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Offline JavierF

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Solutions Triangular Arbitrage
« on: April 23, 2009, 07:05:58 pm »
Triangular class exercise

$-based spot market quotes in LSE
Spot Rate 1: $ 1 = ¥ 107.91
Spot Rate 2: $ 1 = € 0.87

1.) Calculate the implied rate!

The implied rate is calculated by (e.g.) dividing Spot Rate 1 by Spot Rate 2.

1 $ / 1 $ = ¥ 107.91 / € 0.87 <=>
<=> 1 = ¥ 107.91 / € 0.87 <=>     | * 0.87 €
<=> € 0.87 = ¥ 107.91  <=>         | / 0.87
<=> € 1  = ¥ 107.91/0.87 <=>
<=> Implied rate: € 1 = ¥ 124,03 (rounded)



Tokyo Spot Market

Quoted rate


€ 1 = ¥ 128,03


2.) Execute a full arbitrage!

Assumption 1: We own 1,000,000 Euro.

Step 1: Find out, where Euro € is expensive.

London: € 1 = ¥ 124,03 (rounded implied rate, cf. first task)
Tokyo: € 1 = ¥ 128,03

So the Euro is more expensive in Tokyo. Therefore we sell our Euros in Tokyo, "go" to
the LSE (London Stock Exchange), buy Dollars $ with our Yen ¥ there and finally buy
Euros with the obtained dollars. At the end we should have an amount of Euros that
exceeds the amount at the beginning.

Step by step:

Step 2: Buy Yen ¥ at TSE (Tokyo Stock Exchange)

Spot rate: € 1 = ¥ 128,03
Therefore: € 1,000,000 = ¥ 128,030,000

We just bought ¥ 128,030,000.

Step 3: "Go" to London and buy Dollars

Spot rate: $ 1 = ¥ 107.91
Therefore:  x = ¥ 128,030,000 / 107.91 ¥/$ = $ 1,186,451.67

We now have $ 1,186,451.67 and want to convert them back to Euros.

Step 4: Buy Euros with the newly obtained Dollars


Spot rate: $ 1 = 0.87 €
==> 1 € = 1 $ / 0.87 = 1.15 $ (rounded)
Therefore: x = $ 1,186,451.67 / 1.15 $/€ = € 1,032,212.96 (exact exchange rate used)

We finally have € 1,032,212.96.

Comparison before-after:
BeforeAfter
€ 1,000,000€ 1,032,212.96
Difference: + € 32,212.96

3.) Look up the exchange rates for

o $ vs. ¥: $ 1 = 97,8700 ¥     23.04.       18:57:10
o $ vs € : $ 1 =  0,7649 €      23.04.     18:55:04

o Calculate the implied rate!

(for calculation see task 1)

Implied rate: € 1 = 127,95 ¥

END (Hopefully I didn't miss any task).



Sincerely yours,

Javier Friedlmeier







« Last Edit: May 23, 2009, 09:39:55 am by Ted Azarmi »

Offline philippdannecker

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Re: Solutions Triangular Arbitrage
« Reply #1 on: April 24, 2009, 11:40:26 am »
Triangular Arbitrage Class Exercise

Exchange rates (Friday, 24.04 11:00)

1 US Dollar (USD) = 0.76725 Euro
1 US Dollar (USD) = 98.01725 Yen

$1 = 98.02 Yen
$1 = 0.77 Euro

1.) Calculate the implied rate

Dividing  rate 1 by rate 2


98.02 Yen/0,77 €

1        = 98.02 Yen/0,77 €

 0.77€  = 98.02 Yen              |  (/0,77)

  1€  = (98.02/0,77) Yen


Implied rate : 1€ = 127,3 Yen


Tokyo Spot Market


Quoted rate : 1€ = 128.03 Yen



  2.) Full arbitrage"Buy cheap, Sell expensive"

We own 10,000,000 €

2.1 Find out where Euro is more expensive

London (LSE) : 1€ = 127,3 Yen

Tokyo  (TSE) : 1€ = 128.03 Yen

The Euro is more expensive in Tokyo. (128,03 > 127,03)
That is why we sell our Euros in Tokyo.

