Interest Rate Parity Calculator
Compute the theoretical forward rate from spot and two rates under covered interest parity; judge arbitrage.
Input Data
Results
At a glance:The Interest Rate Parity calculator computes the theoretical forward rate under Covered Interest Rate Parity (CIRP) from spot and two rates. Formula: forward = spot × (1 + domestic rate) ÷ (1 + foreign rate) (annualised, one-year; quote is local per foreign unit). The core is no-arbitrage: the rate difference must appear in the spot-forward gap — invest in the higher-rate currency and at forward conversion that currency must depreciate by exactly the spread, so both currencies yield the same FX-adjusted return and the arbitrage vanishes. Compare the theoretical forward with the market forward; a gap implies covered arbitrage in theory (deviations arise from costs/controls in practice).
Formula
Forward = spot × (1 + domestic rate) ÷ (1 + foreign rate).
The rate difference appears in the spot-forward gap (no arbitrage).
$$Forward = Spot \times \dfrac{1 + i_{domestic}}{1 + i_{foreign}}$$How to Use
- Enter the spot rate (local per foreign unit).
- Enter the domestic and foreign annual rates.
- View the theoretical forward rate and compare with the market forward.
At spot 8 (US$1 = HK$8), how the rate spread moves the theoretical forward
| Domestic rate | Foreign rate | Spread | Theoretical forward |
|---|---|---|---|
| 2% | 5% | −3% | 7.7714 |
| 5% | 5% | 0% | 8.0000 |
| 5% | 2% | +3% | 8.2353 |
| 8% | 2% | +6% | 8.4706 |
When domestic rate exceeds foreign (positive spread), the forward is above spot — the domestic currency must depreciate forward by exactly the spread. This is the no-arbitrage result: hedged returns are equal whichever currency you invest in.
Case Studies
Case 1: Forward from spot and two rates
Spot 8 (US$1 = HK$8), HKD one-year rate 5%, USD one-year rate 2%; find the one-year theoretical forward.
Forward = 8 × (1 + 5%) ÷ (1 + 2%) = 8 × 1.05 ÷ 1.02 ≈ 8.2353.
Interpretation: HKD has the higher rate, yet the forward rises from 8 to ~8.2353 — HKD depreciates forward vs USD by exactly the 3% spread, so investing in HKD or USD (hedged) yields the same HKD return; no risk-free arbitrage.
Case 2: Covered arbitrage vs carry trade
If the market forward is 8.15, not the theoretical 8.2353, a covered interest arbitrage exists in theory: borrow foreign, convert to domestic at the higher rate, and lock the cheaper 8.15 forward — risk-free spread. Arbitrage pushes the market back to theory.
Distinguish the uncovered carry trade: borrow low-rate, invest high-rate without hedging, betting the high-rate currency will not depreciate much. That carries FX risk — if it does depreciate (as Uncovered IRP predicts) profits shrink or turn to loss, which is why carry trades sometimes win and sometimes crash suddenly.
Practical notes: (1) CIRP holds well in free-flow, low-cost markets; (2) real deviations come from costs, capital controls, credit risk and post-2008 balance-sheet 'basis'; (3) this tool gives the theoretical no-arbitrage forward, actual quotes per market. Pair with the carry-trade and PPP calculators. Educational/estimation only.
FAQ
What is interest rate parity and why does it hold?
IRP links the interest-rate difference between two currencies to their spot-forward rates under no arbitrage. Covered IRP: forward = spot × (1 + domestic) ÷ (1 + foreign). It holds by the power of no-arbitrage: investing domestically (earn domestic rate) vs investing foreign and hedging with a forward today must yield the same risk-free return, or arbitrageurs push prices until they equalise.
Covered vs uncovered interest parity?
Covered IRP (CIRP, used here) locks the future rate with a forward contract today, so the process is risk-free and the forward is precisely determined — holds well in free markets. Uncovered IRP (UIP) has no forward hedge and relies on expected future spot; it says the rate spread equals the expected FX change (high-rate currency expected to depreciate). UIP involves expectations and FX risk, and often fails empirically — which is why carry trades can profit.
What is IRP for in practice, and why deviations?
Uses: (1) forward pricing — banks quote forwards from spot and two rates via CIRP; (2) arbitrage detection — compare theoretical vs market forward for covered-arbitrage gaps; (3) understanding capital flows. Deviations arise from transaction costs, capital controls, counterparty credit risk, and market stress (post-2008 'basis'). It is a useful theoretical anchor, reliable in normal markets but watch real-world frictions.
Why must a high-rate currency depreciate forward — counter-intuitive?
By no-arbitrage: invest domestically earns the high rate; invest foreign and hedge earns the low rate. If the forward did not adjust, everyone would take the high-rate path — not an equilibrium. So the forward must rise (domestic depreciates forward) so the hedged foreign path earns extra FX to match the higher domestic interest. The high rate is exactly offset by forward depreciation — no free lunch. Hence high-rate currencies trade at forward discount, low-rate at forward premium. Uncovered (no hedge) betting on no depreciation is the carry-trade logic, which carries real risk.
Which is more reliable, covered or uncovered?
Covered (CIRP) is more reliable and rigorous: the forward locks the rate today, so both strategies are risk-free and must yield equal returns — it holds well where capital is free and costs are low, and deviations are quickly arbitraged. Uncovered (UIP) relies on expectations, carries FX risk, and often fails empirically (why carry trades can profit). Even CIRP showed persistent 'basis' deviations in extremes like post-2008. Educational/estimation only.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.