CFA Level II · CFA Level II Exam

Currency Exchange Rates: Understanding Equilibrium Value: formula sheet

Full chapter guide

Key formulas

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.
Covered interest rate parity (forward rate): F(d/f) = S(d/f) × (1 + i(d)) ÷ (1 + i(f)); Quote is domestic per 1 foreign (price/base, base = foreign). Use the same time period for the rates and the forward, scaled for the tenor.
Forward premium or discount: F − S = S × (i(d) − i(f)) ÷ (1 + i(f)); If i(d) > i(f), the base (foreign) currency trades at a forward premium. The higher-rate currency trades at a forward discount.
Uncovered interest rate parity: E(S1) = S0 × (1 + i(d)) ÷ (1 + i(f)); Same form as CIRP but with the expected spot rate. Holds only if investors are risk neutral and have no risk premium.
Approximate UIRP: %ΔE(S) ≈ i(d) − i(f); Use only for small differences. Exact form is better when the exam gives precise numbers.
Absolute PPP: S(d/f) = P(d) ÷ P(f); Basket prices in each currency. Based on the law of one price and rarely holds exactly.
Relative PPP (exact): E(S1) = S0 × (1 + π(d)) ÷ (1 + π(f)); π is inflation over the period. The currency of the higher-inflation country is expected to depreciate.
Relative PPP (approximate): %ΔS ≈ π(d) − π(f); Quote in domestic per foreign: a positive result means the foreign currency appreciates.
Fisher effect: i = r + E(π); Nominal rate equals real rate plus expected inflation (approximate form).
International Fisher relation: i(d) − i(f) ≈ E(π(d)) − E(π(f)); Holds if real rates are equal across countries. It implies equal expected real returns.
Ex-ante version of PPP: E(S1) = S0 × (1 + E(π(d))) ÷ (1 + E(π(f))); Uses expected inflation. Combine with the Fisher relation to link to UIRP.
Uncovered interest rate parity: E(%ΔS) ≈ i(price currency) − i(base currency); With S = price currency per unit of base currency. A positive E(%ΔS) means the base currency is expected to appreciate and the price currency to depreciate. The higher-rate currency is expected to depreciate, whichever one it is. If i_price > i_base, the price currency is expected to depreciate. If i_base > i_price, E(%ΔS) is negative and the base currency is expected to depreciate.
Covered interest rate parity: F = S × (1 + i_price) ÷ (1 + i_base); Holds by arbitrage. The forward premium or discount approximately equals the interest differential. Exactly, F ÷ S − 1 = (1 + i_price) ÷ (1 + i_base) − 1. The higher-rate currency trades at a forward discount.
Carry trade return (unhedged, one period): R ≈ i_invest − i_fund + %ΔS_invest-currency; %ΔS here is the percentage change in the value of the investment currency measured in the funding currency, so a positive number means the investment currency gained. This is not the same sign convention as ΔS in the UIP formula when the investment currency is the price currency. Exact: (1 + i_invest)(1 + %ΔS) − (1 + i_fund) in funding-currency terms.
Break-even depreciation: %ΔS = −(i_invest − i_fund) = i_fund − i_invest (approx.); The investment currency can fall by the carry, i_invest − i_fund, before the carry is wiped out. The %ΔS figure is negative because it is a fall. It uses the same convention as the carry trade return formula: the change in the investment currency's value in funding-currency terms.
Forward rate bias condition: Under UIP: F = E(S future). With bias: E(S future) ≠ F; High-yield currencies trade at a forward discount but depreciate less than that on average.
Balance of payments identity: Current account + Capital account + Financial account = 0; Changes in official reserves are part of the financial account. In practice, a statistical discrepancy (errors and omissions) is needed for the identity to sum to zero. A current account deficit means a net financial account inflow.
Current account and national saving: Current account balance = Private saving + Government saving − Investment = S − I; A deficit means domestic investment exceeds national saving. Equivalent form: CA = (X − M) + net income and transfers.
Marshall-Lerner condition: |ε_X| + |ε_M| > 1; ε_X and ε_M are the price elasticities of export and import demand. If true, depreciation improves the trade balance once volumes adjust.
Mundell-Fleming summary (floating rates, high capital mobility): Expansionary fiscal → domestic currency appreciates; Expansionary monetary → domestic currency depreciates; Both expansionary (or both restrictive) → ambiguous; When fiscal and monetary policy are both expansionary, or both restrictive, their effects on the currency work in opposite directions, so the net result is ambiguous under high capital mobility; look at which effect the vignette says is stronger.
Mundell-Fleming with low capital mobility: Expansionary fiscal → currency depreciates (higher imports); Expansionary monetary → currency depreciates; Both expansionary → currency depreciates; Trade effects dominate because capital flows respond little to interest rate changes. The combined expansionary mix is not ambiguous here.
Policy mix: expansionary fiscal, tight monetary: High interest rates + strong domestic demand → capital inflows → domestic currency appreciates (strongly); Holds with high capital mobility. With low capital mobility, fiscal expansion raises imports and depreciates the currency.
Policy mix: tight fiscal, expansionary monetary: Low interest rates + weaker demand → capital outflows → domestic currency depreciates; The opposite of the case above.
Policy mix: both expansionary: Fiscal pushes rates up, monetary pushes rates down → currency effect ambiguous; usually weaker due to lower rates and inflation fears; Check the question for which effect the vignette emphasizes. Both tight is also ambiguous, with rates effects offsetting.
Dornbusch overshooting: Monetary expansion → immediate depreciation larger than long-run depreciation → gradual partial appreciation as prices rise; Needs sticky goods prices and PPP holding only in the long run.
Long-run effect of money supply change: Long-run % change in spot rate (domestic per foreign) ≈ % change in money supply (PPP holds in long run, real variables unchanged); Short-run change is bigger in size, with the same direction.
Real interest rate: Real rate ≈ nominal rate − expected inflation; Capital flows respond to real rate differentials, not nominal rates alone.
Sterilised intervention: Change in FX reserves offset by an opposite change in domestic securities, so monetary base is unchanged; Sterilisation does not change the money supply. Its effect works mainly through signalling and portfolio balance, and is usually weaker.
Unsterilised intervention: Selling FX reserves → domestic money supply falls → interest rates rise → currency is supported; Buying FX does the reverse: it raises the money supply and puts downward pressure on the currency. It conflicts with domestic monetary goals.
Reserve adequacy check: Reserves ÷ short-term external debt (or months of imports covered); A low ratio signals vulnerability. Compare with the thresholds the vignette gives; do not assume a universal cut-off.
Real exchange rate: Real rate = nominal rate (domestic per foreign) × foreign price level ÷ domestic price level; Under the domestic-per-foreign quote, a fall in the real rate is a real appreciation of the domestic currency, and a rise is a real depreciation. A persistent fall means the domestic currency is appreciating in real terms and may be overvalued.

