Foreign Exchange Market Concepts for CFA Level II

Understand Foreign Exchange Market Concepts

Key formulas to remember

Quote convention

A/B = units of A per 1 unit of B (B is the base currency)

The base currency is the one in the denominator. A rise in A/B means the base currency appreciated.

Inverting a quote

bid(B/A) = 1 ÷ offer(A/B); offer(B/A) = 1 ÷ bid(A/B)

Bid and offer swap when you invert. Never invert each side onto itself.

Cross rate (midpoint)

A/C = (A/B) × (B/C)

Arrange the quotes so B cancels. If a quote is the wrong way round, invert it first.

Cross rate bid-offer, both legs multiplied

bid A/C = bid A/B × bid B/C; offer A/C = offer A/B × offer B/C

Use this when the two quotes chain directly without inversion.

Cross rate bid-offer, one leg inverted

For A/C = (X/C) ÷ (X/A): bid A/C = bid(X/C) ÷ offer(X/A); offer A/C = offer(X/C) ÷ bid(X/A)

Write the cross as a ratio, such as (X/C) ÷ (X/A). The bid takes the bid of the numerator divided by the offer of the denominator. The offer takes the offer of the numerator divided by the bid of the denominator.

Percentage change in base currency

%Δ base = S1/S0 − 1, where S is price currency per base

The price currency changes by S0/S1 − 1, which is not the negative of the base change.

Forward points to forward rate

F = S + points ÷ scale factor

The scale is usually 10,000, and 100 for yen quotes. Points can be negative.

Forward rate from interest rates

F(A/B) = S(A/B) × (1 + i_A × t) ÷ (1 + i_B × t)

A is the price currency and B the base. Rates are for the term t, with the day-count the question gives. The base currency is at a premium when i_A > i_B.

Mark-to-market value of a forward (long base)

Value = (F_t − F_0) × contract size ÷ (1 + i_A × days remaining ÷ 360)

F_t is the current forward price for the remaining term. F_0 is the original forward price. i_A is the price-currency rate. The value is in price currency. A short position has the opposite sign.

Real exchange rate (domestic/foreign)

Real S(d/f) = S(d/f) × CPI_f ÷ CPI_d

A rise means foreign goods became more expensive relative to domestic goods. The currency is the base, so the foreign currency appreciated in real terms.

Change in real exchange rate

Real_t ÷ Real_0 = (1 + %Δ S) × (1 + π_f) ÷ (1 + π_d)

S is domestic per foreign. π is inflation over the same period.

Nominal effective exchange rate index

NEER_t = 100 × Π (S_i,t ÷ S_i,0)^w_i

Use a weighted geometric average of bilateral rates, with weights from trade shares. Quote every rate as foreign per domestic so that a rise means domestic appreciation. A real effective rate also adjusts for relative price levels.

How to solve Foreign Exchange Market Concepts questions

1. 1Find the rates in the exhibit and write each one as A/B with the base currency marked. Note whether it is spot or forward, and bid-offer or midpoint.
2. 2Identify what the question wants: a quote, a cross rate, a percentage change, a forward value or a real rate. State the answer's quote direction (for example JPY/EUR) before you calculate.
3. 3For cross rates, write the target as a product or ratio of the given quotes so the unwanted currency cancels. Invert quotes where needed.
4. 4For bid-offer, take the worst side for the dealer on each leg. When you multiply, use bid × bid and offer × offer. When you divide, use bid ÷ offer for the bid and offer ÷ bid for the offer. Check that bid < offer.
5. 5For forward value, work out F_t − F_0 for the position held (long base gains if F_t is higher). Use the offsetting side of the quote if bid-offer is given. Multiply by the size, then discount at the price-currency rate over the days remaining.
6. 6For real or effective rates, check which currency is the base and which price index goes on top. Convert changes using (1 + change) ratios rather than simple subtraction.
7. 7Check that the answer's currency and direction match the question, and that the size is sensible against the spot rate.

Quickest way: Cancel the units, then pick the side

Common mistakes in Foreign Exchange Market Concepts

• Mixing up the base currency, so a quote is read the wrong way round.

  A/B is easy to read as 'A to B' or 'A in terms of B' when the base is the denominator.

  Fix: Say it aloud: A/B is A per one B. Mark the base currency before using any quote.

• Inverting a bid-offer quote and keeping each side where it was.

  Students invert both numbers separately and keep the order.

  Fix: The inverse of the offer is the new bid, and the inverse of the bid is the new offer. After inverting, bid must still be below offer.

• Using bid × offer, or the wrong side, in a cross rate.

  There is no rule in the head about which side applies, so students mix sides.

  Fix: Use the same side when multiplying. When dividing, the bid divides by the offer and the offer by the bid. The cross spread must come out wider than each leg.

• Discounting a forward's value at the base-currency rate, or not discounting at all.

  The gain is paid at maturity but is measured in the price currency.

  Fix: Discount (F_t − F_0) × size at the price-currency rate for the remaining days. Always use the remaining term, not the original term.

• Getting the sign wrong on forward value.

  Students do not keep track of whether the position is long or short the base currency.

  Fix: A long base position gains when the forward price rises. For short positions, flip the sign. A positive value is an asset for the party you are valuing.

• Flipping the CPI ratio in the real exchange rate.

  The formula is memorised without the quote direction.

  Fix: With S as domestic per foreign, real S = S × CPI_foreign ÷ CPI_domestic. If the nominal rate does not change and foreign prices rise faster, foreign goods are more expensive.

Worked examples