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To wit, why doesn't Delta Neutrality necessarily break even or lose money? I assume the semi-strong form of the EMH, defined in Zvi Bodie, Alex Kane, Alan J. Marcus. Investments (2018 11 edn). p 338.

      The semistrong-form hypothesis states that all publicly available information regarding the prospects of a firm must be reflected already in the stock price. Such information includes, in addition to past prices, fundamental data on the firm’s product line, quality of management, balance sheet composition, patents held, earnings forecasts, and accounting practices. Again, if investors have access to such information from publicly available sources, one would expect it to be reflected in stock prices.

p 733

When you establish a position in stocks and options that is hedged with respect to fluctuations in the price of the underlying asset, your portfolio is said to be delta neutral, meaning that the portfolio has no tendency to either increase or decrease in value when the stock price fluctuates.

p G-4

delta neutral     The value of the options portfolio is not affected by changes in the value of the underlying asset.

What Is Delta?

Delta Spread

Delta spread is an options trading strategy in which the trader initially establishes a delta neutral position by simultaneously buying and selling options in proportion to the neutral ratio (that is, the positive and negative deltas offset each other so that the overall delta of the assets in question totals zero). Using a delta spread, a trader usually expects to make a small profit if the underlying security does not change widely in price. However, larger gains or losses are possible if the stock moves significantly in either direction.

Presume that the stock price does not move significantly in either direction. Doesn't delta neutrality imply break-even (profit)? Then why can a trader usually expect to profit a whit? What about option premiums and transaction costs?

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    $\begingroup$ I didnt read your entire post, given the title of the post, you should read about long vega or a long gamma trade in options. $\endgroup$ – nimbus3000 Apr 18 at 7:13
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    $\begingroup$ The correct bounty-winning answer is given in the above comment. Zero Delta Short Gamma or Short Vega strategies make money a good percentage of the time, but they lose (sometimes heavily) when volatility goes up. So they are not an arbitrage or a violation of the EMH. $\endgroup$ – noob2 May 1 at 18:44
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So @Alex, I think answered your question, but I'll give a go as to further clarify.

First of all, there are the mechanics of trading a delta neutral portfolio. The assumptions of Black-Scholes are continuous hedging. This implies an obvious constant attention and in addition, access to fractional share (or contract) trading. And, of course, no inter- or intra-day jumps. All of which are faulty assumptions. All of which means that even if EMH holds, you can make or lose money on your "imperfect" hedging strategy.

Second, while the EMH may state that the market has all known info and incorporates that into price, there is information that is not known or is narrowly known (or may not be diffusing at a rapid enough pace among participants). So there are surprises, such as earnings, government actions, and, on occasions, pandemics (e.g., right now).

I think finally, be careful about presumptions. Yes, in theory it would be hard should the stock not move far in either direction to make money. But that in itself is a constraint on the distribution, both within an EMH framework and for the moves that are clearly outside of what EMH covers.

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The EMH does not state that it is impossible to ever make money out of the market.

We have good evidence to believe that markets are reasonably informationally efficient. However, that does not mean that when ever you trade in the market, you can't generate a profit. It merely asserts that you cannot systematically outperform the market. In fact, it is awfully difficult to make money by trading (stocks or options).

However, you can of course set up an options trading strategy and get it right and earn money. You simply cannot expect to consistently outperform the market.

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