Quick revision

Quote as price currency per 1 unit of base currency (P/B); inverting the quote gives the opposite pair.
A client buys the base currency at the dealer's offer and sells it at the dealer's bid.
Forward rate from covered interest rate parity: F = S × (1 + i_price) ÷ (1 + i_base), same period.
The currency with the higher interest rate trades at a forward discount in covered parity.
Absolute PPP says price levels are equal across countries when converted; relative PPP links currency changes to inflation differences.
Under uncovered interest rate parity, the expected currency change offsets the interest rate gap.
Forward rate bias means high-yield currencies often do not depreciate as much as parity implies, which is why carry trades can earn profits.
Carry trades carry crash risk: returns tend to be negatively skewed, with sharp losses when risk aversion spikes.
A current account deficit must be matched by a capital account surplus; persistent deficits can pressure the currency.
Policy mixes (Mundell-Fleming model, assuming high capital mobility): tight monetary with loose fiscal policy tends to strengthen the currency (high rates attract capital); loose monetary with tight fiscal policy tends to weaken it; both loose or both tight is ambiguous and depends on conditions. With low capital mobility, trade flows matter more and the outcomes differ, so check which assumption the vignette gives.
Crisis warning signs include fast credit growth, large current account deficits, falling reserves and heavy short-term foreign debt.
Always answer every question; there is no penalty for wrong answers.

Common mistakes

Mixing up the base currency, so a quote is read the wrong way round. 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. 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.
Flipping the quote and applying the ratio upside down. Fix: Write domestic = price currency, foreign = base currency before every calculation. The ratio is always (1 + price currency) ÷ (1 + base currency).
Using annual rates for a six-month or three-month forward. Fix: Scale the rate to the horizon first, for example annual rate × days ÷ 360 for an add-on rate, unless the question states otherwise.
Treating UIP as an observed fact and expecting the high-yield currency to depreciate. Fix: Remember CIP holds by arbitrage. UIP is a prediction that often fails, which is forward rate bias.
Getting the sign of the currency move wrong because of the quote direction. Fix: Write the quote as price/base first. A higher number means the base currency has gained. Then decide which currency you hold.
Saying a current account deficit always weakens the currency. Fix: Remember the deficit is financed by capital inflows. A strong appetite for the country's assets can keep the currency firm for years.
Mixing up Mundell-Fleming results for fiscal expansion under high and low capital mobility. Fix: High mobility: higher rates attract capital, so appreciation. Low mobility: higher imports dominate, so depreciation.
Saying monetary expansion causes only a one-time depreciation to the long-run level. Fix: Remember the order: jump past the long-run value, then reverse partway.
Assuming a larger fiscal deficit always weakens the currency. Fix: With mobile capital and tight money, the higher rates attract inflows and strengthen the currency. Weakness comes with low capital mobility or when the vignette cites debt or inflation fears.

Exam tips

Mark the base currency on every quote in the exhibit before you read the questions. Most wrong answers come from reading a quote the wrong way round.
For cross rates, check that the bid is below the offer. If it is not, you have inverted a side or used the wrong pairing.
The options in a forward value question usually include the undiscounted figure and the wrong sign. Calculate both the sign and the discount before you choose.
In real-rate questions, say aloud which currency is the base and what a rise in the rate means. Then decide which price index goes on top.
Questions come from the vignette, so look for the day-count, the term and whether quotes are bid-offer or midpoint before you start.
Write price/base next to every quote in the vignette before calculating. Most errors in this topic come from direction.
Know which condition is no-arbitrage (CIRP) and which are expectations-based (UIRP, relative PPP, international Fisher). Conceptual questions test this split.
Expect a question on what happens if a parity fails, such as the carry trade profiting when UIRP does not hold, or a real exchange rate that reverts toward PPP.