Trustner AcademyTrustner AcademyCourses
Reading 1CFA L2 EconFull chapter

Currency exchange rates — parity conditions

In this chapter: Covered and uncovered interest parity · Purchasing power parity · International Fisher relation · Forward rate calculation · Carry trade

~3 min readLayer 4 · Professional CertificationsFree

Five parity conditions link spot rates, forward rates, interest rates, inflation. CFA L2 tests calculations + violations (which give rise to arbitrage or carry trade).

Foundation

**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).

Deep Dive

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.

Advanced

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.)

Regulatory references
  • RBI Circular on FX Forward Markets
  • FEMA Rules
  • CFA Institute Economics curriculum
Common mistakes & pitfalls
  • 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?
CIP says forward must offset interest differential. If you can earn higher rate in FC, forward FC must depreciate to prevent arbitrage.
Does UIP hold empirically?
Generally no. Forward rates poor predictors of future spot. Carry trade has been profitable on average — though with crash risk.

Practice questions

Click each question to reveal the answer and explanation.

Q 1
Under CIP, if iDC > iFC, the FC trades at:
  1. (a)Forward premium
  2. (b)Forward discount
  3. (c)Spot only
  4. (d)Cannot determine
Correct: (a) Forward premium
High-DC-rate means FC at forward premium (DC at discount) to offset interest gap.
Q 2
Carry trade profits if:
  1. (a)CIP holds
  2. (b)UIP holds exactly
  3. (c)UIP fails — high-yield currency doesn't depreciate as predicted
  4. (d)Volatility is zero
Correct: (c) UIP fails — high-yield currency doesn't depreciate as predicted
Carry profits when UIP fails — high-yield currency holds value better than UIP suggests.
Q 3
Spot USDINR = 83, 1-yr US rate 5%, India 7%. CIP forward:
  1. (a)83.00
  2. (b)84.58
  3. (c)81.45
  4. (d)85.00
Correct: (b) 84.58
F = 83 × 1.07/1.05 ≈ 84.58.
Q 4
Relative PPP says:
  1. (a)Spot = price ratio
  2. (b)% change in S = inflation differential
  3. (c)Real rates equal
  4. (d)No arbitrage
Correct: (b) % change in S = inflation differential
Relative PPP: change in S over time matches inflation differential (long run).
Q 5
International Fisher relation:
  1. (a)Real rates equal across countries
  2. (b)Nominal rates equal
  3. (c)No PPP
  4. (d)Inflation = 0
Correct: (a) Real rates equal across countries
IFR: real rates equal across countries → nominal rate differential = inflation differential.
Educational purposes only. The numbers, returns, and examples used in this lesson are illustrative. Past performance does not guarantee future results. Mutual fund and securities investments are subject to market risks. This lesson is not investment advice; for advice tailored to your circumstances, consult a SEBI-registered Investment Adviser. Read our full disclaimer.