# Expected Return of a Call Option

A call option is a financial contract that allows the holder to buy or sell an asset, if she so desires, at a predetermined price on a particular date. Options are one of the most volatile instruments: their values can fluctuate wildly, and can easily drop to zero. It is, therefore, critical to understand how to calculate the expected profit from an option.You can calculate the expected return on an option by finding the difference between the purchase price and the price point at which you plan on invoking the contract, and then multiply that difference by the number of options purchased.

#### TL;DR (Too Long; Didn't Read)

Calculating the expected return on a call option can be accomplished by first deterring the return for a single option and then multiplying this by the number of options purchased.

## Understanding Option Basics

An option is a financial contract that allows the holder to lock in a future price for a financial transaction. A call option gives the holder the right, but not the obligation, to buy a specific quantity of an asset at predetermined terms. A put option gives the holder the right, but once again, not the obligation, to sell a fixed quantity of an asset at a specific price and a particular date. The price at which the option holder can execute a trade is referred to as the strike price. The date on which the trade will take place, if the option holder wishes, is known as the expiration date.

## Examples of Call Options

Assume you buy a call option on 1,000 Citibank shares with a strike price of \$40 and expiration date of November 10. If you so desire, you can purchase 1,000 Citibank shares from the person who sold you the option on November 10, at \$40 per share. While you, the option holder, can elect to exercise this option or not to use this privilege, the option's seller — also referred to as the writer — must sell you the stock if you so desire. The option holder always pays the option seller to obtain the privilege of deciding whether to exercise the option.

## Profit/Loss on Call Options

A call option is worth something at the expiration date only if the asset's market price exceeds the strike price. Investors purchase call options if they are bullish on the underlying asset; in other words, if they think that the asset's price will advance. If, for example, Citibank stock is trading at \$39.50 on November 10, the holder will not exercise the option. After all, it's cheaper to ignore the option and purchase Citibank at prevailing prices in the stock market — for 50 cents less per share.

If, however, Citibank stock is trading at \$40.50 on November 10, the option is worth a hefty \$500. The option holder can buy Citibank stock at \$40 from the option's writer and sell each stock for a profit of 50 cents a piece, profiting \$500 on 1,000 shares.

## Evaluating Expected Return

The expected return on a call option equals: (expected price of the asset at the expiration date - the strike price) the quantity of the asset the option allows you to buy, minus the price you paid for the option. Assume you paid \$800 for the Citibank call option in our example, and the expected price of the stock on November 10 is \$42. The expected return equals (\$42-\$40)1,000 - \$800 = \$1,200. A simpler way to arrive at the same figure is that you will sell each stock at a \$2 profit, for a total gain of \$2,000. Since you paid \$800 for the option, your net profit equals \$1,200.