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fin_435_fa_15_hw__2__answers_1__2_.xls

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PROBLEM #1
You are given the following information related to five different forward contract rates at different
Consequently the interest rates and spot rates may differ for each scenario.
You are looking to perform a covered arbitrage trade” where you identify mispriced forward rates
This is where you seek to borrow in the “cheaper” currency and lend the money in the “expensi
To start off the problem you will want want to borrow one (1) million units of whichever currency i
QUESTION A: Identify all the possible arbitrage opportunities. (NOTE: due to rounding, any trade
profit is actually in equilibrium and not a trading opportunity).
QUESTION B: For each covered arbitrage opportunity, identify the undervalued currency and the o
QUESTION C: For each covered arbitrage opportunity, calculate the proper forward contract rate.
QUESTION D: Choose any ONE covered arbitrage opportunity that you have found and describe in
how you would undertake the arbitrage. NOTE: If you want to utilize the IRP “box” feel free to
I just want to see your narrative on what is happening on Day 1 and the Final Day of the transac
QUESTION E: For the arbitrage opportunity you choose in Question D, what was your profit? Again
assume the forward rate is actually in equilibrium/correct.)
Market Values that are Given
Forward Rate ($/€)
Spot Rate ($/€)
Interest Rate (nominal) USD
Interest Rate (nominal) Euro
One Month
Forward
Contract
160%
160%
Three Month
Forward
Contract
192%
180%
6%
6%
9%
4%
PROBLEM #2
You believe that the Australia will depreciate against the US dollar.
You want to utilize futures contracts to speculate on this move and take a position worth 500,000
One (1) contract = 100,000 AUD
The Spot Rate used when you open your position is $0.90/AUD
The following are the daily closing $/AUD rates used to calculate the value of your account.
Margin Requirement (per contract)
$4,000.00
Maintenance requirement (per contract)
$2,500.00
Open Account ($/AUD)
0.90
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7 (Close Account)
0.92
0.92
0.91
0.93
0.89
0.88
0.87
QUESTION A and B: What type of position would you take: Long or short? What actions will you n
Be VERY specific.
QUESTION C: How much profit/loss did you make during the seven trading days. Show your calc
QUESTION D and E: On which days did you need to add money to your account? How much did
PROBLEM #3
A currency trader believes that the Euro will depreciate against the U.S. dollar.
On June 10, he decides to invest in one futures contract (worth 125,000 Euros) with a September 1
QUESTION A: Should he take a long or short position on the Euro? Why??
QUESTIONS B AND C: In taking this position does he lock in the selling price or the purchase price?
The spot rate on is $1.2111/€.
The September futures contract rate on, June 10 , is $1.2253/€
The spot rate on September 15 is $1.2098/€
QUESTION D: What is the trader’s profit or loss on September 15? Show all calculations.
QUESTION E AND F: If the trader had decided to offset his original contract (or close his position) o
when the spot rate was $1.2122/€ and the September 15 contract rate was $1.2153/€, wou
Show your calculations.
PROBLEM 4
Looking at the following options table:
US cents/£
Spot Rate
British Pound Option Prices (U.S. CENTS per Pound, 62,500 pounds pe
Call
Strike Price
May
144.8
144.8
144.8
QUESTION A:
QUESTION B:
QUESTION C:
QUESTION D:
QUESTION E and F:
QUESTION G:
QUESTION H:
144
145
146
0.88
0.42
0.2
Give me one example of an option that is out of the money? Be speci
Give me one example of an option that is in the money? Be specific a
Which, if any, option is at the money? Explain your answer.
Looking at the in-the-money option you choose for Question B. Break
Show your calculations.
If you purchase two (2) June 145.0 call options what will be the total a
When do you pay this premium: on the settlement date or on the da
Today you purchase three (3) June 144.0 Puts. On settlement date th
Show your calculations.
Today you purchase two (2) June 144.0 Calls. On settlement date the
Show your calculations.
orward contract rates at different points in time.
h scenario.
identify mispriced forward rates (per IRP, Interest Rate Parity in the U.S. versus France)
d lend the money in the “expensive” currency.
lion units of whichever currency is undervalued ($ or Euro).
