Call Options ... which to buy ??

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
>Is that useful?
Funny you should ask. I checked around on some discussion forums and the concensus was that it's meaningless or maybe pointless or maybe misleading or maybe ...
>Yeah, yeah, I get the idea.

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

where we've used the Black-Scholes premium and
K = strike price     S = stock price     T = days to expiry     V = volatility     Rf = risk-free rate
>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 ...

>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.

>Haven't you done this before?
Uh ... can't remember.
Wait'll I check:
site search by: FreeFind
>Okay, what if you sell before expiry. What if you buy a 6 month option now and sell after 3 months? What if ...?
Okay, let's consider that:

click for part II