11.1 Foreign Exchange Markets

Foreign Exchange Markets

FMP–9 is the FX toolkit for FRM Part I: how rates are quoted, how forwards and swaps are structured, which corporate exposures matter, and which parity relationships pin down (or fail to pin down) forward and expected spot rates. Almost every multi-currency risk vignette on the exam traces back to these mechanics.

Spot, Forward, and Futures Quotes

An FX quote states how many units of one currency (the price currency / quote currency) buy one unit of another (the base currency). In a EURUSD quote of 1.1000, one euro costs 1.1000 U.S. dollars—EUR is the base, USD is the price currency.

Bid-ask is always from the dealer’s perspective: the dealer buys the base currency at the bid and sells it at the ask. A EURUSD quote of 1.0998 / 1.1002 means the dealer buys EUR at 1.0998 USD and sells EUR at 1.1002 USD. A customer selling EUR receives the bid; a customer buying EUR pays the ask. The spread (here 4 pips) is a transaction-cost and liquidity signal: wider in stress, thin pairs, and odd sizes.

Pip conventions: for most USD pairs quoted to four decimals, 0.0001 is one pip; JPY pairs often use two decimals (0.01). Mid = (bid + ask) / 2 is used in analysis; executable prices are always on the side that hurts you.

Worked example: round-trip cost

Spot EURUSD = 1.0998 / 1.1002. A corporate buys EUR 5 million (pays ask), then later sells the same EUR (receives bid), with an unchanged quote.

Cost of round trip ≈ 5,000,000 × (1.1002 − 1.0998) = $2,000.

If the mid moved favorably by more than the spread, the firm can still profit—but the spread is a hurdle that must be cleared before economic P&L turns positive.

Outright Forwards Versus FX Swaps

An outright forward is a single forward commitment: exchange notional at a future date at an agreed rate F. It is the natural hedge for a known future receivable or payable.

An FX swap is a package: buy (sell) the base currency spot and simultaneously sell (buy) it forward, or roll two forward dates. The economic driver is usually the interest differential, not a directional FX bet. Banks use swaps to fund foreign-currency books and to warehouse client flows.

Swap points (forward points) = F − S, often quoted in pips. If the base currency trades at a forward premium, F > S; at a forward discount, F < S. Under covered interest parity (below), the higher-interest currency trades at a forward discount.

Transaction, Translation, and Economic Risk

Corporate FX risk is not one number—it is three distinct exposures.

Transaction hedges protect cash. Translation hedges protect accounting optics and sometimes covenant ratios—but may create real cash P&L if forwards settle while the accounting exposure is non-cash. Economic exposure is the hardest: a permanent stronger home currency can erode export competitiveness even with no booked receivable today.

Multi-currency option hedges

When exposure size or timing is uncertain (bids, contingent M&A, volume risk), options preserve upside while capping downside. A USD-based exporter expecting EUR receivables might buy EUR put / USD call protection. Multi-currency books sometimes use option baskets, worst-of/best-of, or separate puts on each currency with a shared premium budget. Relative to forwards, options cost premium upfront but avoid locking in an unfavorable rate if the exposure fails to materialize (e.g., lost bid).

Natural hedges matter: match currency of revenues and costs; finance foreign assets in local currency; net group exposures before buying derivatives.

Determinants of Exchange Rates

Short- and medium-run FX drivers include:

1. Interest-rate differentials — capital flows toward higher real (and often nominal) yields, all else equal.
2. Inflation differentials — via purchasing-power parity over longer horizons.
3. Growth, trade, and current-account balances — affect supply/demand for currencies.
4. Risk premia and safe-haven flows — USD, JPY, CHF often bid in stress.
5. Policy and intervention — central-bank rates, QE, capital controls, FX intervention.
6. Terms of trade / commodity prices — for commodity currencies (AUD, CAD, NOK).

No single factor dominates every day; exam questions usually isolate one channel (e.g., “home rates rise unexpectedly → home currency tends to appreciate in the short run”).