 2.2 Buy Yen in Tokyo

We own 10,000,000 €

Qouted rate (TSE) : 1€ = 128.03 Yen   |(*10,000,000)

                      10,000,000€ =1,280,300,000 Yen

We obtain 1,280,300,000 Yen


Then we buy Dollars with our obtained Yen at the LSE.

2.3 Buy Dollars at London Stock Exchange

 Spot rate : 1$ = 98,02 Yen

 1,280,300,000 Yen / 98,02 Yen/Dollar =  13,061,620.88 $

 We now have 13,061,620.88$

Finally, we buy Euros with the obtained Dollars

2.4 Buy Euros at LSE

Spot rate: 1$ = 0,77 €

              1€= 1$/0.77 = 1,299$

      13,061,620.88 $/1,299$/€ = 10,055,135,33 €

We now have 10,055,135,33 €.

2.5 Arbitrage Profit

10,055,135,33 € - 10,000,000.00€ = 55,135,33€


Best regards

Philipp Dannecker

Offline leoniekrauss

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Re: Solutions Triangular Arbitrage
« Reply #2 on: April 24, 2009, 01:05:39 pm »
Triangular Arbitrage Class Exercise


$-based spot market quotes in London     1 $ = 106.91 ¥
1 $ = 0.87 €

Tokia Spot Market quoted rate       1 € = 127.03 ¥


Task 1: Calculate the implied rate

106.91 ¥ / 0.87 € = 1

   122,89 ¥ = 1 €

   In Tokyo Euros are more expensive than in London


Task 2: Triangular Arbitrage

1.   Sell 1,000,000 Euros in Tokyo at 127.03 ¥ / €
Now we have 127,030,000 ¥

2.   Convert 127,030,000 ¥ to $ in London
127,030,000  ¥ / 106.91  ¥/$ = 1,188,195.68 $

3.   Buy cheap € in London
1,188,195.68 $ * 0.87 €/$ = 1,033,730.24 €

   Arbitrage Profit: 1,033,730.24 – 1,000,000 = 33,730.24
   Interest rate is 33.73% which is not very realistic


Task 3: Look up the exchange rates for

a)   $ vs. ¥ : 1 $ = 98.2989 ¥
b)   $ vs. € : 1 $ = 0.7663 €

Calculate the implied rate: 

98.2989  ¥ / 7.663 € = 1
128.2773  ¥ = 1€

Best regards

Leonie Krauß

Offline HannahHerrmann

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Re: Solutions Triangular Arbitrage
« Reply #3 on: April 24, 2009, 01:12:56 pm »
 Triangular Arbitrage Class Exercise

$-Based spot market quotes in London

$1 = 106.91 Yen
$1 = 0.87 Euro

Tokyo Spot Market
Quoted rate:
1€ = 127.03 ¥

Task 1): Calculate the implied rate:

106.91 ¥ / 0.87 € = 1
122.89  ¥ = 1€

-> In Tokyo € is more expensive than in London
 
Task 2): Triangular Arbitrage:

1. Sell 1,000,000 € in Tokyo at 127.03 ¥/€.
   Now, we have got 127,030,000.00  ¥

2. Convert 127,030,000.00 ¥ to $ in London
    127,039,000.00 ¥ / 106,91 ¥/$ =  1,188,195.68$

3. Buy cheap € in London
    1,188,195.68$ * 0.87€/$ = 1,033,730.24€   

-> Arbitrage Profit: 1,000,000.00€ – 1,033,730.24€ = 33,730.24
-> Interest rate: 33.73%

Task 3): Look up the exchange rates for:

- $ vs. ¥: 1$ = 98.2989  ¥
- $ vs. €: 1$ = 0.7663 €

Calculate the implied rate:
98.2989 ¥ / 0.7663€ = 1
128.2773 ¥ = 1€

Best regards
Hannah Herrmann

Offline ElisabethBohnert

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Re: Solutions Triangular Arbitrage
« Reply #4 on: April 24, 2009, 01:22:24 pm »
Triangular Arbitrage Class exercise

$-based spot market quotes in London
$1 = 106.91 ¥
$1 = 0.87 €

Tokyo spot Market
 €1 = 127.03 ¥


Task 1: Calculate the implied rate

106.91¥ / 0.87€ = 1
-> 122.89¥ = 1€

In Tokyo, Euros are more expensive than in London.


