Currency exchange rates — parity conditions
In this chapter: Covered and uncovered interest parity · Purchasing power parity · International Fisher relation · Forward rate calculation · Carry trade
Five parity conditions link spot rates, forward rates, interest rates, inflation. CFA L2 tests calculations + violations (which give rise to arbitrage or carry trade).
**Covered interest parity (CIP)** — strict no-arbitrage: F/S = (1+iDC)/(1+iFC), where DC = domestic currency, FC = foreign. If violated: arbitrage via covered borrowing/lending in two currencies. **Uncovered interest parity (UIP)** — expectational: E(S1)/S0 = (1+iDC)/(1+iFC). Doesn't hold consistently in data → carry-trade profits exist. **Purchasing power parity (PPP)** — long-run: S = P_DC / P_FC. Relative PPP: % change in S ≈ inflation differential. **International Fisher** — combines: iDC – iFC = π_DC – π_FC (real rates equal across countries). **Forward rate as expectation**: under UIP, F = E(S1).
Direct vs indirect quotes: be careful which currency is base. Price DC/FC means how many DC per 1 FC. If DC = INR and FC = USD: 83 INR/USD. Forward premium/discount: - F > S → FC at premium (or DC at discount). - Annualised premium = (F-S)/S × 360/days. If iFC < iDC → FC at premium (foreign currency more valuable forward to compensate lower yield). This is CIP's core intuition. Carry trade: borrow low-yield currency (e.g., JPY), invest in high-yield (e.g., AUD or BRL). Profitable if currencies don't adjust per UIP. Risk: sudden FX correction wipes carry.
L2 vignette pattern: 1. You're given spot rate, two interest rates, time period. 2. Compute forward (CIP). 3. Determine if quoted forward is consistent with CIP. 4. If not — arbitrage strategy. Formula: F/S = (1+iDC×t)/(1+iFC×t) for short rates with simple compounding. CFA exam usually uses this form for short tenors. Memorise: high-yield currency at forward discount; low-yield currency at forward premium. (Counter-intuitive on first sight.)
- RBI Circular on FX Forward Markets
- FEMA Rules
- CFA Institute Economics curriculum
- Confusing direct/indirect quotes — leads to inverted formula.
- Forgetting day-count conventions for forward calculation.
- Treating UIP as exact — empirically UIP doesn't hold, hence carry profits.
Frequently asked
Why do high-yield currencies trade at forward discount?
Does UIP hold empirically?
Practice questions
Click each question to reveal the answer and explanation.
Q 1Under CIP, if iDC > iFC, the FC trades at:- (a)Forward premium
- (b)Forward discount
- (c)Spot only
- (d)Cannot determine
- (a)Forward premium
- (b)Forward discount
- (c)Spot only
- (d)Cannot determine
Q 2Carry trade profits if:- (a)CIP holds
- (b)UIP holds exactly
- (c)UIP fails — high-yield currency doesn't depreciate as predicted
- (d)Volatility is zero
- (a)CIP holds
- (b)UIP holds exactly
- (c)UIP fails — high-yield currency doesn't depreciate as predicted
- (d)Volatility is zero
Q 3Spot USDINR = 83, 1-yr US rate 5%, India 7%. CIP forward:- (a)83.00
- (b)84.58
- (c)81.45
- (d)85.00
- (a)83.00
- (b)84.58
- (c)81.45
- (d)85.00
Q 4Relative PPP says:- (a)Spot = price ratio
- (b)% change in S = inflation differential
- (c)Real rates equal
- (d)No arbitrage
- (a)Spot = price ratio
- (b)% change in S = inflation differential
- (c)Real rates equal
- (d)No arbitrage
Q 5International Fisher relation:- (a)Real rates equal across countries
- (b)Nominal rates equal
- (c)No PPP
- (d)Inflation = 0
- (a)Real rates equal across countries
- (b)Nominal rates equal
- (c)No PPP
- (d)Inflation = 0