# Foreign Exchange Forward Contracts Page

## Foreign Exchange Forwards

Foreign Exchange forward contracts are transactions in which counterparties agree to exchange a specified amount of different currencies at some future date, with the exchange rate being set at the time the contract is entered into. The user is protected from adverse movements in future FX rates, but he also does not benefit from favourable movements.
Foreign Exchange forwards remove uncertainty and are therefore valid instruments for users to mitigate the downside foreign exchange risk for future transactions denominated in a foreign currency.
Foreign Exchange forward rates, Foreign Exchange spot rates, and interest rates are interrelated by the interest rate parity (IRP) principle.
This principle is based on the notion that there should be no arbitrage opportunity between the Foreign Exchange spot market, Foreign Exchange forward market, and the term structure of interest rates in the two countries.

Typical Pricing Function

 Variable Description Fxfwd fair forward FX rate (quoted in units of domestic currency per unit of foreign) Fxspot spot FX rate (quoted in units of domestic currency per unit of foreign) rd domestic interest rate (for term of forward) quoted on a simple interest basis rf foreign interest rate (for term of forward) quoted on a simple interest basis AFd domestic accrual factor AFf foreign accrual factor

Example

Given the following spot FX spot and money market rates, what should be the theoretical 90 day forward FX rate?

spot rate = 1.3500 CAD/USD

Canadian 90-day Libor = 4.50%

US 90-day Libor = 3.80%

answer:                         Fxfwd = 1.35 X (1 + ((90/365) * 0.045)) = 1.3521
(1 + ((90/360) * 0.038))

 Argument Description Sample Data Switch FX_spot spot price of underlying currency (domestic per 1 unit of foreign) 1.35 rate_dom domestic rate (for term of forward) 0.045 rate_for foreign rate (for term of forward) 0.038 d_s settlement date 23-Sep-03 d_del future delivery date 22-Dec-03 acc_dom accrual method for domestic rate 1 actual / 365 acc_for accrual method for foreign rate 2 actual / 360

Result

The fair forward FX rate is \$1.3521 CAD/USD.

The fair basis is \$0.0021, i.e., 21 basis points

Interest Rate Parity

Using the above example to illustrate the principles of IRP, if you borrowed \$100 CAD at 4.5%, bought USD on the spot market, invested the proceeds in the US at 3.80 %, and sold forward the same amount, you should not be able to extract any arbitrage proceeds from the process.

 1. Convert the CAD today (100/1.3500) = \$74.074 USD At the end of 90 days: 2. pay off loan 100 * (1+(0.045*90/365)) =\$101.11 CAD outflow 3. USD investment 74.07 * (1+(0.0380*90/360)) = \$74.778 USD inflow

The forward rate should be (101.11/74.778) = 1.3521 CAD/USD

If the forward rate is higher than this value, then you could make riskless profit by following the above strategy.Suppose the forward rate was 1.3600 CAD/USD. The profit you would make would be (74.778 * 1.3600) - (101.11) = \$0.588 CAD for every \$100 CAD you borrowed.By using \$1 million, your riskless profit would be \$5,880.00. This cannot persist very long in real markets.

If the forward rate was lower than 1.3521, then the reverse strategy can be used.
Suppose the forward rate was 1.3500.
You would then borrow \$100 USD, buy CAD on the spot market, and invest in the Canadian money market, and buy the USD forward to pay off the loan.
This is shown as follows:

 Convert to CAD today 100 * 1.3500 = \$135.00 CAD 90 days from today pay off loan 100 * (1 + (0.0380 * 90/360)) = 100.95 USD outflow CAD investment 135 * (1 + (0.0450 * 90/365)) = 136.50 CAD inflow purchase USD forward 136.50 / 1.3500 = 101.11 USD net profit (per \$100 USD) 101.11 - 100.95 = \$0.16 USD

### Quoting Conventions

The previous example was somewhat oversimplified.
There was no bid-ask spread in the spot FX rate and the loan and investment interest rates were assumed equal.
In reality, to calculate valid forward prices one needs to have the valid bid-ask prices of the spot rates, and separate loan and investment interest rates.

Forward rates can be quoted in two ways, as an "outright" quote, or as forward points (also called a swap rate).
The outright quote is simply a bid-ask price same as the spot market quotes.
The forward points are the amount that needs to be added to or subtracted from the spot rates.
The following illustrates the two quoting methods:

 spot rates 1.3500 - 1.3505 CAD/USD forward points 90 - 95 outright forward rates 1.3590 - 1.3600 CAD/USD

### Premiums and Discounts

As previously discussed, the forward rates are closely related to the spot rates and interest rates of the two countries. A result of the IRP theory is that for the country with the higher interest rate, its currency is weaker in the forward market than in the spot market. As shown in the previous example, the Canadian interest rate was higher than the US interest rate, and the resulting theoretical forward rate was 1.3521 CAD/USD, compared with the spot rate of 1.3500 CAD/USD. The terms premium and discount refer to whether the forward rates are higher or lower than the spot rates. A premium means the forward price is higher than the spot price and a discount means lower.
In this case the forward rate is then at a premium of 21 points.