Task 2: Triangular arbitrage

1.   Sell 1,000,000.00 Euros in Tokyo at 127.03 ¥/€.
Now, we have got 127,030,000.00 ¥

2.   Convert 127,030,000.00 ¥ to dollars in London.
127,030,000.00 ¥/ 106.91 ¥ /$ = 1,188,195.68 $
3.   Buy cheap euros in London:
1,188,195.68 $*0,87 €/$ = 1,033,730.24 €
-> Arbitrage profit: 1,033,730.24 €-1,000,000.00 € = 33,730.24 €
-> Interest rate: 33,73 % (not so realistic)

Task 3: Look up the exchange rates:
a) $ vs. ¥:    1 $= 98.2989 ¥
b) $ vs. €:   1 $= 0.7663 €
Calculate the implied rate:
98.2989 ¥ / 0.7663 € = 1
1 € = 128.2773 ¥

Have a nice weekend!
Elisabeth Bohnert

JuliaKessler

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Re: Solutions Triangular Arbitrage
« Reply #5 on: April 25, 2009, 08:10:03 am »
Solution attached
Have a nice day
Julia Kessler

Homework: Triangular arbitrage

Assumptions:
Currency amount: 1,000,000 €
Exchange rates:
London spot market: $1 = 108.22 ¥
               $1 = 0.88 €
Tokyo spot market: €1= 129.23 ¥

1.   Step:
Implied rate for London spot market:
$1/$1=108.22¥/0.88€
1=122.98¥/€
1€=122.98¥

2.   Step:
Where is Yen cheap (=Euro expensive)?
In Tokyo, because you get less Euro for one Yen and more Yen for one Euro.
Which means that one has to sell Euros first in Tokyo for Yen; then sell Yen in London to get dollars and convert them back into Euros

3.   Step:
Sell 1,000000€ in Tokyo (reason: Euro expensive here and Yen cheap)
1,000,000€*129.23¥/€=129,230,000¥

4.   Step:
Sell 129,230,000¥ in London (reason: get Dollars to buy cheap Euros)
129,230,000¥/108,22¥/$=1,194,141.56$

5.   Step:
Exchange rate 1€=x$:
$1=0.88€
1€=1$/0.88€=1.14$

6.   Step:
Convert 1,194,141.56$ in London (reason: get cheap Euros)
1,194,141.56$/1.14$/€=1,047,492.6€

7.   Step:
Profit:
1,047,492.6€-1,000,000€=47,492.6€

Exchange rates for:
$/¥: 1$=97.14¥
$/€: 1$=0.7549€1
(Date: 25th April; 7:55)

Implied rate: cf. Step 1
1€=128,68¥

All numbers are rounded.
« Last Edit: July 30, 2009, 09:12:51 pm by Ted Azarmi »

Offline Katha

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Re: Solutions Triangular Arbitrage
« Reply #6 on: April 25, 2009, 12:56:40 pm »
Solution attached,

best regards, Katharina Dragon

I.   $-based Spot market in London
$1 = 107.91 Yen
$1 = 0.87 Euro

Calculation of  the implied rate:
1 = 107.91 ¥/ 0.87 €
 0.87 €= 107.91 ¥  1€ = 107.91 ¥/ 0.87 = 124,03 ¥

II.   Exchange Rates: $-based spot market quotes in London  :
$1 = ¥ 97.165
$1 = € 0.7551

Implied rate:
1 = ¥ 97.165/ € 0.7551
 € 0.7551= ¥  97.165 € 1= ¥97.165/ 0.7551 = ¥ 128,68

Cross rate market quotes in Frankfurt :  €1 = 128,5850 ¥

III.   Triangular Arbitrage calculation using the data looked up on the internet:
Assumption: €  1.000.000 to be invested

The Euro is less expensive on the cross market: 
€ 1= ¥ 128,68 (London) > €1 = 128,5850 ¥ (Frankfurt), because in Frankfurt we pay less for each Euro.
Therefore, we should buy Euro cheap in Frankfurt and sell it expensive in the LSE in order to increase the capital amount we obtain assumably at the moment.

