## Introduction

The arithmetic of options opportunities and risk

Put and call options are traded on a wide range of futures contracts encompassing agricultural commodities, financial instruments such as U.S. Treasury securities, foreign currencies, metals, petroleum products, and stock indices. For the individual who has a price opinion (that a particular futures price will change by at least some given amount in a certain direction within a specific period of time), buying options offers the opportunity to realize substantial profits with a predefined, limited risk. The maximum an option buyers can lose-should events prove him wrong about the direction, extent or timing of the price change-is the premium paid for the option plus commissions and other transaction costs. The fact that the option buyer’s potential loss is limited does not necessarily mean a loss is unlikely. Buying options is a speculative investment and many options expire without becoming profitable. In this case the holder of an option would lose his entire investment including transaction costs.

The first step: Calculate the Break-Even Price

Before purchasing any option, it's essential to precisely determine what the underlying futures price must be for the particular option to break even or become profitable if it is exercised. Without this information, there is no way you can make an intelligent decision about whether to buy the option.

The calculation isn't difficult, there are only three things you need to know to figure a given option's break-even point: (1) the options strike price, (2) the premium cost, and (3) the commission and other transaction costs you will be charged if you buy the option.

Determining the Break Even Price for a Call Option

Ex. It's now January and the 1,000 barrel April crude oil futures contract is currently at around \$17.50 a barrel. You expect that over the next several months there may be a significant price increase. That is, you believe that April crude oil futures prices will rise significantly above its present level. To profit from this information, you are considering buying a call option with a strike the price of, say, \$18 a barrel. Assume that the premium for that option is 90 cents a barrel (a total cost of \$900 for the 1,000 barrel option) and that the commission and other transaction cost will be \$100, which amounts to 10 cents a barrel. Before investing, you need to know exactly how far the April crude oil futures price must increase prior to the expiration of the option in order for the option to break even or yield a net profit after expenses. The answer is that the futures price must increase to \$19 a barrel for you to break even and to above \$19 for you to realize any profit. The option will exactly break even if the April crude oil futures price when the option is exercised is \$19 a barrel. For each \$1 a barrel the price is above \$19, the option will yield a profit of \$1,000. At the price below \$19, there will be a loss. But in no case can the loss exceed the \$1,000 total of the premium, commission, and transaction costs. (*No representation is being made that the \$100 commission charge used in this example necessarily typifies commission charges in the industry. Commission charges can vary dramatically from one firm to another.)

Determining the break-even Price for a Put Option

The arithmetic is the same as for a call except that instead of adding the premium and transaction costs to the option strike price, you subtract them. Ex. The price of gold is currently just above \$370 an ounce, but during the next few months, you expect a sharp decline. To profit from a price decrease (if it occurs) you are considering the purchase of a put option with a strike price of \$370 an ounce. The option would give you the right to sell a specified 100-ounce gold futures contract at \$370 an ounce price at any time prior to the expiration of the option. Assume the premium for this particular option is \$11.40 an ounce (a total of \$1,140) and that the commission and transaction costs are \$50 (equal to 50 cents an ounce). For the option to break even or yield a profit when exercised, the futures price must be \$358.10 or lower, determined as follows: The option will exactly break even if the futures price is \$358.10 when the option is exercised. For each \$1 an ounce the futures price is below \$358.10, there will be a profit. However in no case can the loss exceed (unexercised) \$1,190-the sum of the premium (\$1,140) plus the commission and other transaction costs (\$50).

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