FINS3616 · International Business Finance
The Fisher Effect and Interest Rate Parity
Week 3 of UNSW FINS3616 completes the parity framework (Shapiro Ch 4): the Fisher effect (nominal rate = real rate + expected inflation) and the International Fisher effect, then covered and uncovered interest rate parity and the covered-interest-arbitrage loop that enforces it. It ties PPP, Fisher, IFE, IRP and the unbiased forward rate into one consistent system used to forecast exchange rates. These derivations and money-loops are core mid-term calculation questions and reappear on the cumulative 40% final exam.
What this chapter covers
- 01Fisher effect: (1+r) = (1+a)(1+i), approximation r ≈ a + i; solving for the real rate a = (1+r)/(1+i) − 1
- 02Generalised (International) Fisher relation: (1+r_h)/(1+r_f) = (1+i_h)/(1+i_f); real returns equalised by capital flows
- 03International Fisher effect (IFE): e_t = e₀[(1+r_h)/(1+r_f)]^t — the higher-nominal-rate currency is expected to depreciate
- 04Covered interest rate parity: f₁ = e₀(1+r_h)/(1+r_f); approximation (f₁−e₀)/e₀ ≈ r_h − r_f; the low-rate currency at a forward premium
- 05Covered interest arbitrage (CIA): borrow low, convert spot, invest abroad, sell forward — the money-loop that restores parity
- 06The five parity relationships as one wheel: PPP, Fisher, IFE, IRP and the unbiased forward rate (f₁ = E[e_t] + risk premium)
- 07Currency forecasting: market-based (forward rates, interest differentials) vs model-based (fundamental, technical); accuracy vs correctness
- 08Empirical evidence: covered IRP held tightly pre-2008, with deviations during and after the GFC from funding and regulatory constraints
Covered interest arbitrage: locking a riskless profit when parity fails
- +1Test for a covered profit: the covered return on the GBP leg = (1 + r_f) × f/e₀ − 1 = 1.07 × (1.2300/1.2500) − 1 = 1.07 × 0.9840 − 1 = 5.29%. That exceeds the 4% US borrowing cost, so borrow USD and invest in GBP covered.
- +1Borrow $1,000,000 at 4% (you will owe $1,040,000 in one year) and convert to pounds at the spot 1.2500: $1,000,000 ÷ 1.2500 = £800,000.
- +1Invest £800,000 at 7% → £856,000 in one year; simultaneously sell £856,000 one-year forward at 1.2300 USD/GBP, locking £856,000 × 1.2300 = $1,052,880.
- +1At maturity deliver the pounds on the forward, collect $1,052,880, repay the $1,040,000 loan → riskless profit = $1,052,880 − $1,040,000 = $12,880. The arbitrage flows (spot GBP demand up, forward GBP selling → forward down; US rate up, UK rate down) push the market back to parity.
Key terms
- Fisher effect
- The nominal interest rate compensates for a real required return plus expected inflation: (1+r) = (1+a)(1+i), approximately r ≈ a + i. Rearranged, the real rate a = (1+r)/(1+i) − 1.
- International Fisher effect (IFE)
- Combines PPP and the Fisher effect: e_t = e₀[(1+r_h)/(1+r_f)]^t, so a currency with a higher nominal interest rate is expected to depreciate (the high rate reflects high expected inflation). Approximation %Δe ≈ r_h − r_f.
- Covered interest rate parity (IRP)
- The no-arbitrage link between the interest differential and the forward: f₁ = e₀(1+r_h)/(1+r_f), approximately (f₁−e₀)/e₀ ≈ r_h − r_f. The lower-interest-rate currency sells forward at a premium.
- Covered interest arbitrage (CIA)
- When the covered interest differential is non-zero, borrow the low-effective-cost currency, convert at spot, invest abroad, and sell the proceeds forward to lock a riskless profit. The flows push spot and forward rates back to parity.
- Unbiased forward rate (UFR)
- The hypothesis that the forward is an unbiased predictor of the future spot; in equilibrium the forward premium equals the expected % change in the spot. Empirically f₁ = E[e_t] + a risk premium (RP), which can be positive or negative.
- Accuracy vs correctness (forecasting)
- Accuracy is the size of the deviation between the forecast and the actual rate; correctness is whether the forecast gets the direction right. A forecast can be accurate but directionally wrong, or correct in direction but far off in size.
The Fisher Effect and Interest Rate Parity FAQ
How do I know which currency to borrow in a covered-interest-arbitrage problem?
Compute the covered return on the foreign leg, (1 + r_f) × f/e₀, and compare it to the home gross return (1 + r_h). If the covered foreign return is higher, borrow home and invest foreign (covered by selling the proceeds forward); if it is lower, do the reverse. If the two are equal, covered interest rate parity holds and there is no arbitrage. That one comparison drives the whole money loop, so do it first.
What is the difference between covered and uncovered interest parity?
Covered IRP uses the forward rate to lock in the future exchange rate, so it is a pure no-arbitrage condition: f₁ = e₀(1+r_h)/(1+r_f). Uncovered interest parity (the International Fisher effect) instead uses the expected future spot rate and has no forward hedge, so it is an equilibrium/expectations condition and holds only on average: E[e_t] = e₀[(1+r_h)/(1+r_f)]^t. Covered IRP is enforced tightly by arbitrage; uncovered parity is far noisier in the data.
Can you really forecast exchange rates well enough to profit?
Generally no, consistent with market efficiency. The forward rate is the simplest unbiased estimate of the future spot but only out to about a year; interest-rate differentials extend the horizon via IFE/IRP logic; fundamental analysis (PPP-style) and technical analysis are the model-based alternatives. But persistent profitable forecasting is inconsistent with the efficient-market hypothesis, so the course distinguishes accuracy (size of error) from correctness (direction) and stresses that edges rarely survive.
Can AI help me with Fisher and interest rate parity in FINS3616?
Yes. Sia is an AI tutor built to mirror how FINS3616 is taught and assessed at UNSW Sydney: it can walk you through the exact and approximate Fisher relations, an IFE expected-spot calculation, a covered-IRP forward, and a full covered-interest-arbitrage money loop one line at a time, and check which currency you should borrow. Bring your own tutorial question. It checks your reasoning but does not do graded work, and UNSW academic-integrity rules apply — use it to be exam-ready for the mid-term and final.
Exam move
Treat the five parity conditions as one wheel and be able to move between any two spokes: PPP links inflation to the spot change, Fisher links inflation to nominal rates, IFE links nominal rates to the expected spot change, IRP links nominal rates to the forward premium, and the unbiased forward rate links the forward premium to the expected spot change. Memorise the exact forms and their intuitive approximations, and always state which currency should appreciate or depreciate. The highest-value drill is the covered-interest-arbitrage loop: practise the test (covered foreign return vs home return), then the six-step money flow, until you can produce it under time. Keep the Fisher real-rate rearrangement a = (1+r)/(1+i) − 1 sharp, and remember the accuracy-versus-correctness distinction for the forecasting short-answer. All of this is prime Weeks 1–4 mid-term territory and returns on the cumulative 40% final, so rehearse the recorded tutorial questions with your single A4 formula sheet. When the direction of a flow won't click, ask Sia to re-derive it and set a fresh problem.
Working through The Fisher Effect and Interest Rate Parity in FINS3616? Sia is AskSia’s AI Business and Economics tutor — ask any FINS3616 The Fisher Effect and Interest Rate Parity question and get a clear, step-by-step explanation grounded in how FINS3616 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.
