Geoff: I simply don't understand where you are coming up with such rates of return.
I made the following assumption: the price of the stock will be equal or higher than the strike price at the time of expiration. I also used a cash basis for calculating the return. I explicitly assumed that the price of the stock would equal to the strike price at expirey. In other words, I assumed only one outcome, not the entire game.
Given these assumptions, if one were to calculate the rate of return on selling an option expiring in 90 days with a strike price of $50 against a stock currently selling at $50 (a paired transaction):
Cost of the stock = $50. Proceeds from the sale of the option = $3.25. Net out of pocket = $46.75. If the stock is at $50 or better at the end of the 90 day period then the value of the total investment will be $50, which provides a gain of 6.952% for the quarter, or 30.84% annualized.
I agree with your summary of what the B/S model is intended to do. In fact, assuming that there are only two outcomes from the paired transaction cited above, and neglecting interest, you would say that there is a .5 probability that the stock would close at $50, and there is a .5 probability that the stock would close at $43.50.
It seems to me that the real question ought to revolve around the implied volatility. Obviously, the more volatile the stock the greater the chance that the stock will close at a price of less than $50, thus reducing the potential profit on the deal. So the "fairness" of the game really depends on how well implied volatility is estimated. Two points are of note here: first, as you yourself noted from a WSJ article, there seems to be large premia in options these days; and second, Apratim noted that the implied volatility of Dell this month seems to be down sharply from where it was recently. Both of you argued taking an options position on the data you cited. Each of you pointed to what you thought was aberrant pricing -- a departure from EMH.
Based on my very limited examination of stock options, it appears to me (using the CBOE calculator) that implied volatility increases in shorter duration options -- that is, implied volatility seems to increase as the time to expirey decreases.
TTFN,
CTC |
