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 6055 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 4540, 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!
MORE FAQS

After exercising a put option, can I still hold my option contract in order to sell it at a lower price?

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

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

How is a put option exercised?

What is spread hedging?

How do I change my strike price once the trade has been placed already?

How do I set a strike price in an options spread?

How do traders combine a short put with other positions to hedge?

How can I profit with call options?

What is index option trading and how does it work?

Why should investors consider the fully diluted share amount?

An investor has bought 25 call options on oil. The exercise price of the call is $29.45 ...

How risky is a covered call?

When is a call option considered to be "in the money"?

I've noticed executives buy a lot of stock below market value, and then they sell it for a large gain. How can they do this?

How many attempts at each CFA exam is a candidate permitted?

Do financial advisors need to pass the Series 7 exam?

Do financial advisors need to be approved by FINRA?

How does a broker decide which customers are eligible to open a margin account?

Why is the Nasdaq more heavily weighted to tech stocks than other stock exchanges?
RELATED FAQS

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 ... 
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 ... 
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 ... 
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 ... 
What is spread hedging?
Learn about one of the most common riskmanagement strategies options traders use, called spread hedging, to limit exposure ... 
How do I change my strike price once the trade has been placed already?
Learn how the strike prices for call and put options work, and understand how different types of options can be exercised ...

Put
An option contract giving the owner the right, but not the obligation, ... 
Exercise Price
The price at which the underlying security can be purchased (call ... 
Aggregate Exercise Price
The strike price of a put or call option multiplied by its contract ... 
Early Exercise
The exercise of an option prior to its expiration date. Early ... 
Risk Graph
A twodimensional graphical representation that displays the ... 
Call Over
When the buyer of a call option exercises the option. In options ...