**Problem 1.**

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.

**Part 1.** Describe in detail the derivatives you would utilize to achieve the desired payoff.

**Part 2.** Draw the payoff graph for the spread.

**Part 3.** Show the detailed payoffs from each derivative at all relevant stock price ranges.

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