Let's explore what determines FX forward prices.

The first thing to note is that like any forward contract, the forward rate is not a prediction of the spot FX rate at the maturity of the forward contract. Forward prices are at the most fundamental level driven by supply and demand. However, there's a theoretical foundation for their calculation rooted in the no arbitrage principle. The no arbitrage principle essentially states that if there are two or more ways to achieve the same financial outcome or risk profile, the prices of these alternatives must be identical. Why? Because if one route is more expensive than the other market participants could sell the more expensive option, buy the cheaper one, and lock in a risk-free profit. Such arbitrage opportunities should not exist in efficient markets.

To understand how this applies to FX forwards, let's consider an example.

Imagine an investor wants to lock in the price to purchase 100 million Euros against US Dollars six months forward.

There are two primary alternatives available.

The first alternative is to call a market maker and ask for a six month euro Dollar forward quote. This is the most convenient and commonly used approach. This will allow the investor to trade a fixed amount of US Dollars for a fixed amount of Euros in six months time.

This would result in the investor delivering US Dollars and receiving Euros in six months time. But what should this rate be? If there were an alternative route to reaching, having a known amount of US Dollars in exchange for a known amount of Euros in six months time? Well, that relationship between those amounts would need to be the same as the quote FX forward rate for no arbitrage to hold.

And there is an alternative way to that ending position i.e. short US Dollars and long Euros. Which is to replicate the forward trade manually. To do this, the investor would first buy Euros in the spot market today paying US Dollars. If the spot price is 1.0950, the investor would pay 109.5 million US for 100 million Euros. However, because the investor likely doesn't have $109.5 million on hand, they would need to borrow this amount for six months. Incurring interest, meaning they are short US Dollars in six months time. Meanwhile, the 100 million Euros they receive would be invested for six months earning interest, meaning they are long Euros in six months time.

Both methods ultimately achieve the same outcome in six months time. The investor holds or is long Euros and owes or is short US Dollars. According to the no arbitrage principle, the forward price offered by the market maker and the price derived from this replication strategy must match. So to calculate the forward price, we need to determine the effective exchange rate necessary to change the known US Dollars in six months time into the known Euro amount in six months time.

To work through the numbers in detail here, we need to know more than just the spot rate of 1.095. Let's assume the six month US Dollar interest rate is 5.395%, and the six month Euro interest rate is 3.7549%. And let's also assume the forward period is 182 days, and both US Dollar and Euro use an actual over 360 day count convention.

First, we calculate the amount owed in US Dollars in six months time, also referred to as the future value of the US Dollar borrowing. The investor borrows $109.5 million, so we multiply that by one plus the US Dollar interest rates times 182 over 360. This gives us 112.4866 million Dollars.

Next, we calculate the amount of Euros received back that was initially invested, also referred to as the future value of the Euro investments. The investor invests 100 million Euros, so we multiply that by one plus the Euro interest rates times 1 8 2 over 360. This gives us 101.8983 million Euros.

Finally, we calculate the implied forward price by dividing the future value of US Dollars borrowing by the future value of Euro investments. Dividing 112.4866 by 101.8983 gives us a theoretical forward price of 1.10391.

It's important to note though that this theoretical price and more generally, the no arbitrage principle Is based on a couple of simplifying assumptions like for example, identical interest rates for borrowing and investing, no restrictions in borrowing and or investment, and the absence of transaction costs. In practice forward prices might therefore deviate from the theoretical level as they reflect market reality.

If we restate the steps carried out so far as a formula, we arrive at a widely referenced equation. The Interest Rate Parity Formula. The formula states that the forward FX rate equals the spot FX rate adjusted by the interest rate differential between the two currencies. Mathematically, it's expressed as FX forward rate equals FX spot rate multiplied by one plus the interest rate in the quota currency, multiplied by the number of days in the forward period, divided by the basis, all divided by one plus the interest rate in the base currency times by the number of days in the forward period divided by their basis. Here quoted represents the US Dollar in our example and base represents the Euro. The basis for both currencies is 360 days.