Question: You are hired by a financial company in New Zealand and you have instant access to markets. You would like to lock in a 3-month borrowing cost in NZ$ for your client. You consider a NZ$ 1 x 4 FRA. But you find that it is overpriced as the market is thin. So you turn to Aussie. A$ FRAs are very liquid. It turns out that the A$ and NZ$ forward are also easily available. In particular, you obtain the following data from Reuters:
A$/NZS Spot the: 1.17/18
1-month forward: 1.18/22
3-month forward: 1.19/23
4-month forward: 1.28/32
A$ FRA's 1 x 4 8.97
a. Show how you can create a 1 x 4 NZ$ from these data.
b. Show the cash flows.
c. What are the risks of your position (if any) compared to a direct 1 x 4 NZ$ FRA?
d. To summarize the lessons learned from this exercise (if any), do you think there must be arbitrage relationships between the FRA markets and currency forward? Explain. Or better, provide the relevant formulas.