Question

2) Forward exchange rates under no-arbitrage

a) Find the five-year forward AUD/JPY exchange rate under no-arbitrage if the spot exchange rate is 80 yen per Australian dollar, and the five-year risk-free interest rates in Australia and Japan are 4% and 6% per annum, respectively. (1 point)

b) Choose a forward exchange rate that is greater than the no-arbitrage exchange rate you

found in (a), and describe the arbitrage strategy you would use to exploit this situation. Calculate your profits from arbitrage, assuming you're able to borrow 1,000 units of any given currency. (1 point)

c) Choose a forward exchange rate that is lower than the no-arbitrage exchange rate you found in (a), and repeat the steps in (b). (1 point)

d) Forwards and futures exist on cryptocurrencies like Bitcoin. Would you calculate forward prices on these contracts as if Bitcoin was a stock, or forward exchange rates (as if Bitcoin was a currency)? Why? Can you support your answer with research? (2 points)

Answer 1

a
Current JPY/ AUD spot rate=	80	Yen/AUD
Risk free rate in Japan	6%
Risk free rate in Australia	4%
5-year forward rate
=80*(1+6%)^5/(1+4%)^5	87.9939
b
Assume a higher forward rate	100	Yen/AUD
Arbitrage trade-

Borrow 80,000 Yen today @80 Yen/AUD for 5 years, enter into a forward contract to receive @100 Yen/AUD, pay off after 5 years @87.99391 Yen/AUD

Cash flows-
Borrow Today
1000 AUD	80,000.00	Yen
5 years later
Repay borrowing	87,993.91	Yen
Receive from forward contract	100,000.00	Yen
Profit	12,006.09	Yen
c
Assume a lower forward rate	75	Yen/AUD
Arbitrage trade-

Borrow 1000 AUD today @80 Yen/AUD for 5 years, enter into a forward contract to pay @75 Yen/AUD, receive after 5 years @87.99391 Yen/AUD

Cash flows-
Borrow Today
1000 AUD	80,000.00	Yen
5 years later
Receive borrowing	87,993.91	Yen
Pay forward contract	75,000.00	Yen
Profit	12,993.91	Yen

d
Bitcoin, even though is called as a currency, does not behave like a currency. The exchnage rates between any 2 currencies, in long term, depend on the risk free rates in those currencies. As per interest rate parity, the forward exchange rates between 2 currencies will depend on the risk free rates in those 2 currencies. There is no risk free instrument available in Bitcoin. Hence, the implied forward rates cannot be accurately calculated. Hence, we should treat it as a stock-like asset and calculate the forward price accordingly. The risk in pricing a Bitcoin is very high and hence, it has a stock-like nature