NOTE: due to rounding, any trade which nets a profit of less than 10,000 dollars/Euros in
he undervalued currency and the overvalued currency.
he proper forward contract rate.
at you have found and describe in great detail (including dates, rates, amounts, what you are selling/buying)
o utilize the IRP “box” feel free to use it to assist you. That said, I will not interpret the box
1 and the Final Day of the transaction.
on D, what was your profit? Again please note that if your profit is less than 10,000 dollars/Euros
Four Month
Forward
Contract
120%
121%
9%
12%
Six Month
Forward
Contract
111%
120%
nd take a position worth 500,000 AUD.
the value of your account.
12 Month
Forward
Contract
175%
155%
6%
8%
4%
3%
or short? What actions will you need to take given your strategy?
ven trading days. Show your calculations.
to your account? How much did you need to add on those days?
he U.S. dollar.
25,000 Euros) with a September 15 settlement date.
elling price or the purchase price? What is that price?
5? Show all calculations.
al contract (or close his position) on August 1,
contract rate was $1.2153/€, would he have a profit or loss, and how much was it?
NTS per Pound, 62,500 pounds per contract)
Call
Call
June
July
Put
May
Put
June
1.42
1.02 —-0.68
1.44
0.72
0.52
1.06
——–1.75
2.32
hat is out of the money? Be specific as far as month and strike price. Explain your answer?
hat is in the money? Be specific as far as month and strike price. Explain your answer?
y? Explain your answer.
you choose for Question B. Break down the premium into its Intrinsic Value and Time Premium components
all options what will be the total amount of your premium that you need to pay?
the settlement date or on the date that you purchase the options?
44.0 Puts. On settlement date the spot rate = 142.5 cent per pound, what is your net profit/loss?
4.0 Calls. On settlement date the spot rate = 143.5 cent per pound, what is your net profit/loss?
you are selling/buying)
Put
July
————-
e Premium components
t profit/loss?
profit/loss?
PROBLEM #1
Market Values
Forward Rate ($/€)
Spot Rate ($/€)
Interest Rate (nominal) USD
Interest Rate (nominal) Euro
One Month
Three Month
Forward Contract Forward Contract
1.60
1.92
1.600
1.800
6%
9%
6%
4%
Interest Rate (periodic) USD
Interest Rate (periodic) Euro
0.005
0.005
0.0225
0.01
1.60
1.82
Intrinsic future ($/€)
Undervalued Currency
Overvalued Currency
N/A
N/A
USD
Euro
Borrow in
Lend in
N/A
N/A
USD
Euro
Amount Borrowed
Amount owed at Maturity
Convert to investing currency
What you will get at maturity
Converting back at Forward rate
Profit
$
$
€
€
$
$
PROBLEM #2
1,000,000
1,005,000
625,000.00
628,125.00
1,005,000
–
$
$
€
€
$
$
1,000,000
1,022,500
555,555.56
561,111.11
1,077,333
54,833
You believe that the Australian dollar will depreciate against the US dollar. You want to short the A
You want to utilize futures contracts to speculate on this move and take a (short) position worth 5
Given we are taking a “short” position, we will profit when the AUD depeciates vs the US$, and l
I contract = 100,000 AUD
5 contracts gives you a total nominal amount (AUD) equal to
Future’s Contract Exchange Rate used when you open your position is $0.90/AUD
The following are the daily closing $/AUD rates used to calculate the value of your account.
Profit/Loss per $0.01 change in exchange rate = $0.01/AUD x
Open Account ($/AUD)
Day 1
Day 2
Day 3
Day 4
Day 5
Day 7 (Close Account)
Future’s Rate
0.90
0.92
0.92
0.91
0.93
0.91
0.87
500,000 AUD = $5,000
Price change
0.02
0.00
-0.01
0.02
-0.02
-0.04
Profit or Loss = Nominal Amount x (Selling Price – Purchase
Profit or Loss =
500,000
Profit = $
15,000
Since we sold the contracts initally, to open our “short” position,
When we close out the position we need to buy five contracts , w
PROBLEM #3
A currency trader believes that the Euro will depreciate against the U.S. dollar.
