Beta for Stock Options?

[terminator]

I'm just wondering if there is an easy way to find (or calculate) beta for stock options -- or to otherwise determine risk-adjusted returns. Last year at this time a friend & I opened a small account trading LEAPS. The market (DJIA) is up about 22% in that time and I am trying to determine whether our return (about 70%) was "good" or "bad" relative to that in light of the risk we took. I tried doing some searching online but couldn't find anything like that. Thanks.

 

[saluki9]

What you're looking for is called the option "delta" which is just a description of the options sensetivity to changes in the underlying asset which in this case is an index

 

[terminator]

Thanks, saluki that's helpful as now I know a little more where to look.

But isn't the delta non-linear based on where the stock price is relative to the strike price? I.e. If I buy an option when the price is $50, the strike is $60, the duration is 1.5 years and the volatility is .2 and the assumed interest rate is 5%, then the calculators tell me delta is about .4. Then delta keeps going higher as you get in the money, right since it's more of a direct correlation then?

I think what I am really trying to determine is what my return would have been if on May 21st last year I bought a call option on the DJIA which was trading at 11,125 with a strike price of 12,437 with an expiration of Dec-07. (Our average option purchase was 11.8% out of the money and had an expiration of Jan-08).

I see that DJIA options trade under DJX. So, a Dec-07 option (closest to Jan-08) with a 125 strike is worth 14.30/14.60 today. It appears that option (DJWLU) only trades sporadically. An option today that is similarly out of the money (current price $135 strike $151) with a similar duration (Dec-08) costs about $4.85. Is that a valid comparison data point? From the historical DJWLU data it seems like it.

If so, it would seem we woefully underperformed which was kind of my gut feeling about a 70% return on a 22% underlying increase.

I'm just trying to figure out if I'm thinking about this the right way, so any other input is welcome. Thanks.

 

[saluki9]

Thanks, saluki that's helpful as now I know a little more where to look.

But isn't the delta non-linear based on where the stock price is relative to the strike price? I.e. If I buy an option when the price is $50, the strike is $60, the duration is 1.5 years and the volatility is .2 and the assumed interest rate is 5%, then the calculators tell me delta is about .4. Then delta keeps going higher as you get in the money, right since it's more of a direct correlation then?

yes, and that is why another one of your "greeks" is Gamma which represents the change in delta as you get a change in the underlying price.