difficult to estimate than volatility (mathematically the volatility is "signal" and direction is "noise"). If you estimate it wrong, you lose. Same happens with volatility, it's not just "the spread" as retailers blindly repeat some half baked trickled down quant knowledge. Estimating volatility has it's errors too and if the spread gets too narrow, there are good chances they'll lose money. 2) Direction only works one way, volatility doesn't care about direction. In Ajacobson't example, the market maker would have made money also if the stock moved the other way. The retailer would have lost money. So the correct answer is: options trading is a zero-sum game between directional option traders (a.k.a option gamblers) and the stock market (blissfully unaware of the derivatives world above them). The market maker (a.k.a. option arbitrageur) is the intermediary which, under ideal conditions, always makes money. On the other hand, the retailer are just gamblers: they may win or lose, the money comes or goes to the stock market, minus market maker's "spread". By the way, anyone calling themselves a quant should know this.
Thank you gaussian and ajacobson. You have no idea how important this is to me and how much this is troubling me. Great explanations and discussions. Here is my summary of what you both said: 1. There are many methods, objectives and approaches in trading/investing, we all focus on our own subset within this market, so, me and my counter parties can both "win". 2. As long as the total stock market is appreciating, due to economic factors like GDP growth, productivity growth, innovations..., it is not a zero sum game, the appreciating market creates profits/wealth to be share among traders/investors/middlemen... 3. Of course, the total market does not always go up, like during 2008-9, when almost everyone lost money. But the world economy generally has a long term up trend so will create wealth for its participants in the long run. 4. I worry about this because if it is a zero sum, my good fortune is probably just luck. But if 2 and 3 are correct, then in the long run all I need is to piggyback on the general market direction to make money. The only question then is can I beat buy and hold? Best wishes.
I think you are misleading them with your terminology. I also think you are rather crass with a fairly non-academic explanation of the matter and the accusatory tone of the last sentence. The term measure is extremely specific. It refers to a mathematical measure (https://en.wikipedia.org/wiki/Measure_(mathematics)). The Risk-Neutral Measure is far more complicated than just volatility. It is based on the arbitrage free assumption and the fundamental theorem of asset pricing. The true definition of the risk-neutral measure is that the share price is exactly equal to the discounted expectation of the share price. This is more complicated than just simple volatility and is critical to the overall pricing of derivatives. It gets into rather complicated probability and measure theory to explain. I'm not here to show off my talent. I just wanted to make this part clear. Zero sum doesn't imply a random distribution of returns. You may have an edge and you're exploiting it. Poker is a good example of a (relatively) zero-sum game and we can all see that texas hold 'em takes a little more than luck to win. Beating buy-and-hold is a fun question. In general - yes you can. The market supports that assumption as well. If it was true that the efficient market hypothesis dominated the markets then you wouldn't be able to. However, given that people consistently and frequently produce above market returns - something is amiss. What is amiss is the tail risk. The tail risk of the underlying distribution of price changes is far greater than the normal distribution would have you guess. I encourage you to verify this. The standard deviation of price changes of most stocks will regularly and predictably exceed 3 standard deviations. Under the BSM, this would be essentially impossible. There is certainly some exploitability in this.
I think a retail options trader should try to understand option theory at the level of Natenberg's "Option Volatility & Pricing: Advanced Trading Strategies" or even better, Hull's "Options, Futures, and Other Derivatives" or Wilmott's books. But the level of Shreve's "Stochastic Calculus for Finance" books may not be necessary. Having worked with options traders at a large firm, I'd say they are the level of Natenberg or Hull, with stock index options traders being more sophisticated than the single-stock options traders.
Stop being so smug. It's unbecoming of you given you are trying to start a hedgefund on like $500. Volatility is directional too (just in a different space). All options are a zero sum game. What makes it not a zero-sum game is the trading of the underlying to create a synthetic option. This just takes/gives pnl to another asset class which is how both counterparties can earn/lose. On this site, there are a lot of quants as you describe them. Most of them work at real funds like Citadel, SAC, Millenium, and various top tier banks. There are even more on here who have left those careers to pursue other endeavors or to just trade their own money. Most of these guys don't go around shouting "I'M A QUANT. IF YOU WERE A QUANT YOU WOULD KNOW THIS." They don't have to.
Zero sum means one needs an "edge", or a method to win, like playing poker and Blackjack. Positive sum means if I play long enough, I should come out ahead even if I have no edge and trade randomly. The only question is the distribution of the positive sum among us. That is probably why I can make a living trading. Thank you for your coaching.