Question

An individual entire wealth is from one stock. The current value of the stock is $55, and the individual owns one million shares. This individual purchased puts on the stock with an exercise price of $52 to protect his wealth. He bought enough puts to protect his entire holdings of this stock. The expiration of the put is 4 years. Immediately after buying the puts he was appointed to a 4-year government position and was told that if want to stay in the government position his return over the next two years must exactly equal the risk-free rate. The risk-free rate is 10%. You have been asked to construct a spread that will provide the investor with a return over the next two years that exactly equals the return from the risk-free return on his stock holdings. You can only buy the minimum number of needed derivatives given the investors current holdings. A speculator is willing to sell or buy from you any option with any strike price with a two- year exercise.

Question:

Show the detailed payoffs from each derivative at all relevant stock price ranges.

Answer 1

solution:

pay off from PUT alternative, Max( T-S,0), therefore, in the form profit from a Long butterfly spread

• Max Profit = Higher Strike Long Put - Strike of Short Put - Net Premium Financed - Commissions Financed.

Max profit = 66 - 60- 0.5 = $ 5.5

which is equivalent to = $5.5/$55 = 10%.

The Max Profit gained at spot Price of asset = Strike Price of Put sold ($60)