Cross Rates and Forward Premium: CAIIB BFM Forex Arithmetic Guide

Cross rates and forward premium calculations sit at the core of the CAIIB Bank Financial Management forex arithmetic syllabus, and IIBF loves testing both in the same numerical question. If you can only quote USD against INR and USD against GBP, how do you price GBP against INR directly? That is the chain rule. And once you have a spot rate, how much extra do you pay for a forward contract three months out? That is the forward premium. This guide walks through both using illustrative bid-ask quotes, shows exactly how banks build merchant rates on top of interbank rates, and closes with five practice MCQs framed the way CAIIB actually asks them.

🔗 Cross Rates and the Chain Rule

A cross rate is the exchange rate between two currencies derived from their common rate against a third currency — almost always the US dollar. Banks do not maintain live two-way quotes for every currency pair on earth; instead they compute GBP/INR, EUR/JPY, or AUD/INR on the fly using the chain rule: multiply (or divide) the two USD-based rates through the common currency, keeping bid with bid and ask with ask.

Illustrative example: suppose USD/INR is quoted 83.20 / 83.24 (bid/ask) and GBP/USD is quoted 1.2650 / 1.2654. To find GBP/INR, chain the two quotes through USD:

Bid (GBP/INR) = bid(GBP/USD) × bid(USD/INR) = 1.2650 × 83.20 = 105.2480
Ask (GBP/INR) = ask(GBP/USD) × ask(USD/INR) = 1.2654 × 83.24 = 105.3319

So the derived cross quote is roughly 105.2480 / 105.3319 — the bank buys pounds at the lower figure and sells at the higher one. The rule to remember: when both quotes are expressed as "foreign currency per USD" or both as "USD per foreign currency" in the same direction, you multiply along the chain; when one is inverted relative to the other, you divide instead. Read the Exchange Rates and Forex Business chapter for the full inversion logic and additional worked pairs.

💡 Exam Tip: Always chain bid-with-bid and ask-with-ask. Mixing a bid rate from one leg with an ask rate from the other is the single most common error CAIIB numericals are designed to catch.

💱 Bid-Ask Spreads: Interbank vs Merchant Quotes

Every forex quote is really two numbers: the bid (the rate at which the quoting bank buys the base currency) and the ask or offer (the rate at which it sells). The bank always buys low and sells high — the spread between the two is its dealing margin. In the interbank market this spread is razor-thin, often just a handful of paise on USD/INR, because dealers are trading with each other on near-identical information and thin credit risk.

When a bank quotes a retail or corporate customer — a "merchant" in FEDAI/BFM terminology — it does not pass on the interbank rate as-is. It loads an additional exchange margin on top, decided by the bank's own board-approved forex policy, to cover operational cost, credit risk on the underlying trade, and profit. This is why the rate your branch quotes for a foreign remittance is always worse than the rate you see quoted on a treasury screen for the same moment.

The direction of the margin depends on which side of the deal the bank is on. If the customer is selling foreign currency to the bank (an exporter surrendering export proceeds), the bank applies its buying rate — interbank bid minus margin. If the customer is buying foreign currency from the bank (an importer remitting payment), the bank applies its selling rate — interbank ask plus margin. This two-sided margin loading is exactly what widens the merchant spread relative to the interbank spread, and it is a recurring numerical theme across the forex case studies chapter.

📈 Forward Premium and Discount: The Annualised Formula

A forward rate is simply today's agreed rate for a currency exchange that settles on a future date. When the forward rate for a currency is higher than its spot rate, that currency is said to be at a premium in the forward market; when it is lower, it is at a discount. Under interest rate parity, the currency of the higher-interest-rate country trades forward at a discount, and the currency of the lower-interest-rate country trades forward at a premium — this is the same interest-rate-differential logic tested alongside correlation and regression in banking in the ABM paper, since both rely on comparing two series over time.

CAIIB always wants the premium or discount expressed as an annualised percentage, using this formula:

Annualised Premium % = [(Forward Rate − Spot Rate) ÷ Spot Rate] × (12 ÷ Forward Period in Months) × 100

Illustrative example: spot USD/INR (mid) = 83.22, and the 3-month forward (mid) = 83.83. Applying the formula:

Premium % = [(83.83 − 83.22) ÷ 83.22] × (12 ÷ 3) × 100
= [0.61 ÷ 83.22] × 4 × 100
= 0.00733 × 4 × 100
≈ 2.93% per annum

Since the forward rate is higher, the dollar is at an annualised premium of roughly 2.93%, which equivalently means the rupee is at a discount of the same magnitude against the dollar. This is illustrative arithmetic only — always work with the actual quoted rates given in the question, never a memorised number.

⚠️ Common Mistake: Forgetting to multiply by (12 ÷ months) to annualise. A 3-month premium of 0.73% is NOT the annual figure — CAIIB numericals routinely dock marks for reporting the un-annualised rate.

🏦 Merchant Rates: TT Buying, TT Selling and Bill Rates

Once you can compute cross rates and forward premiums, the exam pivots to how banks actually price customer transactions. The core merchant rates are TT (telegraphic transfer) buying rate, TT selling rate, bill buying rate, and bill selling rate — each derived from the base interbank rate with a different margin and, for bills, an added interest/usance adjustment because a bill involves a time lag before the bank receives cover.

TT buying rate applies when the bank is crediting a customer's account against inward remittance already covered by the bank abroad — no usance involved, so it is simply interbank bid minus a small margin. TT selling rate applies when a customer buys foreign currency for outward remittance — interbank ask plus a small margin. Bill buying and selling rates additionally factor in the transit/usance period, since the bank's own funds are locked up until it is reimbursed, which is why an exporter negotiating a usance bill gets a rate marginally worse than a sight TT rate. Corporates raising forward cover for hedging inflows tied to external commercial borrowings in India encounter the same merchant-vs-interbank gap on every forward booking and cancellation.

Banks price and settle these deals under the framework set out in the RBI's Master Direction on Risk Management and Inter-Bank Dealings, which governs permissible forex derivative structures, cover requirements, and reporting for authorised dealers. Actual cover for large trade transactions is typically routed through correspondent arrangements, which is why the mechanics of nostro vostro and loro accounts sit right next to this topic in the BFM syllabus, and are worth revising in the same sitting. Import/export documentation nuances that ride on these rates are covered in the Facilities for Importers and Exporters chapter.

📌 Remember: The bank is always on the favourable side of every quote — it buys at the lower rate and sells at the higher rate, whether the deal is interbank or merchant. Every margin gets added in the bank's favour, never the customer's.

🧠 Practice MCQs: Cross Rates and Forward Premium

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✅ Conclusion: Practice the Arithmetic Until It's Reflex

Cross rates and forward premium questions reward speed and a clean method, not memorised numbers — the exam always gives you the quotes and expects you to apply the chain rule and the annualisation formula correctly under time pressure. Work through the illustrative examples above with pen and paper until the bid-with-bid, ask-with-ask discipline becomes automatic, then move on to full forward premium problems that mix in margins and usance periods. For the wider set of currently-tested BFM numbers and definitions, browse the CAIIB BFM latest updates roundup, revisit more forex topics on the Bank Financial Management tag page, and take a full-length mock from the CAIIB course to see how this arithmetic shows up alongside the rest of the paper.