Solution of Derivative

1 800 flowerscom inc 1 800 attorney inc 1st

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Unformatted text preview: nal Limited 1-800 Contacts, Inc. 1-800 FLOWERS.COM, Inc. 1-800-ATTORNEY, Inc. 1st Constitution Bancorp (NJ) Intel Corporation Juniper Networks, Inc. Yahoo! Inc. Incorporated security symbol OIIM current shares short 2846753 prev. month change in shares % change in average daily shares short short shares short volume 713442 2133311 299 797977 CTAC FLWS 3047592 466209 2571988 532703 475604 -66494 18 -12 190341 57857 ATTY 733 576 157 27 8646 FCCY 132 0 132 0 1099 INTC JNPR YHOO PCLN 74613777 25482068 27236052 3748882 80023642 29421056 27338277 4417898 -5409865 -3938988 -102225 -669016 -7 -13 0 -15 42550432 18507315 9687090 1842726 In general, stocks that lend themselves to some speculation and stocks around corporate events (mergers and acquisition, dividend dates, etc.) with uncertain outcome will have a particular high short interest. It is theoretically possible to have short interest of more than 100%, because some market participants (e.g., market makers) have the ability to short sell a stock without having a locate, i.e., having someone who actually owns the stock and has agreed to lend it. 3 Question 1.12. We are interested in borrowing the asset “money” to buy a house. Therefore, we go to an owner of the asset, called Bank. The Bank provides the dollar amount, say $250,000, in digital form in our mortgage account. As $250,000 is a large amount of money, the bank is subject to substantial credit risk (e.g., we may loose our job) and demands a collateral. Although the money itself is not subject to large variations in price (besides inflation risk, it is difficult to imagine a reason for money to vary in value), the Bank knows that we want to buy a house, and real estate prices vary substantially. Therefore, the Bank wants more collateral than the $250,000 they are lending. In fact, as the Bank is only lending up to 80% of the value of the house, we could get a mortgage of $250,000 for a house that is worth $250,000 ÷ 0.8 = $312,500 . We see that the bank factored in a haircut of $312,500 − $250,000 = $62,500 to protect itself from credit risk and adverse fluctuations in property prices. We buy back the asset money over a long horizon of time by reducing our mortgage through annuity payments. 4 Chapter 2 An Introduction to Forwards and Options Question 2.2. Since we sold the stock initially, our payoff at expiration from being short the stock is negative. In order to obtain the profit diagram at expiration, we have to lend out the money we received from the short sale of the stock. We do so by buying a bond for $50. After one year we receive from the investment in the bond: $50 × (1 + 0.1) = $55 . The second figure shows the graph of the sold stock, of the money we receive from the investment in the bond, and of the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. 5 Part 1 Insurance, Hedging, and Simple Strategies Question 2.4. a) The payoff to a long forward at expiration is equal to: Payoff to long forward = Spot price at expiration – forward price Therefore, we can construct the following table: Price of asset in 6 months 40 45 50 55 60 b) agreed forward price 50 50 50 50 50 payoff to the long forward -10 -5 0 5 10 The payoff to a purchased call option at expiration is: Payoff to call option = max[0, spot price at expiration – strike price] 6 Chapter 2 An Introduction to Forwards and Options The strike is given: It is $50. Therefore, we can construct the following table: Price of asset in 6 months 40 45 50 55 60 strike price 50 50 50 50 50 payoff to the call option 0 0 0 5 10 c) If we compare the two contracts, we immediately see that the call option has a protection for adverse movements in the price of the asset: If the spot price is below $50, the buyer of the call option can walk away, and need not incur a loss. The buyer of the long forward incurs a loss, while he has the same payoff as the buyer of the call option if the spot price is above $50. Therefore, the call option should be more expensive. It is this attractive option to walk away that we have to pay for. Question 2.6. We need to solve the following equation to determine the effective annual interest rate: $91 × (1 + r ) = $100 . We obtain r = 0.0989 , which means that the effective annual interest rate is approximately 9.9 % Remember that when we drew profit diagrams for the forward or call option, we drew the payoff on the vertical axis, and the index price at the expiration of the contract on the horizontal axis. In this case, the particularity is that the default-free zero-coupon bond will pay exactly $100, no matter what the stock price is. Therefore, the payoff diagram is just a horizontal line, intersecting the y-axis at $100. The textbook provides the answer to the question concerning the profit diagram in the section “Zero-Coupon Bonds in Payoff and Profit Diagrams”. When we were calculating profits, we saw that we had to find the future value of the initial in...
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