Problem 4. Suppose you have a great decade-or a really great yearin the stock market. But, your fortunes are largely tied to a single stock, most likely the shares of the company you work for . Knowing about the risk of putting all your eggs in one basket, you want to hedge your bets and protect yourself against the bottom falling out. To be sure, the simplestand often the best--strategy for many investors is to sell some stock and use the proceeds to diversify. Not everyone can sell stock when they want to. Hedges are particularly popular among entrepreneurs and executives who have sold their companies in exchange for restricted stock that can't be unloaded for certain time. The hedging strategy-stock collar-has been popular. The creative hedging strategy cuts the risks of a concentrated stock portfolio. A big advantage of the strategy over the standard call and put options is that there can be little or no upfront cash outlay. It is impossible to precisely gauge the popularity of the hedge, but derivatives specialists suggest that hundreds, perhaps even a couple thousand, are executed each year. Wall Street firms regularly pitch the strategy to wealthy clients who want to sleep better at night. In early Feb 2000, it was reported that executives using such strategies included Ted Turner, founder of CNN and former chairman of Time Warner Inc. His hedge was estimated to cost more than $190 million. At the time, his shares of Time Warner were worth nearly S9 billion. A long position in a collar is the purchase of a put option and the sale of a call option. In addition, it has the following three special features. First , both options having the same underlying asset. Second, the two options expire on the same date. Third, the strike price of the call is higher than the strike price of the put. A collar written if the positions in the put and call are reversed. Suppose a 45-strike call on the share of DogCollar Inc. trades at $0.97 premium and a 40-strike put on the same underlying trades at $1.99 premium. Both options are European and expire in three months. Suppose the risk-free interest rate is 8%. (a) Construct a spreadsheet by filling the cells in the following table. In the table, the stock price, the payoff, and the profit are all on the expiration day of the options. In addition, create a graph that shows the payoff and profit of a long position in the collar. Based on the graph, what can you say about the payoff and profit of the collar? Assignment 2: page 3 maturity: 3/12 Collar Time Call 45.00 0.97 NA ?.?? +1.00 Payoff -1.00 Profit Interest rate: 8% Security Put Strike price 40.00 Security price 1.99 Position +1.00 Stock price Payoff 30.00 7.72 32.50 ?.?? 35.00 ?.?? 37.50 ?.?? 40.00 ?.?? 42.50 7.72 45.00 ?.?? 47.50 2.22 50.00 ?.?? 52.50 ?.?? 55.00 ?.?? Payoff 7.72 ?.?? ?.?? ?.?? 2.22 2.72 ?.?? 2.22 ?.?? 7.72 ?.?? ?.?? ?.?? 7.27 7.72 7.72 7.72 7.?? 2.22 7.72 ?.?? ?.?? 7.72 ?.?? 7.?? 7.?? 7.72 7.22 ?.?? ?.?? ?.?? (b) In practice collars are frequently used to implement insurance strategies by investors. For this, an investor buys a collar on the stock he owns. This type of position is often called a collared stock position. Suppose you own some shares of DogCollar Inc. for which the current price is $40 per share, and you wish to buy insurance. Naturally, you do this by purchasing put options. You can reduce the cost of the insurance by selling some of the appreciation-selling an out-of-the-money call. Create a table of the payoffs and profits for this set of transactionsbuy the stock, buy a 40-strike put, sell a 45-strike call. Then, plot the payoffs and profits in two separate figures. Based on the figures, what can you say about the payoff of the collared stock? (c) Which of the spread strategies that we have discussed in class has a profit function that resembles the profit of stock collar strategy? Can you combine the strategy in your answer with some cash to construct a trade that gives the same payoff as the collared stock? Using the trade you just constructed, can you figure out the premium of the three-month call option with $40 strike price on the same stock? (The premium should make the profit of your combination exactly same as the profit of the collared stock.)