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:
=((K+S*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T/365)/(V*SQRT(T/365)))K*EXP(Rf*T/365)*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T/365)/(V*SQRT(T/365))V*SQRT(T/365)))/S)^(365/T)1
where we've used the BlackScholes premium and
K = strike price S = stock price T = days to expiry V = volatility Rf = riskfree 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 Riskfree rate R_{f} (like 4%) and the spreadsheet calculates the BlackScholes 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?
RIGHTclick here and Save Target to download a ZIPd spreadsheet.


>Haven't you done this before?
Uh ... can't remember.
Wait'll I check:


>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
