The other day I was thinking of buying a Call Option and ...
>What! You always lose money on options!
Yes ... true, but I was thinking about which I would choose ... of a jillion choices I could make.

So here's my problem: I've identified the stock (example), but I can pick various T = Days to Expiry and various K = Strike Price. I look (for example) at Calls which expire in T = 126 days and see (for example) Figure 1. Should I pay a Premium of C = $9.30 for a Call with a Strike of K = $7.50 ... or maybe C = $3.00 for a Strike of K = $15.00 ... or maybe ... >Why 126 days ... to expiry? Well, I'll look at other Days to Expiry of course and get another table like Figure 1 and ... >So what's the best choice? That, my friend, is the problem

Figure 1

So here's what I think I'll do:

• For each choice of T = Days to Expiry and K = Strike Price I determine the annualized return necessary to make money on that particular option.
• Remember, I have the privilege of buying the stock at the Strike $K any time before Expiry, but it costs me the premium $C to buy that privilege.
• That means that, if there are T Days to Expiry and the stock is currently selling at $S then, in order to make money, the stock price has to increase to at least K + C and that's an increase of (K+S)/S in T days or an annualized return of [(K+C)/S]^(365/T) - 1.

>Your total cost is K + C? Well ... if we ignore the commission to buy the option (which is what we'll do since that depends upon the broker). From Figure 1 we'd need the stock to increase (for each choice of option) as in Figure 2. That'd give our Breakeven stock price. >So, what's the best? Okay, for each choice of K = Strike Price we've determined our Breakeven = K + C. Now we calculate (for each K), the annualized return required to achieve that Breakeven stock price ... that's [(K+C)/S](365/T) - 1.

Figure 2

In any case, in Excel, this percent would be:

>What's S again? The current stock price which, for this example, happens to be S = 15.00 so, for example, if I bought the 7.50 option I'd need the stock to increase at the annual rate of: [(K+C)/S](365/T) - 1 = [(7.50+9.30)/15](365/126) - 1         = [16.80/15](365/126) - 1         = 0.389 or 38.9% >Fat chance! Well, there are lots of choices and ... >I assume there's a spreadsheet? Yes. You stick in the current stock price S, a Volatility V (or Standard Deviation, annualized, like 30%) and some Risk-free rate Rf (like 4%) and the spreadsheet calculates the Black-Scholes Premum C for various values of T or various values of K and then computes the required annualized return in order that the stock price achieve breakeven in T days and ... >Examples? Yes >So what'll you buy? I think I'll pass ... >Because you don't know what you're doing, right? Well... uh ... >So, where's the spreadsheet? RIGHT-click here and Save Target to download a ZIPd spreadsheet.

click for part II