No, I am not concerned with a couple of pennies, or a few dollars. My original concern was more with the effect of changes in volatility, since the amount of money committed to the long ITM call is different than the amount of money commited to the put in the married put senario. In the table posted above (for GRMN), the resultant large swing in volatility I tested impacts the value of the call position more significantly than the married put position if the option goes near the money or slightly out, and the difference is greater the farther away from expiration the option is, as your proofs point out. This is important because things do not stay constant, and in developing a plan B an investor may want to see the severity of these moves. With respect to another position where there are equivalents, the risk reward of a collar may be 1:1 and for some investors that is acceptible. An eqivalent put spread the R:R may be higher say 3:1 or 4:1 at max loss. To some investors, that attribute may make the put spread unattractive as a bear market hedge, and that may be a dealbreaker. However, if an investor buys a call spread, the max loss has lessened considerably and the investor has an equivalent. So, perhaps in terms of equivalents, one equivalent position is more equal than another. Thanks for helping me thru this Tom
I'm not sure I understand your conclusions. Change in volatility isn't going to significantly change the amount of money committed to either side at inception. Whatever the put goes up, the call goes up and vice versa . It will change the premium relationships and therefore the degree of profitability (or loss) prior to but not at expiration. Change in time has a different carry cost and will alter the relative put to call prices but still evens out when all components are factored in. A collar with a 1:1 R/R would not be equivalent to a collar with a 3:1 or 4:1 R/R. Can't happen. And the put spread and call spread are equivalent when fairly priced so I don't see the advantage that you perceive in terms of hedging. In fact, they're poor hedges, in and of themself.
I now understand the volatility part of this. My original calculations failed to include the net premium earned on the put spread, and i was thinking out of the money spread, and that is the mistake I made. The equivalents I used SPY collar, spy @107.13, sell Dec 112 call, buy Dec 102 put VS. Buy Dec 102 call VS. Sell Dec 112 buy Dec 102 put spread Max profit 419, 440, 466 Max loss 580, 660, 532 R/R 1:1 give or take Investment: $10,7ish, $660, margin requirement on put spread $544 I hope these numbers make more sense, and I am sorry to have rattled off at the keyboard.
I'll take your word for it since I'm not tracking the numbers. The important thing is that you have sorted out the differences and have had a light bulb moment