When I apply the literal definition of "two sigmas" I don't come up with a workable strategy at all. For the OEX, the ANNUAL sigma can be approximated by the current value of VIX (recall that VIX is the implied volatility of a selected group of OEX options. I.V. = SD = sigma). With the OEX at 553.15 and the VIX at 20.24, the market is pricing an annual SD (aka sigma) of 0.2024 into the near-the money options.
If we were considering this strategy using options with EXACTLY one year until expiration, then the "two sigma" points would be at 553.15+/-(2.00x0.2024x553.15) or at 553.15+/-223.92 = 777.07 for the call CS and 329.23 for the put CS. Obviously this is bogus since there probably aren't many June '99 puts and calls at these strikes that trade with any liquidity. For the purists out there: Yes, I'm ignoring the fact that for an index, the assumed distribution of index returns is *log* normal.
OK, so what if we only want to play the game with short-term options, ones with only a month until expiration. Then the way we find the two sigma points is as follows:
2SP = Current OEX +/- [2.00x0.2024xSQRT(30/365)]
So, for one-month options, the 2SP's are 553.15 +/- 64.19 or 617.34 for the call CS and 488.96 for the put CS. Again, it's doubtful you'd get much of a credit for writing this butterfly.
In fact, there aren't any July 620 calls. On the other hand, you could write the July 480/490 put credit spread for 1/8 net credit! Given a margin requirement of about $1,000 per contract, the idea of getting a $12.50 credit doesn't seem terribly exciting.
I have a hard time seeing how Schiller can call this a "two sigma" strategy since, as far as I can tell, it's not based on the index's sigma values at all!
Two other asides:
1) As I understand it, the Bollinger bands show the +/- 2 SD values for a stock or index.
2) The probability that a normally distributed random variable winds up between -2SD and +2SD is NOT 96%, that's the probability that it'd wind up *below* +2SD. "Below +2SD" could also mean -3SD, -4SD, -5SD, etc. The chances of winding up between -2SD and +2SD is actually about 92%.
3) If the index is in the depths of a correction, writing a call CS may not be the best idea since the market is so badly oversold. If you sell calls when the market is at the -2SD marker, a snap back to 0SD puts the call you just wrote right at the money! Under such circumstances, it's quite likely it *would* snap back. Similarly, selling puts when the market is surging to the upper end of its Bollinger Band is not a good strategy since, when it's so heavily overbought, it could easily fade back to the center of the band (right to the strike of your short put!)
Maybe he uses the term "two sigma" figuratively since he feels it works about 96% of the time?
Beats me! |
