A cross-rate forward outright is a type of foreign exchange contract that involves three currencies. It is a combination of two outright forward contracts with different base currencies but the same settlement date. For example, if a U.S. company wants to buy goods from a Japanese supplier and pay in Japanese yen, but it only has euros, it can use a cross-rate forward outright to lock in the exchange rate between euros and yen for a future date. This way, it can avoid the risk of unfavorable currency fluctuations and plan its budget more accurately.
To do this, the U.S. company would enter into two outright forward contracts: one to sell euros and buy U.S. dollars, and another to sell U.S. dollars and buy Japanese yen. The exchange rates for these contracts are determined by the spot rates and the interest rate differentials between the currencies. The cross-rate between euros and yen is then calculated by dividing the first contract rate by the second contract rate. This is the rate that the U.S. company would pay for its Japanese goods in euros on the settlement date.
A cross-rate forward outright can also be used for speculation or arbitrage purposes, if the market cross-rate differs from the calculated cross-rate. For example, if the market cross-rate between euros and yen is higher than the calculated cross-rate, the U.S. company can profit by buying euros and selling yen at the market rate, and then reversing the transaction at the calculated rate on the settlement date. This would result in a net gain of euros.
Basic Theory:
The basic theory behind cross-rate forwards outright involves the concept of arbitrage, where traders seek to profit from discrepancies in exchange rates between different currency pairs. In a cross-rate forward outright, two currencies are involved, and the forward rate is determined by the interest rate differentials between the two currencies.
Basic Theory:
The basic theory behind cross-rate forwards outright involves the concept of arbitrage, where traders seek to profit from discrepancies in exchange rates between different currency pairs. In a cross-rate forward outright, two currencies are involved, and the forward rate is determined by the interest rate differentials between the two currencies.
The formula for calculating the forward rate (F) is as follows:
![\[ F = S \times \left(1 + \frac{r_1}{n}\right)^n \div \left(1 + \frac{r_2}{n}\right)^n \]](https://excelcalculations.refrigeratordiagrams.com/wp-content/ql-cache/quicklatex.com-004f8bfc75ac8a970fea7331939afcde_l3.svg "Rendered by QuickLaTeX.com")
Where:
is the forward rate,
is the spot rate,
and 
are the interest rates of the two currencies,
is the number of compounding periods.
Procedures:
- Gather Information:
- Identify the spot exchange rate (S).
- Determine the interest rates for the two currencies (r1 and r2).
- Choose the number of compounding periods (n).
- Calculate the Forward Rate:
- Apply the formula to calculate the cross-rate forward outright.
Explanation:
Let’s consider a scenario involving the exchange rate between the US Dollar (USD) and the Euro (EUR).
- Spot Exchange Rate (S): 1 USD = 0.85 EUR
- Interest Rate in the US (r1): 2%
- Interest Rate in the Eurozone (r2): 0.5%
- Compounding Periods (n): 4
Excel Calculation:
Create an Excel table with the following columns:
| Item | Value |
|---|---|
| Spot Rate (S) | 0.85 |
| Interest Rate (r1) | 2% |
| Interest Rate (r2) | 0.5% |
| Compounding Periods | 4 |
| Forward Rate (F) | [Formula Result] |
In Excel, the formula for the Forward Rate (F) would be:
=F2 * (1 + C2/B2)^B4 / (1 + D2/B2)^B4
The calculated Forward Rate represents the agreed-upon rate for exchanging USD to EUR at a future date.
Result:
In the given scenario, the calculated Forward Rate is approximately 0.8617 EUR for 1 USD.
Other Approaches:
- Excel Goal Seek:
- Use the Goal Seek function in Excel to set the Forward Rate to a desired value by adjusting the interest rates.
- Data Tables:
- Create a data table in Excel to analyze how changes in interest rates affect the Forward Rate.
- Scenario Manager:
- Use the Scenario Manager in Excel to evaluate different scenarios by changing variables.
