To Chuz - re: returns on call options
I have several problems with your analysis. The first is your method of computing an investor's expected return from writing call options. You assumed - inexplicably - that the price of the underlying stock would finish no lower than the strike price at the option's expiry. Why on earth make such an unwarranted assumption??? Given that the price may well finish lower, failure to take that into account obviously produces biased and misleading figures on returns available from writing call options.
A preferable way to calculate an option's profitability is to compute its expected return. The return from writing an option can be viewed as a random variable with an underlying probability distribution. The expected value of this variable can be found by assigning probabilities to each potential outcome and then finding the weighted average of all outcomes.
A second difficulty I have is that, in computing returns on options, you assume the writer owns the stock. It is unnecessary to make this assumption, and it needlessly complicates the analysis. The expected return on the option will be the same whether the writer owns the stock or not. If the investor owns the stock, the return on it can be separated from the options return. Let me remind you of a theorem in statistics which says:
If we have two random variables X and Y, the expected value of the sum X+Y is equal to the sum of the respective expected values.
Therefore, suppose X is the return on the stock and Y is the return on the option. The sum X+Y, which is the return to a covered options writer, can be found by computing E(X)+E(Y). Because of this "separability," the problem can be analysed as if the writer were "naked," keeping the investor's stock ownership out of the picture. This won't affect the result yet it does simplify the analysis.
In the Black-Scholes model, the the market is assumed to be efficient. The expected rate of return for any stock, its my impression, is the stock's required rate of return, i.e., the risk free rate of return plus a risk premium. So, suppose you write call options on Dell, what is your expected return according to B/S? Let's assume the required rate of return on Dell shares is 20%. If you are writing covered calls, the expected return is:
E(X)+E(Y) = .20 + 0 = .20.
And if you are writing naked calls,
E(X)+E(Y) = 0+0 = 0.
The zero value of E(Y) assumes the market is a fair game for all participants. This will be the case if the EMH holds, ignoring transactions costs. It is the B/S model that attempts to give a formula for determining what the efficient prices are.
Chuz, hope you have a happy Thanksgiving!
Geoff
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