Derivatives & Risk Management
Q1-22 are pretty normal. After that, they get a bit offbeat, so don’t lose too much sleep over them.
Some of these questions are newly written. So if you think there are errors/ambiguities in questions or answers,
let me know so that I can fix it up for next year.
The convention is to quote exchange rate as AUD 1.00 buys
For example, AUD 1.00 = NZD
However, it simplifies the intuition if we view the foreign currency as just another commodity. Q: How
much does it cost to buy one NZD? A: AUD 0.8197. This practice also helps us understand the jargon of
currencies ‘strengthening’ and ‘weakening’.
If the NZD strengthens, it becomes more expensive to buy. Buying NZD 1.00 will cost more than AUD
0.8197. Let's say it has strengthened to AUD 0.8500. The quoted exchange rate after strengthening is
thus 1/0.8500 = 1.1765.
So you can see why the quoting convention is counter-intuitive. NZD quotes have gone from 1.2200
down to 1.1765, yet this is in fact a strengthening of the NZD.
The way to make money is to sell at a higher price than that at which you bought
(i.e. buy low, sell
high). If we are speculating the NZD will strengthen, part (a) showed us this means the cost of the NZD
will rise. So we want a
position in the NZD.
Even ignoring the availability of a forward contract, we could speculate by taking a long position in
NZD (i.e. just buy some today at cost of AUD 0.8197). We hold the NZD, hope they strengthen, then
sell them at the higher price (i.e. convert them back to AUD).
The question wants us to speculate using the forward contract. Again, we would take a
contract on NZD at the six-month rate of 1.18. To profit from this speculation, we not only need the
NZD to strengthen, but to strengthen beyond the quoted forward rate of 1.18. This happens in part (d)
and we do in fact profit.
Entering a long forward contract at 1.18 gives us the right to buy NZD in six month's time at a fixed
price of AUD 0.8475.
The spot exchange rate at 31 October maturity is 1.3000. This represents a weakening of the NZD
(thus, our calculation below must show a loss). The quoted forward rate for delivery on 31 Oct must
also be 1.3000 (else trivial arbitrage opportunity – see tutorial question from next week). So the ‘price’
of a NZD is 0.7692. We must close out by selling NZD 100,000 at this low price.
(in May) Enter long forward contract
(in Oct) Close out by selling forward contract
Note: when we enter this long forward contract
money changes hands. It is just a contract which has
a notional value of $84,750. Likewise, when we close out by selling the contract, we do not receive the
notional value of $76,920. The only cashflow is us handing over $7,830.
If the spot exchange rate on 31 October is 1.05, the NZD has strengthened considerably. The price of a
NZD is AUD 0.9524.