Percentage Gains

When Option_Experts expound on options, they display charts like so:

Gains for a Bull Spread, as a dollar amount

The idea (when comparing "stock purchase" vs "options") is to buy either 100 shares of stock ... or option contracts (each covering 100 shares). The chart seems to indicate that your downside losses are limited when you do the option thing. That's misleading. When the chart shows a loss of some \$1100 (the red line), you've lost 100% of your investment! Is that limiting your downside risk?!

Instead, let's plot the same Gains (or, as some prefer, the "Profits & Losses") as a percentage of your initial investment. It'll look like so:

Gains for a Bull Spread, as a percentage

See? 100% loss! However, options provide a greater gain (percentage-wise) well into the \$70 range of stock prices (for this particular example). Indeed, let's consider just buying a Call option:

Gains for a Call contract, as a percentage

Now the Call option looks much like a highly leveraged stock purchase, no? Y'all can make MUCH more (as a percentage). For example, it is Sept 30, 2000 and AT&T is trading at \$29. We can buy a January call option, with strike = \$55, for about \$0.06 - because who expects AT&T stock to increase to \$55 in a few months! If, however, AT&T does manage to get to, say, \$60 by expiry in January, the option would be worth about \$5. We paid \$.06, so the gain is 5/.06 - 1 = 82 or 8200%. Mamma mia! (Of course, you can also lose much more, like 100% of your investment if the stock doesn't make it to \$55!)

The above chart is interesting. The Option is deep in the money (\$45 strike price with the stock trading at \$60). If we plot the Dollar Gains (as opposed to the Percentage Gains), it'll look like so:

Dollar Gains for a deep-in-the-money Call Option

See? The option gains follows the stock gains.
The stock goes up \$10 (dreamer!); the option goes up \$10 (very nearly).
Owning the Call is like owning the stock, right?

In fact, if we make a small change in the stock price and look at the corresponding (small) change in the option price ... and divide the latter by the former (that's the ratio {option change}/{stock change}), then this ratio has a name; it's called the delta of the option. For the above chart, the delta is (very nearly) equal to 1 ('cause the change in option price is very nearly equal to the change in stock price - the two lines lie one atop the other - so the ratio is very nearly 1).

 delta = Change_in_Option_Price/Change_in_Stock_Price

Well, let's qualify that statement - and others we've made(!). The charts we've been showing illustrate what happens at expiry of the option. It's natural to ask (so we DO ask):

1. What is the option price BEFORE expiry?
2. Does the market determine option prices by some kind of "supply and demand" mechanism?
3. For a deep-in-the-money Call, does it STILL track the stock price?

In 1973 (or thereabouts) a couple of guys generated a formula for the "fair" price of options (and won a Nobel Prize): the Black-Scholes formula.

That's next ... in Part six

One last thing:

Consider this:

Stare at the chart
It's August 28, 2000
We BUY an oct/70 Call and WRITE an oct/80 Call
The BUY costs us \$4.916 and the WRITE gives us \$.906
The stock is trading at \$70.00
To make any money on this Bull Spread the stock must attain a price of \$74, and since the Calls expire on Oct 21, 2000, there's just 55 days to go. That means that MSFT stock must increase at the rate of 36%/year. Fat Chance!

On the other hand, we have:

Here, any increase in stock price will make us money

Note, however, that the maximum loss of \$700 is 100% of your investment! If that's scary, remember, too, that the possible gains are much greater than owning the stock ... if the stock goes up!

Thanks to "Howard" for this example ... and there's more of this kind of calculation in part six.

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