Expected Exchange Rate Calculator
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Projected Results
Expected Future Exchange Rate
—
—
Forward Premium / Discount
—
Annualized percentage difference
Understanding Expected Exchange Rates
The Expected Exchange Rate Calculator uses the theory of Interest Rate Parity (IRP) to forecast future currency exchange rates. In international finance, the difference in interest rates between two countries determines the "forward" exchange rate, which is often used as an unbiased predictor of the future spot rate.
How the Calculation Works
The calculation assumes that investors should not be able to earn arbitrage profits by borrowing in a low-interest currency, converting it, and lending it in a high-interest currency without the exchange rate adjusting to offset the gain. This relationship is defined by the following formula:
F = S × [ (1 + rq)^t / (1 + rb)^t ]
- F: The Expected Future (Forward) Rate.
- S: The Current Spot Exchange Rate.
- rq: Interest rate of the Quote Currency (Domestic).
- rb: Interest rate of the Base Currency (Foreign).
- t: Time period in years.
Quote vs. Base Currency
In a currency pair like EUR/USD = 1.10:
- EUR is the Base Currency (the unit being bought/sold).
- USD is the Quote Currency (the price being paid).
If the interest rate on the Quote Currency (USD) is higher than the Base Currency (EUR), the market expects the Base Currency to trade at a "premium" (higher exchange rate) in the future to offset the interest differential, although technically, the high-interest currency often depreciates in the long run according to Uncovered Interest Parity.
Factors Influencing Future Rates
While this calculator focuses on Interest Rate Parity, real-world exchange rates are influenced by multiple factors:
- Inflation Differentials (Purchasing Power Parity): Countries with consistently lower inflation generally see their currency value appreciate.
- Current Account Deficits: A country spending more on foreign trade than it is earning may see its currency depreciate.
- Public Debt: Large-scale debt can encourage inflation, putting downward pressure on the currency.
- Terms of Trade: If export prices rise faster than import prices, the currency tends to strengthen.
Example Calculation
Let's assume the following market conditions:
- Spot Rate (GBP/USD): 1.2500
- US Interest Rate (Quote): 5.0%
- UK Interest Rate (Base): 3.0%
- Time Horizon: 1 Year
Using the formula:
Expected Rate = 1.2500 × (1.05 / 1.03) ≈ 1.2743
In this scenario, because the US interest rate is higher, the GBP is expected to appreciate against the USD in the forward market to equate the returns.
function calculateExchangeRate() {
// Get Input Values
var spotRate = parseFloat(document.getElementById('spotRate').value);
var quoteRate = parseFloat(document.getElementById('quoteInterestRate').value);
var baseRate = parseFloat(document.getElementById('baseInterestRate').value);
var timeValue = parseFloat(document.getElementById('timeValue').value);
var timeUnit = document.getElementById('timeUnit').value;
// Validation
if (isNaN(spotRate) || isNaN(quoteRate) || isNaN(baseRate) || isNaN(timeValue)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (spotRate = 0 ? "+" : "";
document.getElementById('rateChangeResult').innerText = sign + percentageChange.toFixed(2) + "% Change";
document.getElementById('rateChangeResult').style.color = percentageChange >= 0 ? "#38a169" : "#e53e3e";
// Premium calculation display
var premiumText = percentageChange >= 0 ? "Premium" : "Discount";
document.getElementById('premiumResult').innerText = sign + percentageChange.toFixed(2) + "% (" + premiumText + ")";
document.getElementById('premiumResult').style.color = percentageChange >= 0 ? "#38a169" : "#e53e3e";
// Interpretation Logic
var baseCurrencyName = "Base Currency";
var quoteCurrencyName = "Quote Currency";
var interpretation = "";
if (quoteRate > baseRate) {
interpretation = "Because the Quote Currency interest rate (" + quoteRate + "%) is higher than the Base Currency rate (" + baseRate + "%)" +
", the Base Currency is trading at a Forward Premium. Interest Rate Parity suggests the exchange rate should rise to " + expectedRate.toFixed(4) + ".";
} else if (baseRate > quoteRate) {
interpretation = "Because the Base Currency interest rate (" + baseRate + "%) is higher than the Quote Currency rate (" + quoteRate + "%)" +
", the Base Currency is trading at a Forward Discount. Interest Rate Parity suggests the exchange rate should fall to " + expectedRate.toFixed(4) + ".";
} else {
interpretation = "Interest rates are identical. The expected exchange rate remains neutral relative to the spot rate.";
}
document.getElementById('interpretationText').innerText = interpretation;
}