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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.
(Blank page - additional space for question 4b answer)
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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
(Blank page - additional space for question 5 answer)
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)
(Blank page – extra space for question 8 answer)
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- hre.7arrow_forwardName: Grade and Section: 6- PART II: A MATHEMATICS 6 4th QUARTER-PROBLEM SET 1 TOPIC: SOLID FIGURES Parent's Signature: Date: Score: Teacher: What Is Big, Gray, and Lives in California? Find the volume of each prism. Write the letter of the exercise in the box above the answer at the bottom of the page. 4.5 cm A 6 cm 5.8 cm 25 in. P T 10 m N 8m 6.4 cm 30 25 in. A 8 cm 30 in. 20 in. 30 in. 6.2 cm 20 in. 9.6 cm 12 cm N 7.5 mi 4.3 cm H DOA B = 52 m² B = 19.7 cm² 5 in. 6 in. 8.5 in. 83.8 cm³ 357.12 cm3 76.8 cm³ 8,800 in 3 92.31 cm3 84.71 cm³ 156.6 cm³ 114.5 in.3 364.5 m3 7,500 in.3 127.5 in.3 15,000 in.3 390 m³ 160 m³ 349.22 cm³ MATHEMATICS 6 | FOURTH QUARTER I PROBLEM SET 1 PREPARED BY: SIR Karrow_forwardPowerSchool Leaming : Portal : D A ANet Online 4DC a login.achievementnetwork.org/tutti/learn/assignments/viewAssignment.svc?ciid3FE954372A54D406885C1144055.. A1 Math Algebra II 20-21 Form MT Online Screen Settings 9 of 9 * Full Screen I Sa Main Street Bank has savings accounts that earn 0.8% interest per month. All deposits, interest payments, and account closures are processed on the first day of a month Part A Assume a customer deposits the same amount of money, x, in dollars, each month. Write an expression that can be used to determine how much money would be in a savings account from Main Street Bank after n months. Respond in the space provided. Part B Luciana and Valerie are both opening savings accounts at Main Street Bank and will close their savings accounts at the end of their savings strategy Luciana's savings strategy is to deposit $200 each month for 24 months. Valerie's savings strategy is to deposit $400 each month for 12 months. Whose savings strategy will result in…arrow_forward
- Assignment 6.1: Session 6 Comprehensive Problem (Chapter 8) Instructions In this session, we have a 6-part comprehensive problem. Download the Session 6 Comprehensive Problem Templates below to complete the 6 required parts of the problem. You will need your Bergevin and MacQueen book for reference. Rancho Cucamonga Inc. began business on January 1, 2020. The firm earned $100 from sales in its first year of business. Rancho Cucamonga collected $90 of revenue earned in cash during 2020 and reported a $10 account receivable on its 2020 balance sheet. The firm paid $70 cash for operating expenses in 2020 and reported a $5 account payable for unpaid operating expenses on its 2020 balance sheet. Income tax laws only recognize cash collected from sales and cash paid for expenses as taxable items in the year collected or paid. Rancho Cucamonga also reported a $10 fine, paid in cash, to the federal government for unfair business practices. Generally accepted accounting principles allow firms…arrow_forwardHistory Bookmarks Window Help Fri Feb 5 く> A mathxl.com Post- Chapter 2 Homework P Do Homework - Post- Chapter 2 Homework 201 Sec04 (Spring2021) Brionna Washington & omework: Post- Chapter 2 Homework Save re: 0 of 58 pts 15 of 15 (14 complete) v HW Score: 42%, 42 of 100 pts -61A (similar to) Question Help ▼ ring the first month of operations, Johnson Services, Ic., completed the following transactions: (Click the icon.to view the transaction data.) ead the requirements. More Info s. Exclude explanations from journal entries.) Lequirement 1. Record each transaction in the Mar 2: Johnson Services received $62,000 cash Mar 2 Johnson Services received $62,000 cash and issued common stock to the Journal stockholders. Accounts 3 Purchased supplies, $600, and equipment, $11,400 on account. Date 4 Performed services for a customer and received cash, $5,500. 7 Paid cash to acquire land, $38,000. Mar 11 Performed services for a customer and billed the customer, $4,300. Johnson expects to collect…arrow_forward= Homework: Homework 3 Using the simple interest formula, determine the number of days until $1256.00 will earn $22.14 interest at 8-% p.a. The number of days required is (Round up the final answer to the nearest day as needed. Round all intermediate values to six decimal places as needed.)arrow_forward
- Font Paragraph Styles Editing Dictate Editor Paste Undo Clipboard Styles Voice Editor a) Will credit cards help? The average undergraduate student leaves college with a diploma and around $2750 in credit card debt (graduate students; $4800). Suppose you have a credit card with a balance of $2750 and an interest rate of 19.8% APR. The minimum payment is $45.00. The amount of interest due each month is figured as current balance where r is the rate (decimal form) and n is 12. Fill in the table, making minimum payments. Current balance Month Interest Payment Amount applied to principal 1 $2750.00 $45.38 $45.00 -$0.38 $2750.38 $45.00 $45.00 4 $45.00 $45.00 $45.00 $45.00 8. $45.00 9. $45.00 10 $45.00 11 $45.00 12 $45.00 Page 4 of 6 1011 words DFocus 80% P Type here to search 立arrow_forwardConnect Problem 01-13 (algo) Next Friday, you plan to sell cakes at a bake sale to raise money for your school. You plan to charge $30 per cake, and you anticipate that you will sell 10 cakes. You can either purchase cakes to sell or bake them yourself. If you purchase the cakes, they will cost $23 each. If you bake your own cakes, your cost depends upon the number of cakes you bake, as shown in the table below. Number of cakes you bake Bake $ 0 1 2 3 4 5 6 7 8 9 10 a. How many cakes should you bake? How many cakes should you purchase? Instructions: Enter your answer as a whole number. cake(s) and purchase cake(s). b. Given your answer to part a, how much in total will the 10 cakes cost you? Instructions: Enter your answer as a whole number. Total cost of baked cakes ($) 0 10 22 36 52 70 90 112 136 162 190 c. How much would it have cost you to bake all 10 cakes?arrow_forwardP Do Homework - Homework 2 - Google Chrome A mylab.pearson.com/Student/PlayerHomework.aspx?homeworkld=617070625&questionld=12&flushed=true&cld=6813423¢erwin=yes BAB110 NII, W22 Question 12, 6.4a HW Score: ! = Homework: Homework 2 Part 1 of 2 O Points: Find the rate of markdown and the markdown. Regular Selling Price $31.20 Rate of Markdown Markdown Sale Price ? $18.70 The rate of markdown is %. (Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed.)arrow_forward
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