Consider speculating in a stock that currently trades for 40

Consider speculating in a stock that currently trades for $40, which has a call option with a strike of $42.50 trading for $1. You consider investing $1,000. What return do you make when buying the stock or buying the option if the price moves up to $47.50 when the option matures? What if the price drops to $35?

Solution

Call is an option that gives right to the holder to buy the stock at a specific price (exercise price) and during specific time interval.

Payoff for a Call Option Buyer = Max(0, Stock Price - Stock Price) - Option Premium

You have $1000 with you to invest, stock price = $40, Option Price = $1.

So, number of stocks to purchase = $1000/$40 = 25

Number of options to purchase = $1000/$1 = 1000

Now let us take the first case, when stock price moves to $47.50 when option matures

If you purchased stock directly, the gain would have been = Number of stocks * (Final Price - Initial Price) = 25 * (47.50 - 40) = $187.5

Return % = 187.5/1000 * 100 = 18.75%

If call option was purchased, the payoff, based on the payoff formula above would have been:

Payoff = 1000 * [Max(0, 47.5 - 42.5) - Premium] = 1000 * [Max(0,5) - 1] = 1000 * [5 -1] = 4000

So, Return % = 4000/1000 * 100% = 400%

Now let us take the second case, when stock price drops to $35, when option matures

If you purchased stock directly, the gain would have been = Number of stocks * (Final Price - Initial Price) = 25 * (35 - 40) = - $125 (Loss of $125)

Return % = - 125/1000 * 100 = -12.5%

If call option was purchased, the payoff, based on the payoff formula above would have been:

Payoff = 1000 * [Max(0, 35 - 42.5) - Premium] = 1000 * [Max(0,-7.5) - 1] = 1000 * [0 -1] = -1000

So, Return % = -1000/1000 * 100% = -100% (But the loss here is capped to $1000)