Foreign Exchange Markets

EC3214 International Finance Revision Cheat Sheet | Dr Zhengnan Yin 1. Foreign Exchange Markets 1.1 Core Concepts Term Definition Exchange Rate (P/B) Price of one unit of BASE currency expressed in PRICE currency. E.g. USD/EUR = 1.1650 means 1 EUR = 1.1650 USD. Spot Rate Rate for immediate delivery (T+2 settlement for most currencies). Forward Rate Rate agreed today for delivery > T+2. Quoted as points added/subtracted from spot. Bid Price Price at which the DEALER buys 1 unit of base currency from the client. Offer (Ask) Price Price at which the DEALER sells 1 unit of base currency to the client. Pip Smallest price increment. 0.0001 for most currencies; 0.01 for JPY. Spread Offer ? Bid = dealer compensation. Offer is always > Bid. 1.2 Bid-Ask Mechanics The party REQUESTING a quote can deal at either the bid (to sell base) or the offer (to buy base). The dealer makes a profit from the spread. Action Rate Used Example (USD/EUR = 1.1648/1.1652) Client sells EUR (buys USD) Dealer BID Client receives 1.1648 per EUR Client buys EUR (sells USD) Dealer OFFER Client pays 1.1652 per EUR Dealer offsets in interbank Interbank rate (tighter) 1.1649/1.1651 — dealer profits ~1 pip 1.3 Factors Affecting Bid-Ask Spread Currency pair liquidity — majors (USD/EUR, JPY/USD) have tighter spreads than exotic crosses Time of day — tightest during London-New York overlap (8am–11am NY time) Market volatility — uncertainty widens spreads Transaction size — larger trades = wider spreads (harder to offset in interbank) Client relationship — favoured clients may get tighter quotes 1.4 Cross Rates (Triangulation) When no direct interbank quote exists, cross-rates are calculated via a third currency (usually USD or EUR). The key rule: Scenario Formula Example Same BASE currency (A/C and B/C ? A/B) A/B = A/C ÷ B/C (invert one leg) CHF/GBP = CHF/EUR ÷ GBP/EUR Same PRICE currency (C/A and C/B ? A/B) A/B = C/A ÷ C/B (invert one leg) NZD/AUD = USD/AUD ÷ USD/NZD Mixed (A/C and C/B ? A/B) A/B = A/C × C/B (multiply) SGD/GBP = USD/GBP × SGD/USD To INVERT a quote: Bid of inverse = 1 / Offer of original; Offer of inverse = 1 / Bid of original. 2. Covered Interest Rate Parity (CIRP) 2.1 Core Idea A fully currency-hedged foreign investment must yield the same return as an equivalent domestic investment. This is enforced by arbitrage — it is a NO-ARBITRAGE condition. Using the day-count convention (Actual/360): In Price/Base notation: 2.2 Two Investment Alternatives Option A: Domestic Option B: Covered Foreign Invest 1 unit at domestic rate i_d for 1 year Convert at spot S(f/d), invest at i_f, lock forward rate F(f/d) Final value: (1 + i_d) Final domestic value: S(f/d) × (1 + i_f) × (1/F(f/d)) Risk-free in domestic currency Risk-free because FX risk is hedged CIRP requires Option A = Option B. If not, arbitrage eliminates the discrepancy instantly. 2.3 Forward Premium / Discount Condition Forward Status Interpretation i_f > i_d (foreign rate higher) F > S ? foreign currency at DISCOUNT; domestic at PREMIUM Higher foreign rate is offset by forward discount on foreign currency i_f < i_d (domestic rate higher) F < S ? foreign currency at PREMIUM; domestic at DISCOUNT Lower foreign rate is offset by forward premium on foreign currency 2.4 Forward Points In professional FX markets, forwards quoted as POINTS (added/subtracted from spot) Divide quoted points by 10,000 for 4-decimal currencies, then add to spot Bid < Offer always. Negative points = foreign currency discount. Larger maturity = larger absolute points Points are already scaled to the maturity — do not annualise them 2.5 Key Assumptions for CIRP to Hold Exactly Zero transaction costs Domestic and foreign instruments are identical in liquidity, maturity, and default risk Free capital flows and liquid FX markets In practice: Where these conditions are met, covered interest rate differentials are close to zero. 3. Uncovered Interest Rate Parity (UIRP) 3.1 Core Idea UIRP does NOT use a forward contract. The investor bears FX risk. Under UIRP, the EXPECTED depreciation of the high-yield currency exactly offsets its yield advantage, equalising expected returns. In Price/Base notation: Where ?S_e = EXPECTED percentage change in the spot exchange rate. A positive value means the foreign currency is expected to appreciate relative to domestic (or equivalently, f/d rises). 3.2 Investor Return Logic Investment Expected Return (domestic terms) Domestic instrument i_d (certain) Foreign, unhedged i_f ? %?S_e(f/d) ? i_d (under UIRP) 3.3 UIRP vs CIRP Feature CIRP UIRP FX risk Hedged via forward contract Unhedged (exposed to spot movements) Arbitrage enforced? YES — pure arbitrage condition NO — based on expectations + risk neutrality Holds empirically? Generally holds well Poor short/medium term; better long term Key assumption Capital mobility, liquid markets Risk-neutral investors 3.4 Empirical Reality Short-to-medium term: high-yield currencies often STRENGTHEN rather than depreciate — this is the 'carry trade' opportunity Long term: UIRP shows better empirical support Implication: investors can overweight high-yield currencies (carry trade) and earn excess returns over short horizons 3.5 Forward Rate Parity Forward Rate Parity states the forward rate is an UNBIASED predictor of the future spot rate: Does NOT claim perfect forecast — just unbiased (errors cancel over time) Holds IF both CIRP (arbitrage) AND UIRP (expectations) both hold Since CIRP always holds but UIRP often fails short-term, forward rates are poor short-term predictors 4. Purchasing Power Parity (PPP) 4.1 Law of One Price (Foundation) Identical goods should trade at the same price across countries when expressed in a common currency: 4.2 Three Versions of PPP Version Absolute PPP Formula S(f/d) = P_f / P_d Relative PPP %?S(f/d) ? ?