MGMT_41150_Homework1_1_18_2024_no_answers (4)

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Apr 3, 2024

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Homework#1 - 150 Points Total *Due in class on February 20 th . Please type as much as possible of your answers using your computer, to aid grading. Whenever needed (e.g., if you need to write equations), feel free to do so by hand. Bear in mind that if these equations are difficult to read, I may not understand what you wrote. **You may work in groups of up to 4 people . Make sure each one of you is listed at the top of the page (with their full names, and email address clearly legible). Make sure you only submit once per team. To keep things simple I am going to ask that if you plan on working with others, you choose from colleagues in your same section. Note: Working in group is not a requirement, and I do not grade homework from individuals differently from homework submitted by groups. ***Please print this HW one-sided and write in the space provided (I will try to leave plenty of space, but use an additional page if you need to). ****Please show all work for full credit!
Q1 (15 points) A trader buys a European call option and sells a European put option. The options have the same underlying asset (a stock of Apple), strike price ($230), and maturity (June 2024). 1a) Describe the trader’s position in a graph that shows on the x-axis the price of the Stock at expiration, and on the y-axis the overall payoff of the strategy ? Hint: start by drawing the payoffs from the long and the short position separately, then combine them. You do not need to provide the separate graphs, this is just suggested for you to get started.
1b) What other derivative contracts offer the same payoff from the overall strategy ? Hint: Think of the payoff from other derivatives we have seen in class. 1c) Based on your answer to 1b), under what circumstances does the price of the call equal the price of the put? Hint: Think of how you could setup an arbitrage strategy between the strategy in 1a) and the strategy in 1b).
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Q2 (25 points) One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2021 a company sells a March 2023 orange juice futures contract for 120 cents per pound. At the end of December 2021 the futures price is 140 cents; at the end of December 2022 the futures price is 110 cents; and in February 2023 it is closed out at 125 cents. The company has a December 31 year end. What is the company's overall profit or loss on the contract?
Q3 (15 points) In an influential paper in 1974, Bob Merton describes: equity in a firm as a call option on the value of the firm (henceforth A) with strike price equal to the outstanding debt the firm has (henceforth D). Debt in the same firm as the combination of a long position in the assets of the firm (A) and a short put option with strike D. 3a) Draw a graph of the payoff from equity according to Merton. Hint: the graph has on the x- axis the value of the firm . Hint: the graph has on the x-axis the value of the firm .
3b) Draw a second graph of the payoff from debt according to Merton. 3c) Explain why, in the event the company takes on more debt, the value of equity becomes lower reduced. Hint: Think of how the graph in 1d) changes as you change “D”.
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Q4 (20 points) You have a $9,000,000 portfolio that has a beta of 1.5 to the S&P 500. You have decided you want to hedge this portfolio over the next 12 months. The 13-month S&P 500 futures price is $4100, and the current S&P 500 index value is $4000. The 12-month continuously compounded risk-free rate is 5% and the annual dividend yield on the S&P 500 is 2%. As a reminder, futures contracts are based on $250 multiplied by the index value. 4a) What position in futures contracts will you need to hedge your portfolio?
4b) Now check to see if your answer to part a) hedges your position effectively or not. Find the value of your portfolio in one year (including the futures position) if the S&P drops to $1900, if it drops to $3900, and if it increases to $5800. For these three scenarios, assume that one year from today, the S&P 1-month futures price will be $1909, $3911, and $5815, respectively.
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Q5 (20 points) You look up a 15-month bond forward contract and find the following: the current price of the bond is $1150, and the forward price is $1090. It will pay a coupon of $45 in 4 months and 10 months. The annualized, continuously compounded risk free rate is 4% for 4 months, 5% for 10 months, and 6% for 15 months. Find an arbitrage trade, and show the profit from your trade. Hint: You can follow the table/like representation I used to discuss this in the slides of Chapter 5
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Q6 (15 points) You just took a long position in 5 futures contracts for crude oil, at day 1 settlement price of $52 per barrel. Each contract is for 1,000 barrels. The initial margin is $11,000 per contract, and the maintenance margin is $7,000 per contract. The settlement price on days 2 through 8 are: $51, $38, $41, $44, $46, $43, $50. You then decide the close the trade on day 9, at a price of $55. Make a table similar to the one on page 30 in the textbook (also see the example on margin account in the lecture slides for Chapter 2 showing your margin account).
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Q7 (20 points) You are working on a currency arbitrage desk. You look up exchange rates and interest rates for the USD versus the Canadian Dollar (CAD) and find the following: The current spot rate is 0.769 USD/CAD. The 10-month forward exchange rate is 0.713 USD/CAD (note: Canadian dollar futures contracts are 100,000 CAD each). The 10-month T- bill yield in the USA is 2.54% (assume this is continuously compounded and annualized) and the 10-month risk-free rate in Canada is 1.94% (also continuously compounded and annualized). What is the arbitrage trade, and what is your profit per futures contract? (Blank page – extra space for question 1 answer)
Q8 (20 points) You have a short position on a Treasury bond futures contract. The most recent settlement price is 101-06. The bond you have chosen to deliver is a 9% coupon bond with 19 years, 5 months and 12 days left until maturity, with accrued interest of $0.47. What will you receive at delivery? (Reminder: Treasury bond futures contract size is $100,000)
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