Derivatives Homework: Analysis of Hedging and Investment Strategies

This document provides solutions to a derivatives homework assignment. The solutions cover various aspects of derivatives, including foreign currency hedging for a German airline paying in Euros and an American company importing from Japan, bond hedging, and the use of futures contracts. The assignment analyzes different scenarios, such as an insurance company hedging against interest rate changes and an investor hedging against currency fluctuations in Brazil. It also includes calculations for forward prices, profit and loss on hedges, and the application of betas to assess investment volatility. The assignment includes multiple choice questions involving the identification of different hedge strategies and calculations related to bond duration and yield. Overall, the assignment offers a comprehensive overview of derivatives applications and problem-solving techniques.

Derivatives
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Question 1
Ans. 1 Foreign currency hedge
Lufthansa (a German airline) company is to due to pay €273.311 million to its Boeing (an
American company) on July, 5th.
So: $1.3808/€
September futures contract fo: $1.3492/€ (Contract size: 1, 25,000 Euros)
N= -S/f = -273.311m/0.125 = - 2186.488 or Long hedge by buying 2190 contracts
On July, 5th
St= $1.2656/€
ft= $1.243/€
To buy €273.311 million*$1.2656/€ = $-345.902
Long futures (t=0) $1.3492*2190*0.125 = $-381.662
Sell futures = $1.243*2190*0.125 = $ 340.271
Cost of € 273.311m = -$345.902 - $41.391 = -$387.293
Actual rate = $1.243/€
Question 2
Ans.
Pay by the investors = 100,000*(9/100/2)18
= $45, 00
Question 3
Ans. 3 Nf = - MDb/MDf* b/f
MDb = 9
MDf = 8
b = 5, 00,000*1.140 = 5, 70,000
f = 104,938
= -9/8*570,000/104,938 = -1.125*5.432 = -6
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Profit on the hedge is 570,000 – 500,000*113/100+8 * (117,933 – 104,938) = -79,100 + 103,960
= 24,860.
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Question 4
Ans. 4
In this situation we are using
hedge method of derivatives
to protect from loss.
You are importing Italian
sports cars, have to make
payments in Euros, and
expect the Euro to
strengthen.
In this situation the company
is not using hedge method to
protect from loss.
An insurance company will
have to make large
payments to the survivors of
a natural disaster. It is
planning to finance the
payments by the future sale
of a bond held in its
portfolio. The insurance
company expects that
interest rates will fall in the
short run.
In this situation the Ian
Ackerman is not using
hedge method.
Ian Ackerman has made a
large short bet against a
pharmaceutical. The stock
market is in an expansion
phase.
In this situation the hedge
method of derivatives is not
used.
The city of Boston is
planning to issue a new bond
with a 5% coupon to finance
the construction of a new
city hall. Currently we are in
the planning phase. The
mayor and treasurer expect
the Fed to raise interest rates
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in the short term
Question 5
Ans. 5
The forward prices of T- bond is 800* 1,021 = $816,800. The hedge instrument is a T-bond with
100,000* $82.29 = $82, 29,000 and MD = 7.55
N*f = - MDb/MDf* b/f
= -9.1/7.55* 816,800/82, 29,000 = -1.205*0.099 = -11
Profit on the hedge is $816,800 – 800,000 = $16,800
Question 6
Ans. The effective amount received by the farmer was = $213,500 + ($23,000- $14,000) =
$222,500
Question 7
Ans.
Stock Investment (million$) Beta
Alpha Co. 2.5 1.6
Gamma Inc. 2.3 2.3
Theta Corp. 1.5 1.35
Phi Inc. 0.5 0.37
In the case of Alpha Co. the beta is equal to 1 and it is not volatile in the nature.
Gamma Inc., the beta is more than 1 and it is volatile in the nature and risky to the investors.
Theta Corp., the beta is 1 and it is not volatile in the nature and even no risky to the investors.
Phi Inc., the bets is less than 1 and not in volatile nature.
Question 8
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Ans.
On August 15, if the positions with Technology Futures at 640.9
Purchase = $100*650.13 = $65,013
Sale = $100* 640.9 = 64,090
Loss = 65,013 – 64,090 = $923
On August 15, if the positions with Finance Futures at $110.59
Purchase = $100* 132.28 = 13,228
Sales = $100* 110.59 = 11,059
Loss = 13,228 – 11,059 = $2,169
Question 9
Ans.
Bond Price = $1,135.41
Duration = 3 and its yield is 6.55%
$1,135.41*(6.55/100)3 = 0.319
= $1,135.41 + 0.319 = $1135.73
Question 10
Ans.
Yes it is using short hedge. An American company
importing from Japan pays
quarterly for the shipped
goods in Yen. The hedge
will be for the Japanese Yen.
Yes it is using short hedge. An investor has invested a
substantial sum with a
venture capital fund in
Brazil. The money will be
tied up for the next three
years, during which the
investor wishes to use
futures to guard against
adverse movements in the
Brazilian Real exchange
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rate.
No it is not using short
hedge.
GE needs to repay a
corporate loan on June 15th,
at which time the company
plans to refinance the
amount with a new 3%
coupon bond issue. GE is
worried that if interests rates
move adversely, the new
issue will be selling under
par.
Yes it is using short hedge. A company is expecting to
repatriate profits from its
foreign subsidiary in foreign
currency at the end of the
year. (The underlying of the
futures is the foreign
currency.)
No it is not using short
hedge.
A company is preparing to
conduct an SEO in two
weeks. It plans to hedge
against adverse market
movements in the meantime.
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