Forward Rates & Cross Rates

Forward rates and cross rates are essential concepts in foreign exchange management for bankers. Forward contracts help businesses and banks hedge against exchange rate risk, while cross rates enable currency conversion when a direct quote is not available. This is a calculation-heavy topic in the JAIIB exam, requiring both conceptual understanding and numerical proficiency.

A forward rate is the exchange rate agreed upon today for a foreign exchange transaction that will be settled at a specified future date (beyond the spot date).

Key Features of Forward Contracts

• Customised: Tailored to the parties' needs (amount, maturity, currency)
• OTC traded: Negotiated directly between parties (not on an exchange)
• Binding: Both parties are obligated to execute at maturity
• Hedging tool: Protects against adverse exchange rate movements

Annualised Premium/Discount Formula

Premium/Discount % = [(Forward Rate - Spot Rate) / Spot Rate] x (12/n) x 100

where n = number of months of the forward contract

Worked Example 1: Forward Premium

Spot Rate (USD/INR) = Rs 83.00, 3-month Forward Rate = Rs 83.75

Premium = 83.75 - 83.00 = Rs 0.75

Annualised Premium = (0.75 / 83.00) x (12/3) x 100 = 0.00904 x 4 x 100 = 3.61% p.a.

Worked Example 2: Forward Discount

Spot Rate (GBP/INR) = Rs 105.00, 6-month Forward Rate = Rs 103.50

Discount = 105.00 - 103.50 = Rs 1.50

Annualised Discount = (1.50 / 105.00) x (12/6) x 100 = 0.01429 x 2 x 100 = 2.86% p.a.

Using Interest Rate Parity (IRP)

The forward rate is determined by the interest rate differential between two countries:

Forward Rate = Spot Rate x [(1 + r_home x n/12) / (1 + r_foreign x n/12)]

where:

• r_home = domestic interest rate (annualised)
• r_foreign = foreign interest rate (annualised)
• n = number of months

Worked Example 3: Forward Rate from Interest Rates

Spot USD/INR = Rs 83.00, Indian interest rate = 7% p.a., US interest rate = 5% p.a., Period = 6 months

Forward Rate = 83.00 x [(1 + 0.07 x 6/12) / (1 + 0.05 x 6/12)]

= 83.00 x [(1 + 0.035) / (1 + 0.025)]

= 83.00 x [1.035 / 1.025]

= 83.00 x 1.00976

= Rs 83.81

Since the forward rate (83.81) > spot rate (83.00), USD is at a forward premium against INR.

In interbank markets, forward rates are quoted as swap points (pip differences from spot):

Forward Rate = Spot Rate +/- Swap Points

Example

Spot USD/INR = 83.00/83.05, 3-month swap points = 25/30

Since swap points are ascending (25 < 30):

• 3-month Forward Buying = 83.00 + 0.25 = 83.25
• 3-month Forward Selling = 83.05 + 0.30 = 83.35

A cross rate is the exchange rate between two currencies, calculated through a third (common) currency — typically the US Dollar.

When to Use Cross Rates

• When a direct quote between two currencies is not available
• Example: To find GBP/JPY rate when only GBP/USD and USD/JPY rates are available

Calculating Cross Rates

Method 1: Both rates quoted against USD

If USD/INR = 83.00 and USD/JPY = 150.00

Then INR/JPY = USD/JPY / USD/INR = 150.00 / 83.00 = 1.807

Or JPY/INR = USD/INR / USD/JPY = 83.00 / 150.00 = 0.5533

Method 2: One rate is USD/X and the other is Y/USD

If GBP/USD = 1.27 and USD/INR = 83.00

Then GBP/INR = GBP/USD x USD/INR = 1.27 x 83.00 = Rs 105.41

Worked Example 4: Cross Rate with Bid-Ask Spread

Given:

• USD/INR = 83.00/83.10 (bid/ask)
• EUR/USD = 1.0850/1.0860 (bid/ask)

Calculate EUR/INR:

EUR/INR (bid) = EUR/USD bid x USD/INR bid = 1.0850 x 83.00 = 90.055

EUR/INR (ask) = EUR/USD ask x USD/INR ask = 1.0860 x 83.10 = 90.245

So EUR/INR = 90.055 / 90.245

To calculate a forward cross rate:

1. Calculate the forward rate for each currency against the common currency (USD)
2. Then compute the cross rate using the forward rates

Example

3-month forward USD/INR = 83.80, 3-month forward USD/JPY = 149.50

3-month forward INR/JPY = 149.50 / 83.80 = 1.784

If the calculated cross rate differs from the quoted cross rate, an arbitrage opportunity exists:

1. Calculate the theoretical cross rate
2. Compare with the actual quoted rate
3. If different, buy where cheap and sell where expensive
4. The profit is the arbitrage gain (before transaction costs)

Example

Given: USD/INR = 83.00, EUR/USD = 1.0850 Theoretical EUR/INR = 1.0850 x 83.00 = 90.055

If the actual EUR/INR quote is 90.50:

• EUR is overvalued against INR in the direct quote
• Arbitrageur can sell EUR for INR at 90.50 and buy EUR through USD at 90.055
• Profit = 90.50 - 90.055 = Rs 0.445 per EUR

Combines spot and forward transactions with borrowing/lending to exploit interest rate differentials:

1. Borrow in low-interest-rate currency
2. Convert to high-interest-rate currency at spot rate
3. Invest in high-interest-rate country
4. Simultaneously sell investment proceeds forward
5. If profit exceeds transaction costs, arbitrage exists

• Forward premium: Forward rate > Spot rate; Forward discount: Forward rate < Spot rate
• Annualised formula: [(Forward - Spot) / Spot] x (12/n) x 100
• Forward rate is determined by interest rate differential (Interest Rate Parity)
• If domestic interest rate > foreign rate, home currency trades at a forward discount
• Swap points ascending (low/high) = add to spot (premium); descending = subtract (discount)
• Cross rate = Exchange rate derived through a third currency (usually USD)
• For cross rates: if both against USD, divide; if one is X/USD and other is USD/Y, multiply
• With bid-ask spreads: Bid cross = bid x bid; Ask cross = ask x ask
• Arbitrage exists when theoretical cross rate differs from actual quoted rate
• Forward contracts are OTC, customised, and binding — different from exchange-traded futures
• FEDAI governs forward contract practices in India