In order to apply forward points to a spot rate to come up with an outright quote for the forward price,
one needs to know whether the forward points are premiums or discounts.
For premiums, bid forward points are added to bid spot prices and ask forward points are added to ask spot prices.
For discounts bid forward points are subtracted from ask spot prices and ask forward points are subtracted from bid spot prices.
If all this seems confusing, just remember the rule that the
bid-ask spreads of the forward price should always be greater than the spot price, and that the sum of the bid-ask spreads of the spot price and forward points should equal the spread of the forward price.
The bigger spread in the forward market can be viewed as compensation for the increased risk the market maker takes in the forward market relative to the spot market.

 Example of a premium: Spread spot rates 1.3500 - 1.3505 CAD/USD 5 points forward points (+90) - (+95) 5 points outright forward rates bid = 1.3500 + 0.0090 = 1.3590 ask = 1.3505 + 0.0095 = 1.3600 1.3590 - 1.3600 CAD/USD 10 points Example of a discount: Spread spot rates 0.7405 - .7410 USD/CAD 5 points forward points (-90) -(-95) 5 points outright forward rates bid = 0.7405 - 0.0095 = 0.7310 ask = 0.7410 - 0.0090 = 0.7320 quote = 0.7310 - 0.7320 CAD/USD 10 points

### Detailed Forward Rate Calculation

We will now provide sample calculations of both a premium and a discount forward price using more realistic data.Consider the following scenario:

 spot rate CAD/USD 1.3500 - 1.3506 spot rate USD/CAD 0.7404 - 0.7407 90 day Canadian interest rates 5.98 % investment 6.02 % loan 90 day US interest rates 3.92 % investment 3.98 % loan

Example of a forward premium calculation:

If a Canadian company needs to have USD in 90 days, it can buy USD forward, or pursue the following strategy.
Borrow CAD, convert to USD, invest in USD for 90 days.

 Canadian borrowing costs 1 + (0.0602 * (90/365)) = 1.01484 CAD Converting CAD to USD 1.3506 CAD Total cost 1.01484 * 1.3506 = 1.3706 CAD US investment income 1 + (0.0392 * (90/360)) = 1.0098 USD

The forward price required for the two strategies to break-even (i.e. no arbitrage) would be 1.3706 / 1.0098 = 1.3575 CAD/USD.
Note this is the forward ask price of the USD.
The inverse of this (1 / 1.3575 = 0.7366) is then the forward bid price of the CAD (i.e. sell USD / buy CAD).

CAD/USD forward points = 1.3575 - 1.3506 = +0.0069 (a premium)
USD/CAD forward points = 0.7366 - 0.7404 = -0.0038 (a discount)

Example of a forward discount calculation:

If a US company needs to have CAD in 90 days, it can buy CAD forward, or pursue the following strategy.
Borrow USD, convert to CAD, invest in CAD for 90 days.

 US borrowing costs 1 + (0.0398 * (90/360)) = 1.00995 USD Converting USD to CAD 0.7407 USD Total cost 1.00995 * 0.7407 = 0.7481 USD Canadian investment income 1 + (0.0598 * (90/365)) = 1.01475 CAD

The forward price required for the two strategies to break-even (i.e. no arbitrage) would be 0.7481 / 1.01475 = 0.7372 USD/CAD.
Note this is the forward ask price of the CAD.
The inverse of this (1 / 0.7372 = 1.3565) is then the forward bid price of the USD (i.e. sell CAD / buy USD).

USD/CAD Forward points = 0.7372 - 0.7407 = -0.0035 (a discount)
CAD/USD Forward points = 1.3565 - 1.3500 = +0.0065 (a premium )

 To summarise the results Spread Forward rate CAD/USD 1.3565 - 75 0.0010 Forward points CAD/USD (+0.0065) - (+0.0069) 0.0004 Forward rate USD/CAD 0.7366 - 72 0.0006 Forward points USD/CAD (-0.0035) - (-0.0038) 0.0003 Recall the spot rates Spot rate CAD/USD 1.3500 - 1.3506 0.0006 Spot rate USD/CAD 0.7404 - 0.7407 0.0003

As a check on the calculation, note that the spread of the spot plus the spread of the forward points equal the spread of the outright forward price.