Q:
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?
A:
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!

Have a Financial Question?

RELATED FAQS

  1. What's the smallest number of shares I can buy?

    Unlike mutual funds, which can be purchased in fractional units, shares of stock cannot be divided. So, the smallest number ...
  2. 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 ...
  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 ...
  4. How do I set a strike price in an options spread?

    Find out more about option spread strategies, and how to set the strike prices for bull call spreads and bull put spreads ...
  5. 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 ...
  6. What is spread hedging?

    Learn about one of the most common risk-management strategies options traders use, called spread hedging, to limit exposure ...
RELATED TERMS
  1. Put

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

    The price at which the underlying security can be purchased (call ...
  3. Aggregate Exercise Price

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

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

    A type of option which is always settled in cash. Upon exercise, ...
  6. Call Over

    When the buyer of a call option exercises the option. In options ...
Hot Definitions
  1. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  2. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  3. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
  4. Job Market

    A market in which employers search for employees and employees search for jobs. The job market is not a physical place as ...
  5. Yuppie

    Yuppie is a slang term denoting the market segment of young urban professionals. A yuppie is often characterized by youth, ...
  6. SEC Form 13F

    A filing with the Securities and Exchange Commission (SEC), also known as the Information Required of Institutional Investment ...
Trading Center