# How do I calculate the return on my stock _call_ option, similar to my _put_ example?

I'm trying to figure out the effective percentage return when I write ("sell to open") a stock call option.

I think I've figured it out for put options.

# Consider this put example

• I think XYZ stock will stay above \$40/share,
• It's 25 days until the the third Saturday (an options oddity),
• I want to earn 20% effective return on my money, and
• It's an IRA--the money is tied up while the put is active.

So what what premium should I sell the put contract for? I calculate that one this way:

``````  capital = \$40 strike price * 100 shares/contract = \$4000
premium = (capital * rate * fraction_of_year + fee) / shares
= (4000    * 0.20 * 25/365           + 8)   / 100
= \$0.63
``````

# But my question is about call options

What value do I use for the "capital"?

I'm tempted to do the math exactly the same, but to use the current value of the underlying stock instead of the strike price.

But, you see, the money isn't sitting as cash in my brokerage account, as in the "put" case. I already own the underlying stock, so it's invested. If it's value rises above the strike price, I'll have to sell it. But if not, I'll have done no worse than I would have done without selling a call.

This might be an esoteric point, but I want to accurately calculate the return so I know what premium to charge for accurate comparison with the other ways I might choose to invest.

You are missing a few variables from your calculation, particularly implied volatility. Even so it does not look like it would be too great a predictor even if incorporated. You should focus on calculating the option price at a different point in time (with a different underlying price) instead of using a total position value as that can be done afterwards.

I programmed and use the standard Black-Scholes model to calculate expected returns.

There are many tools online to help you without doing the programming or calculations yourself.

• Totally agree with BAR. Your formula needs a few variables, and one of the most important is implied vol. – Escachator Nov 24 '14 at 9:32

The other answer that you received has to do with expected return which is different from what you are asking which is what put premium must you receive in order to generate a 20% annual return when selling a cash secured put that expires in 25 days, with the assumption that the put expires worthless.

Your answer is close but not quite correct because the cash secured amount is the strike price less the premium received which is lower than \$4,000.

The equation would be (P - 8) / (4000 - P + 8) = (.20) * 25 / 365 and the premium required would be \$62.05

Since you're long gone, I'll stop there.