Homework 1 on Triangular Arbitrage with Bid-Ask Spread S(E/E)-S (S/E)/S (s/e) Su

Question

Homework 1 on Triangular Arbitrage with Bid-Ask Spread S(E/E)-S (S/E)/S (s/e) Suppose Citibank's quote: $1.5445-1.5460 /€ Barclay's quote: $1.9443 -1.9453 /£ Dresdner's quote: 1.2789 1.2799/E Cross-rate between Citibank and Barclay should be 1.2589 E, compared to the actual Dresdner quote of1.2789 /£ Is triangular arbitrage possible if an investor starts with follows the following two strategies independently? 1 million and (a) Euros to Dollars to Pounds to Euros. (b) Euros to Pounds to Dollars to Euros. ° ° If there are arbitrage gains or losses in either case, how much?

Explanation / Answer

Solution:

As per the information given in the question we have the following quotes:

                                             Bid      -      Ask

Citibank's quote: ( $ / € ) : $ 1.5445    -    $ 1.5460

Barclay's quote: ( $ /£ ) : $ 1.9443    -     $ 1.9453

Dresdner's quote: (€ /£ ) : € 1.2789    -     € 1.2799

Option 1:             

Euros to Dollars to Pounds to Euros                                

As per the information given in the question we have € 1,000,000.

Applying the strategy we have

a. Conversion of 1 Million Euros to Dollars

We shall sell the Euros to buy Dollars. Since the quote given is in Euros we shall take the Bid rate for the conversion.

Hence we will use the Bid rate of One Euro = $ 1.5445 offered by Citibank

Thus, we have € 1,000,000 * $ 1.54445 = $ 1,544,500                      

b. Conversion of 1,544,500 Dollars to Pounds

We shall sell Dollars to buy Pounds. Since the quotes given is in Pounds we shall use the Ask rate for the Conversion

Hence we will use the Ask rate of one pound = $ 1.9453 offered by the Barclay’s bank    

Thus we have ($ 1,544,500 / $ 1.9453 ) = £ 793,964.94

c. Conversion of 793,964.94 Pounds to Euros

We shall sell Pounds to Buy Euros. Since the quote given is in Pounds we shall use the Bid rate for the conversion.

Hence we will use the Bid rate of one Pound = € 1.2789 offered by the Dresdner’s bank

Thus we have £ 793,964.94 * € 1.2789 = € 1,015,401.76

Thus the Above option 1 will make an arbitrage profit of € 1,015,401.76 -   € 1,000,000.00 = € 15,401.76

                                                                                                                                           

Option 2:                        

Euros to Pounds to Dollars to Euros    

As per the information given in the question we have € 1,000,000.

Applying the strategy we have

a. Conversion of 1 Million Euros to Pounds

We shall sell the Euros to buy Pounds. Since the quote given is in Pounds we shall take the Ask rate for the conversion.

Hence we will use the Ask rate of One Pound = € 1.2799 offered by Dresdner

Thus, we have € 1,000,000 / € 1.2799 = £ 781,311

b. Conversion of 781,311 pounds to dollars

We shall sell the pounds to buy dollars. Since the quote given is in Pounds we shall take the Bid rate for the conversion.

Hence we will use the Bid rate of One £ = $ 1.9443 offered by Barclay’s.

Thus, we have £ 781,311 * $ 1.9443 = $ 1,519,103

c. Conversion of 1,519,103 Dollars to Euros

We shall sell the Dollars to buy Euros. Since the quote given is in Pounds we shall take the Ask rate for the Conversion.

Hence we will use the Ask rate of One € = $ 1.5460 offered by Citibank

Thus we have $ 1,519,103 / $ 1.5460 = € 982,602.23

Thus the Above Option 2 will make an arbitrage loss of € 982,602.23 - € 1,000,000.00

= - € 17,397.77

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