Lets assume the stock market is Random. In that scenario, shouldn't the below strategy make you the "house" and over time be profitable? With DIA trading at 177.94 (Friday's close) you could put on a strategy with the following characteristics at Jan 30 expiration: Unchanged: You make money, breakeven point moves down to 177.26 At + or - 1 pt change your risk/reward is 1 to 5 (i.e if DIA moved up 1 pt to 178.94 you would make 5 times as much as an equidistant move down 1 pt to 176.94 would lose) At + or - 2 pt change your risk/reward is 1 to 2 at + or - 3 pt change your risk/reward is 1 to 1.2 at + or - 4 pt change your risk/reward is 1 to 1.13 at + or - 5 pt change your risk/reward is 1 to 1.1 This trend continues where your reward is always greater than your risk for any given point change. The ratio continues to shrink but always remains where reward is greater than risk for any size move. Thoughts?
Let me answer this in different way by asking another question, can you construct a "reverse" position with the reward/risk > 0 as below? e.g. you make money when the market is unchanged or move down, break even when the market move to 178.62 and loss money when the market move beyond 178.62 and maintain the following risk/reward: At + or - 1 pt change your risk/reward is 1 to 5 (i.e if DIA moved down 1 pt to 176.94 you would make 5 times as much as an equidistant move up 1 pt to 178.94 would lose) At + or - 2 pt change your risk/reward is 1 to 2 at + or - 3 pt change your risk/reward is 1 to 1.2 at + or - 4 pt change your risk/reward is 1 to 1.13 at + or - 5 pt change your risk/reward is 1 to 1.1 Also, do you ever take the commission and slippage into your account ? Can you really get this price in real (not those "mid" price showed in your broker simulator) ? What happen when the greeks (vega and etc) change ?
You have to apply probabilities to each of those moves and add it all up. The dangerous thing is: How reliable are the probabilities? That's model risk. It's blown up a lot of banks. Just put on the trade and cross your fingers.
Creating the reverse position is much harder due to puts being more expensive. I can create a position that makes a "small" amount when unchanged and moves the breakeven up a little. However,the risk reward differential is much smaller more like 1 to 1.05..