Currency Quotes, Forward Pricing, and Triangular Arbitrage

How Level II tests FX quotations, bid-offer spreads, forward premiums, triangular arbitrage, and mark-to-market value.

Level II economics often begins with what looks like FX market vocabulary and quickly turns into a pricing problem. The exam wants to know whether you can read the quotation correctly, identify which side of the market applies, and decide whether the currency relationship is merely quoted differently or is actually mispriced.

Why This Lesson Matters

Candidates usually lose points here in two ways:

  • they use the wrong bid or offer because they never decide which currency they are buying
  • they see three exchange rates and do not test whether a triangular arbitrage actually exists

The stronger answer slows down and reads the trade direction first.

Start With The Quotation Before Doing The Math

What to identify firstWhy it matters
Base currency and price currencyTells you what one unit of the base currency costs
Bid and offer sideTells you whether you are selling or buying the base currency
Spot versus forward quoteTells you whether the question is about immediate exchange or a future commitment

The exam often hides the real work inside quotation format rather than difficult arithmetic.

Bid-Offer Logic Is A Direction Problem

For a quoted currency pair:

  • the bid is the dealer’s price to buy the base currency
  • the offer is the dealer’s price to sell the base currency

The bid-offer spread is:

$$ \text{Spread} = \text{Offer} - \text{Bid} $$

If you want to…Use the…
Buy the base currencyOffer
Sell the base currencyBid
Measure transaction cost in quote formBid-offer spread

That sounds basic, but Level II still tests it because one wrong side of the market ruins the rest of the vignette.

Forward Premium Or Discount Comes From Spot-Versus-Forward Comparison

A common annualized approximation is:

$$ \text{Forward premium or discount} \approx \left(\frac{F_0}{S_0}-1\right)\frac{12}{n} $$

where (n) is the number of months to maturity.

If the forward is above spotThe base currency is at a forward premium
If the forward is below spotThe base currency is at a forward discount

Level II often tests interpretation rather than memorization. The candidate has to explain what the forward relationship implies, not just compute the sign.

Triangular Arbitrage Exists Only When The Cross-Rate Chain Breaks

Three exchange-rate quotations should be mutually consistent. If they are not, the candidate should be able to identify a sequence of exchanges that locks in a profit.

StepWhat to check
1Start with one currency and translate through the quoted pairs using the correct bid or offer at each step
2Return to the original currency through the third pair
3Compare the ending amount to the starting amount

If the ending amount is larger after respecting the quoted dealing sides, an arbitrage opportunity exists.

The exam often gives rates that look close enough to lull the candidate into skipping the chain.

Mark-To-Market Value Of A Forward Is Separate From Its Original Price

At initiation, a forward contract is typically set near zero value. Later, as spot and forward conditions move, the contract gains or loses value.

For a long position, a common intuition is:

$$ V_t = \text{current forward value of what is received} - \text{present value of the contracted payment} $$

The exact computation can be framed in several equivalent ways, but the exam is mainly testing whether you understand the distinction between:

  • the original forward price
  • the current market forward price
  • the current contract value

How CFA-Style Questions Usually Test This

  • by forcing the candidate to choose the correct side of the market quote
  • by asking for a forward premium or discount and then asking what it means
  • by providing three currency quotes and asking whether a triangular arbitrage profit exists
  • by asking for the mark-to-market value of an existing forward after rates have moved

Mini-Case

A vignette gives three dealer quotes for USD/EUR, EUR/JPY, and USD/JPY. A candidate plugs the midpoint quotes into a cross-rate comparison and concludes that arbitrage exists.

That answer is weak because it ignores the trading side of the market.

A stronger answer applies bid and offer prices consistently through the entire exchange chain. On Level II, the direction of the trade is part of the question, not just a footnote.

Common Traps

  • using midpoint quotes when the dealer spread matters
  • mixing up base and price currency
  • calling a forward premium an expected appreciation without checking the broader framework
  • valuing an existing forward as if it were still at initiation

Sample CFA-Style Question

An investor wants to buy the base currency in a quoted pair. Which dealer price applies?

Best answer: The offer.

Why: The dealer sells the base currency at the offer, so the investor buying it must transact on that side of the market.

Continue In This Chapter

Revised at Thursday, April 9, 2026