On June 10, he decides to invest in two (2) futures contract (1 contract = 125,000 Euros) with a Se
On June 10
the spot rate is $1.2111/€.
On June 10
the September futures contract rate is $1.2253/€
On September 15
the spot rate is $1.2098/€
QUESTION A: Should he take a long or short position on the Euro? Why??
Since the trader believes the Euro will decrease in value versus the $, he will want to sell now (go
QUESTIONS B : In taking this position does he lock in the selling price or the purchase price?
By going short a futures contract, the trader locks in the selling price today. That price is the Jun
QUESTION C : What is the price/exchange rate that is locked-in when the trader initiates his posit
The price that is locked in is the September future’s price on the day the position is opened. $1.
QUESTION D: What is the trader’s profit or loss on September 15? Show all calculations.
To calculate the profit/loss we need to find the difference between the rate at which the trader
The Sales Price = The June 10 rate of $1.2253/€ for the September Contract
Purchase Price = The September 15 spot rate of $1.2098/€.
Profit /Loss = (Number of Contracts) x (Number of currency units per contract) x (Sales Price – Pu
Profit/Loss = (2) x (125,000 Euros) x ($1.2253/€ – $1.2098/€)
Profit = $
3,875.00
USE THE FOLLOWING INFORMATION FOR QUESTIONS E & F
On August 1
the spot rate is $1.2122/€
On August 1
the September 15 (pound sterling) contract rate is $1.2153/€
On September 15
the spot rate is $1.2098/€
QUESTION E : If the trader decides to close his position early (on August 1), what action/trade wo
To close his position the trader must take the exact opposite actions that he used to open his po
To close, he would BUY TWO (2) Sept. pound sterling contracts.
QUESTION F: If the trader decided to close his original position) on August 1, would he have a pro
The Sales Price = The June 10 rate of $1.2253/€ for the September Contract
Purchase Price = August 1st September 15 contract rate of $1.2153/€.
Profit /Loss = (Number of Contracts) x (Number of currency units per contract) x (Sales Price – Pu
Profit/Loss = (2) x (125,000 Euros) x ($1.2253/€ – $1.2153/€)
Profit = $
2,500.00
PROBLEM #4
Looking at the following options table:
US cents/£
Spot Rate
British Pound Option Prices (U.S. CENTS per Pound, 62,500 pound
Call
Strike Price
May
144.8
144.8
144.8
QUESTION A:
QUESTION B:
QUESTION C:
QUESTION D:
QUESTION E:
QUESTION F :
QUESTION G:
QUESTION H:
QUESTION H:
US cents/£
Spot Rate
144
145
146
0.88
0.42
0.2
Give me one example of an option that is out of the money? Be s
Give me one example of an option that is in the money? Be speci
Which, if any, option is at the money? Explain your answer.
Looking at the July 144 CALL option, break down the option’s pre
Show your calculations.
Looking at the June 146 PUT option, break down the options pre
Show your calculations.
If you purchase two (2) June 145.0 call options what will be the to
Referring to QUESTION F, when do you pay the option premium,
Today you purchase three (3) June 144.0 Puts. On settlement dat
Show your calculations.
Today you purchase two (2) June 144.0 Calls. On settlement date
Show your calculations.
British Pound Option Prices (U.S. CENTS per Pound, 62,500 pound
Call
Strike Price
May
144.8
144
0.88
144.8
145
0.42
144.8
146
0.20
QUESTION A:
Give me one example of an option that is out of the money? Be s
For an options to be out of the money, the option has NO instrin
For a CALL the Strike Price > Spot Rate. It does NOT makes sen
that is higher than the spot rate (144.8).
