How to work out the forward outright price from the bid/ask quotes?

Question

I'm facing this problem:

Spot AUD/USD is quoted at 0.7634/39; six-months swaps are 112.1/111.1; at what forward outright rate can a price taker sell USD value spot/6 months?

On the spot side, the market is willing to buy the base currency (AUD) at 0.7634 (best bid), and it is willing to sell the base currency at 0.07639 (best ask). The spread is 5 pips.

On the swap side, the thing is a bit more complicated. From my understanding, in a general swap contract:

• The buyer goes short on base currency (AUD) and long on counter currency (USD)
• The seller goes long on base currency (AUD) and short on counter currency (USD)

So, in our case the agent wants to sell USD, therefore she is the seller of the swap contract, matching the swap market on the buy-side. She will therefore sell a swap contract at 111.1 (best bid).

The formula to compute the forward outright rate is

$$ FOR = \text{Spot Price} \frac{1+(i_C \frac{\text{Days} }{360 } )}{1+(i_B \frac{\text{Days} }{360 } )} $$

where $i_C$ is the counter currency rate $i_B$ is the base currency rate

But actually I'm missing many inputs here, or I don't see how I can do it since the quotes I have for the swap don't look like rates. Is there anyone who has an idea on how to proceed? Thank you.

Answer 1

You wrote "the quotes I have for the swap don't look like rates".

FX swaps are quoted in terms of "forward points" which have to be added or subtracted from the spot quotation.

Sometimes the sign of the swap points is given explicitly. More often a quoting convention is followed that suppresses the negative signs if any. The quote you have is 112.1/111.1 which looks very strange, because the left side number (the bid) is larger than the right hand number (the ask), which seems impossible. This is a clue that the actual points are -112.1/-111.1 once the missing minus signs have been restored. Now it all makes sense.

In conclusion if Spot AUD/USD is quoted at 0.7634/39 and six-months swaps are -112.1/-111.1 it would mean that the 6 month forward is quoted 7634-112.1 pips i.e. 0.75219 on one side and 7639-111.1 i.e. 0.75279 on the other side.

Since you are a price-taker who wants to sell the counter currency and thus buy the base currency, you can do it at 0.75279.

(Another way to tell that the swap points are negative is that interest rates in the base currency (USD) are lower than in the quotation currency (AUD).)