** OT **
Would you not agree that in this special case - given the EMH assumption, that long term is better?
Okay, I've thought about it and I don't agree. Given the EMH (strong form) the positions ought to be equivalent. But I still think that the short-term is superior judging from the numbers generated from the Black Scholes model.
The following numbers come from the CBOE. The theoretical price of a $50 call at the money, with 30% implied volatility and a 4% interest rate (no dividends): 90 days ($3.25), 60 days ($2.625), 30 days ($1.8125) and 15 days ($1.25). Now, assuming that a covered call is written, and that the position is liquidated at the strike price on the day of expirey, we have the following annualized rates of return:
30.84%, 38.21%, 55.75%, and 83.61% respectively. The rates of return were calculated as:
(1+premium/($50 - premium))^n-1;
where n is the number of periods in the year. I assumed a 360 day year for these calculations.
In fact, the more I think about it, the more confused I get. For example, the Black-Scholes model is supposed to result in a fair price for options. But one of the terms, implied volatility, is really a plug factor. If you know the other parameters you can calculate the implied volatility. But there is no way to estimate this parameter directly. The best you can do is to key off of historic implied volatility.
I guess what we really need to do is to look at some actual data and track them.
TTFN,
CTC |
