A:
A portfolio hedge is purchased in the form of a spread.
1) The call is an option on ABC Corp. with a \$3 premium and a \$55 exercise.
2) The put is an option on ABC Corp. with a \$1 premium and a \$45 exercise.
What is the value of the hedge with a 20% probability of ABC E(v) at \$40, a 60% E(v) at \$50 (current price), and a 20% E(v) at \$60?
First, calculate the net gains/losses under each probability.

At 50, the value is: cost of the spread (\$1 x 100 share put) + (\$3 x 100 share call). So 100 + 300 = \$400 cost (or -400) of the spread.
1) The \$50 per share level has no gain or loss with a cost of -400, so at \$50 per share the profit/loss is -\$400.

2) At \$60 per share, the put is worth zero since the price of the stock is more than the put's exercise price (45). The call is worth 60-55 or \$500 for 100 shares with a cost of -400, or a net of \$100, so at \$60 per share the profit/loss is \$100.

3) At \$40 per share, the call won't be exercised because the ABC stock price is under the exercise price of the call (\$55). The put is worth 45-40, or \$500 with a cost of -400, so at \$40 per share the profit/loss is \$100.

Finally, sum the probabilities:

.6 * -400 = -240
.2 * 100 = 20
.2 * 100 = 20

The value of the hedge turned out to be -\$200. What would it be if there were a 40% chance of stability (no gain or loss) and a 40% chance the put would be exercised at an actual of 30? Knowing how these sensitivities work, and the direction ups and downs take the end result, is key to quick responses on many of the CFA questions!

RELATED FAQS
1. ### After exercising a put option, can I still hold my option contract in order to sell ...

Once a put option contract has been exercised, that contract does not exist anymore. A put option grants you the right to ... Read Answer >>

3. ### How do you use put options to profit from a bear market?

Learn how traders use put options in their trading strategies to remain profitable, even in a bear market. Everyday investors ... Read Answer >>
4. ### How is a put option exercised?

A put option is a contract that gives the option holder the right, but not obligation, to sell a set amount of shares (1 ... Read Answer >>
5. ### What is index option trading and how does it work?

Learn about stock index options, including differences between single stock options and index options, and understand different ... Read Answer >>
Related Articles

### Understanding Bull Spread Option Strategies

Bull spread option strategies, such as a bull call spread strategy, are hedging strategies for traders to take a bullish view while reducing risk.
2. Taxes

### Tax Treatment For Call & Put Options

A brief intro to the complex US tax rules governing call and put options with examples of some common scenarios.

### What Is A Bull Put Spread?

Investopedia explains: A bull put spread is a variation of the popular put writing strategy, in which an options investor writes a put on a stock to collect premium income and perhaps buy the ...
4. Managing Wealth

### Explaining Underlying Assets

An underlying asset is the financial instrument from which a derivative's price is based.

### The Best Strategies to Manage Your Stock Options

We look at strategies to help manage taxes and the exercise of incentive and non-qualified stock options.

### How To Manage A Bull Call Spread

A bull call spread, also called a vertical spread, involves buying a call option at a specific strike price and simultaneously selling another call option at a higher strike price.

### Debit Spreads: A Portfolio Loss Protection Plan

There are ways to control risks, reduce losses and increase the likelihood of success in your portfolio. Find out how spreads can help.

### How To Sell Put Options To Benefit In Any Market

As long as the underlying stocks are of companies you are happy to own, put selling can be a lucrative strategy.

### Prices Plunging? Buy A Put!

Investors can make money on a falling stock by going long on a put.
RELATED TERMS
1. ### Put

An option contract giving the owner the right, but not the obligation, ...
2. ### Aggregate Exercise Price

The strike price of a put or call option multiplied by its contract ...
3. ### Early Exercise

The exercise of an option prior to its expiration date. Early ...
4. ### Cash-Based Option

A type of option which is always settled in cash. Upon exercise, ...
5. ### Call On A Call

A type of compound option in which the investor has the right ...
6. ### Fiduciary Call

A cost effective strategy designed to limit the costs associated ...
Hot Definitions
1. ### Five Cs Of Credit

A method used by lenders to determine the credit worthiness of potential borrowers. The system weighs five characteristics ...

An options strategy in which the investor holds a position in both a call and put with the same strike price and expiration ...
3. ### Trickle-Down Theory

An economic idea which states that decreasing marginal and capital gains tax rates - especially for corporations, investors ...
4. ### North American Free Trade Agreement - NAFTA

A regulation implemented on Jan. 1, 1994, that eventually eliminated tariffs to encourage economic activity between the United ...
5. ### Agency Theory

A supposition that explains the relationship between principals and agents in business. Agency theory is concerned with resolving ...
6. ### Treasury Bill - T-Bill

A short-term debt obligation backed by the U.S. government with a maturity of less than one year. T-bills are sold in denominations ...