For a PUT the Strike Price < Spot Rate. It does NOT makes sens that is lower than the spot rate (144.8). QUESTION B: Give me one example of an option that is in the money? Be speci For an options to be in the money, the option has an instrinsic v For a CALL the Strike Price < Spot Rate. It makes sense for the that is lower than the spot rate, therfore th For a PUT the Strike Price > Spot Rate. It makes sense for the h
that is higher than the spot rate, therfore t
QUESTION C:
Which, if any, option is at the money? Explain your answer.
For any option (PUT or CALL) to be at the money, the option’s s
With this problem, there are NO options at the money. We get
QUESTIONS D & E:
Looking at the July 144 CALL option, break down the option’s pre
Show your calculations.
Looking at the June 146 PUT option, break down the options pre
Show your calculations.
I have broken down a few extra premiums for you for practice
May 144 Call
June 144 Call
July 144 Call
May 146 Put
June 146 Put
QUESTIONS F & G
Total Premium =
0.88
1.42
1.44
1.75
2.32
If you purchase two (2) June 145.0 call options what will be the to
When do you pay this premium: on the settlement date or on th
Amount of currency units covered by two options = 2 x 62,500 p
Premium/Pound =
1.02
Total Premium = Premium (cents/£) × Amount of currency
The premium is paid at the time the options are purchased.
QUESTION H
Today you purchase three (3) June 144.0 Puts. On settlement dat
Show your calculations.
Amount of currency units covered by three options = 3 x 62,500
Profit/Loss per £ = Sales Rate/Price – Purchase Rate/Price
Total Premium = Premium (cents/£) × Amount of currency
Premium/Pound =
Net Profit/Loss =
(Amount of Currency Units x Profit/Unit) Profit on Contracts
– Premium
Net Profit
QUESTION H:
Today you purchase two (2) June 144.0 Calls. On settlement date
Show your calculations.
Given the Call options are out-of-the money on settlement date
Therefore the only cost (or loss) to the buyer is the premium pa
Total Premium = Premium (cents/£) × Amount of currency
1.42
alma 7
Four Month
Forward Contract
1.20
1.210
9%
12%
Six Month
12 Month
Forward Contract
Forward Contract
1.11
1.75
1.200
1.550
6%
4%
8%
3%
0.03
0.04
0.03
0.04
4%
3%
1.1984
1.19
1.57
N/A
N/A
Euro
USD
USD
Euro
N/A
N/A
Euro
USD
USD
Euro
$
$
€
€
$
$
€
€
$
$
€
€
1,000,000
1,030,000
826,446.28
859,504.13
1,031,405
1,405
Consider this to be
in equlibrium
given the profit is
less than $10,000
1,000,000.00
1,040,000.00
1,200,000
1,236,000
1,113,514
73,514
$
$
€
€
$
$
1,000,000
1,040,000
645,161.29
664,516.13
1,162,903
122,903
S dollar. You want to short the Australian dollar.
d take a (short) position worth 500,000 AUD by selling five contracts.
AUD depeciates vs the US$, and lose when the AUD appreciaties vs the US$.
minal amount (AUD) equal to
(500,000) AUD
on is $0.90/AUD
he value of your account.
00,000 AUD = $5,000
Profit/Loss
$
$
$
$
$
$
$
(10,000)
5,000
(10,000)
10,000
20,000
15,000
mount x (Selling Price – Purchase Price)
x (0.90 – 0.87)
ly, to open our “short” position, the $0.90/AUD represents the Sales Price.
we need to buy five contracts , which we do on Day 7 at the rate of $0.87/AUD (the purchase price).
e U.S. dollar.
tract = 125,000 Euros) with a September 15 settlement date.
rate is $1.2253/€
he $, he will want to sell now (go short) with the hope of purchasing Euro cheaper at a later date.
ice or the purchase price?
price today. That price is the June 10th September contract rate of $1.2253/€ futures
hen the trader initiates his position
day the position is opened. $1.2253/€
? Show all calculations.
en the rate at which the trader purchases the Euro and the rate at which he sold the Euro
er Contract
per contract) x (Sales Price – Purchase Price)
g) contract rate is $1.2153/€
August 1), what action/trade would he make on August 1? BE VERY SPECIFIC!!!
