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Homework 1 MGMT 41150 Key

This homework assignment has three questions related to hedging a portfolio with futures contracts, analyzing a bond forward arbitrage opportunity, and tracking margin requirements for a crude oil futures position. Students are asked to show their work and can work in groups of up to four people. The document provides relevant financial details needed to answer each multi-part question, such as portfolio value, futures and index prices, risk-free rates, and daily settlement prices.

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Laxus Dreyer
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365 views6 pages

Homework 1 MGMT 41150 Key

This homework assignment has three questions related to hedging a portfolio with futures contracts, analyzing a bond forward arbitrage opportunity, and tracking margin requirements for a crude oil futures position. Students are asked to show their work and can work in groups of up to four people. The document provides relevant financial details needed to answer each multi-part question, such as portfolio value, futures and index prices, risk-free rates, and daily settlement prices.

Uploaded by

Laxus Dreyer
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Name(s)_____________________________________________________________________________

Homework #1 – 80 Points Total


*Due at the beginning of class on Wednesday, September 19th.
**You may work in groups of up to 4 people, just put all of the names at the top of this page.
**Please print this HW one-sided and write in the space provided (I will try to leave plenty of
space, but use the back of the page if you need to). Please show all work for full credit!

Question 1 (30 points)


You have a $6,000,000 portfolio that has a beta of 1.9 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 $2300, and the
current S&P 500 index value is $2250. The 12-month continuously compounded risk-free rate is 1% 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.

a) What position in futures contracts will you need to hedge your portfolio?

Homework #1
MGMT 41150 – Futures and Options
Professor Boquist
b) 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 $1200, if it drops
to $2100, and if it increases to $3200. Assume the S&P 1-month futures price is $1205, $2107,
and $3215, respectively. (Hint: table 3.4 in the textbook should help with this question.)

Homework #1
MGMT 41150 – Futures and Options
Professor Boquist
Question 2 (25 points)
You look up a 15-month bond forward contract and find the following: the current price of the bond is
$1200, and the forward price is $1190. It will pay a coupon of $50 in 4 months and 10 months. The
annualized, continuously compounded risk free rate is 0.5% for 4 months, 1% for 10 months, and 2% for
15 months. Find an arbitrage trade, and show the profit from your trade.

Homework #1
MGMT 41150 – Futures and Options
Professor Boquist
Homework #1
MGMT 41150 – Futures and Options
Professor Boquist
(Blank page - additional space for question 2 answer)

Homework #1
MGMT 41150 – Futures and Options
Professor Boquist
Question 3 (25 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: $49, $46, $41, $34, $46,
$40, $49. You then decide the close the trade on day 9, at a price of $53.50. Make a table similar to the
one on page 30 in the textbook (Slide 14 in the Chapter 2 lecture notes has a simplified version also)
showing your margin account.

Homework #1
MGMT 41150 – Futures and Options
Professor Boquist

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