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!
RELATED FAQS

The popular trading system "Instinet" is situated in which of the following markets ...
Free info on financial certification exams including study guides, exam questions, and much more! 
When a floor broker asks a specialist, “How’s PDQ?” ...
The correct answer is d) When the specialist gave the floor broker the quote of “59.20 to 35; 6 by 11,” the quote meant ... 
A person purchases stock XYZ (an Over The Counter stock) from a company who is also ...
The correct answer is c When the firm is a market maker in the stock then it must act as a principle. Principal is the main ... 
An individual made a lumpsum deposit into a variable annuity of $25,000 ...
The correct answer is c). Early withdrawal from a nonqualified annuityprior to age 59½, except for death or disability, ...
 No results found.