Purchasing-Power Parity (PPP)

Absolute PPP says the exchange rate should equal the ratio of price levels: S (price/base) ≈ P_price / P_base. Relative PPP is more usable: the percent change in the spot rate approximates the inflation differential.

Relative PPP (price currency per base):

%ΔS ≈ π_price − π_base

If U.S. inflation exceeds euro-area inflation, EURUSD (USD per EUR) tends to rise over time—more dollars per euro—so the dollar depreciates. PPP is a long-run anchor, not a tight short-run predictor; sticky prices, barriers, and risk premia create persistent gaps.

Worked PPP sketch

U.S. inflation = 4%, euro-area inflation = 2%. Relative PPP suggests EURUSD increases by about 2% per year (dollar weakens vs euro). If spot is 1.10, a rough one-year PPP-consistent level is 1.10 × 1.02 = 1.122.

Nominal Versus Real Exchange Rates and Interest Rates

The nominal exchange rate is the quoted market rate. The real exchange rate adjusts for relative price levels (competitiveness).

Roughly: real S ≈ nominal S × (P_base / P_price), with definition matching the quote convention used in the question.

Similarly, real interest ≈ nominal interest − expected inflation. Capital flows respond more cleanly to real rate differentials than to raw nominal gaps when inflation differs sharply. A country with 15% nominal rates and 14% inflation is not “high carry” in real terms versus a 3% nominal / 2% inflation peer.

Interest-Rate Parity: Covered Versus Uncovered

Covered interest-rate parity (CIP) is a no-arbitrage link among spot, forward, and risk-free rates in the two currencies. For a quote as price per base (e.g., USD per EUR), with r_price the USD rate and r_base the EUR rate:

F / S = (1 + r_price × τ) / (1 + r_base × τ)

for simple money-market periods of length τ (in years), or with continuous compounding:

F = S × e^((r_price − r_base) × T)

Intuition: holding the higher-interest currency should be offset by a forward discount large enough that covered returns equalize. Deviations create covered interest arbitrage (borrow low, lend high, cover with forward)—subject to balance-sheet, regulatory, and credit frictions that can open small CIP bases in stress.

Uncovered interest-rate parity (UIP) replaces the forward with the expected future spot:

E[S_T] / S ≈ (1 + r_price × τ) / (1 + r_base × τ)

UIP says the high-interest currency is expected to depreciate. Empirically, UIP often fails (the “forward premium puzzle” / carry trade): high-interest currencies frequently do not depreciate enough, so uncovered carry can earn positive average returns with crash risk. Exam distinction: CIP = arbitrage (with forwards); UIP = expectation (risky).

Worked forward FX calculation

Spot EURUSD S = 1.1000 (USD per EUR). USD 1-year rate r_USD = 5%, EUR 1-year rate r_EUR = 3% (annual compounding, one-year horizon).

F = 1.1000 × (1.05 / 1.03) = 1.1000 × 1.019417 ≈ 1.1214

EUR is the lower-interest (base) currency here relative to USD, so EUR trades at a forward premium in USD terms (F > S): you need more dollars forward to buy one euro. Equivalently, the dollar is at a forward discount.

Money-market hedge check: to create a synthetic one-year forward to buy EUR, borrow USD, convert spot to EUR, and invest in EUR. The all-in USD cost per EUR replicates F under CIP.

Arbitrage sketch if mispriced

If the quoted forward is 1.1300 while CIP says 1.1214, the forward is too high (too many USD per EUR). Arbitrage: sell EUR forward at 1.1300, and buy EUR synthetically via the money market (borrow USD, buy EUR spot, lend EUR). At maturity the EUR loan repays the forward delivery, and you pocket the USD gap (ignoring frictions).

Putting FX Markets Together

A treasurer with a firm EUR payable in six months faces transaction exposure: buy EUR forward (or futures) or buy a EUR call. Translation exposure on a euro subsidiary may be left open if cash will not be repatriated. Economic exposure to a stronger dollar against emerging-market revenues may need pricing power and local-cost shifts, not just a one-month forward. When rates diverge, use CIP to mark the fair forward and treat UIP/carry as a risk view, not a free lunch.