_f ? ?_d Ex Ante PPP %?S_e(f/d) = ?_e_f ? ?_e_d Assumption Holds in Practice? All goods tradable; same price baskets with same weights Rarely — price levels differ due to non-tradeables & costs Transaction costs constant over time; focuses on changes Better than absolute; holds long-term Uses EXPECTED inflation rates Long-term anchor; short-term poor 4.3 Key Intuition — Relative PPP The currency of the HIGH-INFLATION country should DEPRECIATE by the inflation differential: If foreign inflation = 9% and domestic = 5%: S(f/d) must rise by ~4% to maintain competitiveness If S(f/d) stayed flat, high foreign inflation would erode foreign competitiveness 4.4 Empirical Evidence 1-year horizon: little relationship between inflation differentials and exchange rate changes 5+ year horizon: strong positive relationship — PPP is a valid long-run framework Short-run exchange rates appear close to random walk; long-run they gravitate toward PPP equilibrium 4.5 Fisher Effect The nominal interest rate can be decomposed as: For foreign and domestic countries: 4.6 International Fisher Effect (IFE) If real interest rates are equal across countries (real interest rate parity: r_f = r_d), then: The nominal yield spread equals the expected inflation differential. This is the International Fisher Effect. Real interest rate parity: r_f ? r_d = 0 (real rates equalise globally) IFE breaks down when currencies carry different risk premiums (e.g., emerging markets require a risk premium above IFE) 5. International Parity Conditions — The Big Picture 5.1 Summary of All Key Formulas Parity Condition Formula Enforced by Covered Interest Rate Parity (CIRP) F(f/d)/S(f/d) = (1+i_f)/(1+i_d) Arbitrage — always holds Uncovered Interest Rate Parity (UIRP) %?S_e(f/d) = i_f ? i_d Risk-neutral expectations — often fails short-term Forward Rate Parity F(f/d) = S_e(f/d) Requires CIRP + UIRP both hold Absolute PPP S(f/d) = P_f / P_d Goods arbitrage — rarely holds exactly Relative PPP %?S(f/d) ? ?_f ? ?_d Inflation differentials — holds long-term Ex Ante PPP %?S_e(f/d) = ?_e_f ? ?_e_d Expected inflation — long-term anchor International Fisher Effect (IFE) i_f ? i_d = ?_e_f ? ?_e_d Real interest rate parity + Ex Ante PPP Real Interest Rate Parity r_f ? r_d = 0 Derived from UIRP + Ex Ante PPP 5.2 The Parity Triangle — How They Link There are 3 parity relationships, but only 2 independent ones (any 2 imply the 3rd): If These Hold Then This Is Implied Relative PPP + UIRP International Fisher Effect IFE + UIRP Relative / Ex Ante PPP PPP + IFE Uncovered Interest Rate Parity 5.3 Real-World Behaviour of Parity Conditions Condition Short-Term Empirical Performance Long-Term Empirical Performance CIRP Holds well (arbitrage enforced) UIRP FAILS — high-yield currencies often appreciate (carry trade works) Holds reasonably well Forward Rate Parity FAILS — forward rates are poor short-term predictors Holds well Holds reasonably well Relative PPP Poor — exchange rates appear close to random walk Strong positive relationship with inflation differential Ex Ante PPP Poor Valid long-run framework / anchor IFE / Real Rate Parity Often fails due to risk premiums Holds approximately in developed markets 5.4 If ALL Parity Conditions Held Simultaneously Expected %?Spot = nominal yield spread = expected inflation differential = forward premium/discount No consistent profits from currency speculation or forward exchange trading High-yield currencies would depreciate exactly in line with yield advantage All markets would offer identical currency-adjusted returns — no incentive to shift capital In practice, these conditions represent long-run equilibrium anchors. Short-run deviations create trading opportunities (carry trades, momentum strategies). 5.5 Exam-Style Quick Reference Question Type Key Relationship to Apply Fully hedged foreign return = domestic return? CIRP — arbitrage ensures equality Unhedged foreign return = domestic return? UIRP — equality only if expected depreciation = yield spread Forward rate as predictor of future spot? Forward Rate Parity (requires CIRP + UIRP) Exchange rate change from inflation data? Relative or Ex Ante PPP Nominal spread = inflation differential? International Fisher Effect Real interest rates equal across countries? Real Interest Rate Parity (from IFE + PPP) Which conditions are arbitrage-enforced? Only CIRP. All others are expectation-based. Currency overvalued / undervalued? Compare current S to PPP equilibrium EC3214 — Revision Cheat Sheet | Covers Lectures I–V | Dr Zhengnan Yin | UCC