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IBBC CAPITAL ACADEMY / 2027

Cross-rates, forward points and covered parity

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Build a cross-rate by canceling currency units and respecting bid/ask direction.
  • Calculate forward rates and interpret a premium without calling it a forecast.

Draft · approximately 45 minutes, excluding further revision.

Cancel units before multiplying numbers

If one euro costs 1.10 US dollars and one US dollar costs 150 yen, the yen price of one euro is 1.10×150=165. If quotes are instead USD per EUR and USD per JPY, divide the first by the second. A reciprocal quote inverts and reverses bid and ask: if a dealer buys foreign at 1.10 and sells at 1.11 domestic per foreign, the reciprocal bid is 1/1.11 and ask is 1/1.10.

A synthetic cross bid reflects what the dealer pays to buy the base currency through the intermediate currency; the ask reflects the cost of selling it. With compatible quotes, cross bid can multiply bids and cross ask can multiply asks. Do not multiply arbitrary displayed numbers without tracing the actual conversion path. An apparent triangular difference is not an arbitrage unless executable bid/ask prices, costs and timing leave a profit.

Forward pricing follows a financing comparison

For S quoted domestic per foreign and matched annual-effective rates, covered parity is F=S(1+rd)^T/(1+rf)^T. It equates appropriately funded and currency-hedged investment paths under the model. Credit, collateral, funding, capital and transaction constraints can create deviations from the simple textbook relationship. Forward pricing is not a statement that the future spot must equal F.

Forward points are a quotation increment, not always a percentage. State the point scale. For a four-decimal quote, +25 points at scale 0.0001 means add 0.0025. A foreign currency trades at a forward premium in domestic-per-foreign terms when F>S; the simple annualized premium is (F/S−1)/T under that convention. Reversing the quote changes the premium/discount interpretation.

Formula and assumptions

Cross-rate: cancel currency units; reciprocal bid=1/ask; F=S(1+rd)^T/(1+rf)^T; forward=spot+points×point scale

A cross spread and a forward quote

  1. USD per EUR bid/ask=1.10/1.11; JPY per USD=150/151. Synthetic JPY per EUR bid=165 and ask=167.61.
  2. Separately, spot USD per EUR=1.10 and +25 forward points at 0.0001 per point give F=1.1025. Over one year, simple premium=1.1025/1.10−1=0.2273%.
  3. For a different one-year parity example, rd=4%, rf=2% and S=1.10 imply F=1.121569. Different assumptions explain the different forward; do not mix the two examples.

Calculation lab

Errors to catch

  • Inverting a spread without swapping bid and ask.
  • Treating forward points as percentages or forward rates as guaranteed future spots.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.