Question

5. Royal Bank of Canada quotes C$1 = US$ 0.7265. Citibank quotes A$ 1 = US$0.6980. ANZ bank quotes A$ 1 = C$0.9350. a. If these quotes are simultaneously observed spot rates, can you make an arbitrage profit? If so, calculate what profit would you make if you started with AS 1 million. Assume that there are no transaction costs. (10 marks) b. What would be your arbitrage profit if you were to incur the following transaction costs? (10 marks) Conversion from Australian dollar to Canadian dollar Canadian dollar to US dollar US dollar to Australian dollar Australian dollar to US dollar Canadian dollar to Australian dollar US dollar to Canadian dollar Transaction cost (based on value) 1.5% 2.0% 1.0% 1.09 1.5% 1.5% (20 marks)

Answer 1

Answer to question 5

Part a:

Investment Amount = A$ 1 million

Step1: First to convert the A$ to US$@ 0.6980 = US$ 698000 (1000000 X 0.6980)

Now I have US$ 698000

Step2: Covert the US$ to C$ @ 0.7265 = C$ 960770.82 (698000/0.7265)

Now I have C$ 960770.82

Step3: Finally convert C$ to A$ @ 0.9350 = A$ 1027562.37 (960770.82/0.9350)

Finally, I have 1027562.37 A$

Arbitrage Profit on above transaction = current value minus investment

                                                            = A$ 1027562.37- A$ 1000000

                                                            =A$ 27562.37

Answer: Hence, I made a profit of A$ 27562.37 in arbitrage.

Part b

Since there is cost involved in the transaction, the value of above conversion will be decreased by the same.

Step1: First to convert the A$ to US$ @ 0.6980 = US$ 698000 (1000000X0.6980)

            Less Transaction cost @ 1% then value of US$ = US$698000 less 1% transaction cost

                                                                                        = US$ 691020 (698000X99%)

            Step2: Convert US$ to C$ @ 0.7265 = C$ 951163.11 (691020/0.7265)

            Less Transaction Cost @ 2% then value of C$ = C$ 951163.11 less 2% trans cost

   = C$ 932139.85

            Step3: Finally, convert C$ to A$ @ 0.9350 = A$ 996941.01 (932139/0.9350)

            Less transaction cost@ 1.5% then value of A$ = A$996941.01 less 1.5% trans cost

                                                                                       = A$ 981986.90

            So, there is loss on arbitrage where transaction cost is involved as shown below

            Current Value = A$ 981986.90

            Investment value = A$ 1000000

            Net Loss = A$ 18013.10 ( 1000000 less 981986.90)

            Answer: Hence, I made a loss in arbitrage when there is transaction cost involved.

References:

Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., & Obłój, J. (2019). Pointwise arbitrage pricing theory in discrete time. Mathematics of Operations Research.

Frahm, G. (2018). Arbitrage Pricing Theory in Ergodic Markets. International Journal of Theoretical and Applied Finance, 21(05), 1850036.