FIN550 Week 8 Homework

Hello all,

I have been getting some good questions about the homework in Chapter 20. As some of you have already determined, the homework is probably the most difficult that you have seen this term. As such, I am going to try to help you out some.

Looking at problem 3, a key aspect to this problem is that the investor owns the stock that is valued at $50.00. All this investor is attempting to do is protect the value of this investment in case the price declines. You are to determine what the payout would be to the investor, given the different types of options that the investor may enter into.

The first option is a ‘short position in a forward option’. A short position means the investor is entering a contract to sell what she owes at some future price. In this case, the future price is $50.00. Because she already owns the stock, and has agreed to sell the stock for $50.00, no matter what the stock price does, she is obligated to sell it for $50.00. You have to develop a payoff matrix to determine what the net payoff would be to the seller, given changes in the stock price. I am inserting this payoff matrix here:

The far left column are the projected values of the stock that are given as a part of the problem. These values will remain constant throughout this problem. Column two represents the payoff at the time of expiration, should the stock reach the level as indicated in the far left column. For instance, on the first row, if the stock drops to $25.00, the investor still sells the stock for $50.00, because that is the contract price. You can also think of this as the investor selling the stock for $25.00 and having a gain on the contract of $25.00. The same principle applies for each row and looking at the last row as an example, if the stock price goes to $75, the investor can sell the stock for $75, but loses $25.00 on the contract. In the short sell, there is no premium, as such, the combined terminal position will be the far right column.

The second option is a long position in a put option with an exercise price of $50.00 and a front end premium expense of $3.23. First, some definitions are required. A ‘long position’ means you are buying an option. A ‘put option’ is the option to sell the stock. If you enter into a ‘long put’, you have bought the right to sell (but not the obligation to sell) at the exercise price, which of course is $50.00. For this right, you have paid a premium of $3.23. If the stock drops in price, no matter what it drops to, your payoff will be $46.77. Looking at the payoff matrix below, you can see that if the price of the stock is $25.00 at the time of the sale of the stock, the investor sells the stock for $50.00, regardless. Effectively, the investor sells the stock for $25.00, but makes $25.00 on the contract, and then deducts the premium of $3.23. If the stock price increases to $75.00, then the investor does not exercise their right to sell at $50.00. They don’t have the obligation, so why sell it at $50.00. They sell it at the market price of $75.00 and their profit is the $75.00 minus the cost of the premium in the amount of $3.23. Please see the matrix.

The third option is a short position in a call option with an exercise price of $50.00 and a front end premium receipt of $5.20. Again, some definitions are needed. A ‘short’ position is the selling side of the options contract. If you are entering into a short option, you are obligating yourself to fulfill your part of the contract. A ‘call’ option is the option to buy the stock at a certain price. What our investor has done with this position is to sell to another investor the right to buy this stock at $50.00, and this is an obligation of our investor. Sounds kind of backwards, doesn’t it? In the payoff matrix seen below, if the stock drops to $25.00, the counter party (buyer of the call) will not exercise their right to buy, and the option will expire. Our investor is then stuck selling the stock for $25.00, but they did get a premium of $5.20. Looking at the other end of the matrix, if the stock goes up to $75.00 per share, then the counter party investor exercises their right to buy the stock at $50.00, and our investor is obligated to sell the stock at $50.00, therefore losing the opportunity to gain $25.00 per share. So the net to our investor will be the $50.00 per share, plus the premium paid to her in the amount of $5.20. Please see the matrix below.

This gets you started on the homework. You will have to complete several payoff matrices throughout this chapter’s homework assignment, however, they will be similar to the ones above. The key to completing the assignment is to follow the money trail. Who is selling what? Who is buying what, etc. Understand who the players are, and what their payout will be when the transaction expires.

Hope this helps.

Dr. Bliss

Expiration Date

Sophia Stock Price

(S)

Expiration Date

Derivative Payoff

Initial Derivative

Premium

Combined

Terminal Position

$25$250$50

$30$200$50

$35$150$50

$40$100$50

$45$50$50

$50$00$50

$55($5)0$50

$60($10)0$50

$65($15)0$50

$70($20)0$50

$75($25)0$50

Expiration Date

Sophia Stock Price

(S)

Expiration Date

Derivative Payoff

Initial Derivative

Premium

Combined

Terminal Position

$2525.00$ ($3.23)$46.77

$3020.00$ ($3.23)$46.77

$3515.00$ ($3.23)$46.77

$4010.00$ ($3.23)$46.77

$455.00$ ($3.23)$46.77

$50-$ ($3.23)$46.77

$55-$ ($3.23)$51.77

$60-$ ($3.23)$56.77

$65-$ ($3.23)$61.77

$70-$ ($3.23)$66.77

$75-$ ($3.23)$71.77

Expiration Date

Sophia Stock Price

(S)

Expiration Date

Derivative Payoff

Initial Derivative

Premium

Combined

Terminal Position

$25-$ 5.20$ $30.20

$30-$ 5.20$ $35.20

$35-$ 5.20$ $40.20

$40-$ 5.20$ $45.20

$45-$ 5.20$ $50.20

$50-$ 5.20$ $55.20

$55(5.00)$ 5.20$ $55.20

$60(10.00)$ 5.20$ $55.20

$65(15.00)$ 5.20$ $55.20

$70(20.00)$ 5.20$ $55.20

$75(25.00)$ 5.20$ $55.20