1.   Sell € 1.000.000 in London:
€ 1.000.000/(0,7551 €/$) = 1324327,90 $

2.    Convert 1324327,90 $ in ¥ in London:
1324327,90 $ * (97.165¥/$) = 128678320,8 ¥

3.   Sell ¥ expensive in the corss rate market:
128678320,8 ¥/ (128,5850 ¥/€) = 1000725,75 €

4.   Comparison of capital before and after arbitrage:
1.000.725,75€ - 1.000.000€ = 725,75€
Our gain from arbitrage assuming that exchange rates did note change during the time of execution are 725,75€. Note that the profit is lower as in former examples due to a smaller rate difference between the countries.
« Last Edit: July 30, 2009, 09:11:05 pm by Ted Azarmi »

Offline B.Tisch

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Re: Solutions Triangular Arbitrage
« Reply #7 on: April 25, 2009, 02:55:11 pm »
Homework attached. Please excuse the format, I created a pdf-file, which unfortunately cannot be uploaded, so I took screenshots and saved into PP. Hope you can read it though.
Best regards,
Barbara Tisch

Offline christine84

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Re: Solutions Triangular Arbitrage
« Reply #8 on: April 25, 2009, 07:00:04 pm »
The solution is attached!

Best regards,
Christine Scheef

Homework Triangular Arbitrage

Exchange rates 25/04/2009 (yahoo finance):

•   1 $ = 97.245 Yen
•   1 $ = 0.755 €

Implied exchange rate

   97.242 Yen = 0.755 €
   1 € = 97.242/0.755 Yen
   1 € = 128.797 Yen

Tokyo Spot Market

   1 € = 128.03 Yen

   Arbitrage possibility
(Euro is expensive in London and cheap in Tokyo; Yen is cheap in London and expensive in Tokyo)

Arbitrage

1. Step
Sell 1,000,000 € in London and receive 1,000,000 € / 0,755 €/$ = 1,324,503.311 $

2. Step
Sell 1,324,503.311 $ in London and receive 1,324,503.311 $ / (1$/97,245 Yen) = 128,801,324.5 Yen

 3. Step
Sell 128,801,324.5 Yen in Tokyo and receive 128,801,324.5 Yen / 128.03 Yen/€ = 1,006,024.561 €

   Arbitrage profit = 1,006,024,561 € - 1,000,000 € = 6,024.561 €

« Last Edit: July 30, 2009, 09:13:59 pm by Ted Azarmi »

Offline mia

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Re: Solutions Triangular Arbitrage
« Reply #9 on: April 25, 2009, 07:02:21 pm »
Hallo,
I am Miaomiao Zhu,  you can call me Mia. My homework is attached.
Have a nice weekend!

Offline Sandra Hokenmaier

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Re: Solutions Triangular Arbitrage
« Reply #10 on: April 26, 2009, 12:00:55 pm »
Exercise attached.

Best regards,
Sandra Hokenmaier

Offline martina.weisser

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Re: Solutions Triangular Arbitrage
« Reply #11 on: April 26, 2009, 12:22:31 pm »
The solution is attached,

Best regards,
Martina Weisser

Offline TanjaKroh

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Re: Solutions Triangular Arbitrage
« Reply #12 on: April 26, 2009, 01:10:50 pm »
The exercise is attached.

Best regards,
Tanja Kroh

Offline skstein

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Re: Solutions Triangular Arbitrage
« Reply #13 on: April 26, 2009, 02:23:21 pm »
My solutions to the first homework are attached.

See you in class on Thursday.

Thank you,

Sarah K. Stein

Offline larissa

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Re: Solutions Triangular Arbitrage
« Reply #14 on: April 26, 2009, 04:21:55 pm »
Solution is attached.
Best regards
Larissa Mader