ons that he used to open his position.
n August 1, would he have a profit or loss, and how much? Show your calculations!!!
er Contract
per contract) x (Sales Price – Purchase Price)
CENTS per Pound, 62,500 pounds per contract)
Call
Call
June
July
Put
May
1.42
1.02 —-0.68
1.44
0.52
—–
0.72
1.75
n that is out of the money? Be specific as far as month and strike price. Explain your answer?
n that is in the money? Be specific as far as month and strike price. Explain your answer?
ney? Explain your answer.
on, break down the option’s premium into its Intrinsic Value and Time Premium components
on, break down the options premium into its Intrinsic Value and Time Premium components
0 call options what will be the total amount of your premium that you need to pay?
do you pay the option premium, on the settlement date or on the date that you purchase the options?
e 144.0 Puts. On settlement date the spot rate = 142.5 cents per pound, what is your net profit/loss?
144.0 Calls. On settlement date the spot rate = 143.5 cents per pound, what is your net profit/loss?
CENTS per Pound, 62,500 pounds per contract)
Call
Call
June
July
1.42
1.44
1.02
—-0.68
0.72
Put
May
0.52
—-1.75
n that is out of the money? Be specific as far as month and strike price. Explain your answer?
money, the option has NO instrinsic value.
See options in
ot Rate. It does NOT makes sense for the holder of the call to exercise the option and buy at a rate
er than the spot rate (144.8).
Any Call with a strike price of 145 or 146.
t Rate. It does NOT makes sense for the holder of the put to exercise the option and sell at a rate
er than the spot rate (144.8).
Any Put with a strike price of 144.
n that is in the money? Be specific as far as month and strike price. Explain your answer?
ey, the option has an instrinsic value greater than zero.
See options in
ot Rate. It makes sense for the holder of the call to exercise the option and buy at a rate
er than the spot rate, therfore the CALL has value. Any Call option with a strike price of 144.
t Rate. It makes sense for the holder of the put to exercise the option and sell at a rate
er than the spot rate, therfore the PUT has value. Any Put with a strike price of 145 or 146.
ney? Explain your answer.
be at the money, the option’s strike = the spot rate.
options at the money. We get close with the 145.00 options, but these are not at the money given the so
on, break down the option’s premium into its Intrinsic Value and Time Premium components
on, break down the options premium into its Intrinsic Value and Time Premium components
Intrinsic Value +
0.80
0.80
0.80
1.20
1.20
Time Premium
0.08
0.62
0.64
0.55
1.12
0 call options what will be the total amount of your premium that you need to pay?
on the settlement date or on the date that you purchase the options?
ed by two options = 2 x 62,500 pounds =
£
125,000
cents per pound, OR
0.01020 dollars per pound
cents/£) × Amount of currency covered by options (£ ) =
$
the options are purchased.
1,275.00
e 144.0 Puts. On settlement date the spot rate = 142.5 cent per pound, what is your net profit/loss?
ed by three options = 3 x 62,500 pounds =
£
Price – Purchase Rate/Price
= (144.0 – 142.5) =
cents/£) × Amount of currency covered by options (£ ) =
1.06 cents per pound =
187,500
1.5 cents/£, OR
$
1,987.50
0.0106 dollars per pound
f Currency Units x Profit/Unit) – Premium Paid =
$
$
$
$
825.00
2,812.50
1,987.50
825.00
144.0 Calls. On settlement date the spot rate = 143.5 cent per pound, what is your net profit/loss?
f-the money on settlement date (Strike Price > Spot Price) the buyer would not exercise them.
to the buyer is the premium paid.
cents/£) × Amount of currency covered by options (£ ) =
$
1,775.00
125,000
Put
June
Put
July
1.06 ————2.32 —–
e the options?
t profit/loss?
profit/loss?
Put
June
1.06
—-2.32
Put
July
————-
cells.
buy at a rate
sell at a rate
cells.
money given the sopt rate = 144.8.
profit/loss?
0.015 dollars per pound
per pound
profit/loss?
…
Purchase answer to see full
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