Term interest rate parity

What Is Term Interest Rate Parity?

Term interest rate parity (TIRP) is a fundamental concept in International Finance that describes a theoretical relationship between interest rates and exchange rate differences between two countries over a specific future period. It suggests that the differential between the forward and spot exchange rates should be equal to the interest rate differential between two currencies. This principle is a core component of how participants in the foreign exchange market determine forward exchange rates, ensuring that no risk-free profit, or arbitrage, opportunities exist when borrowing in one currency, converting it, investing it at a foreign interest rate, and simultaneously locking in a forward exchange rate to convert it back to the original currency. Term interest rate parity extends the concept of interest rate parity to cover forward contracts of various maturities, acknowledging that interest rate differentials can vary across different time horizons.

History and Origin

The concept of interest rate parity, from which term interest rate parity is derived, has roots in the early 20th century, becoming more prominent with the advent of flexible exchange rates and the growth of international capital markets. Early economists observed that discrepancies in interest rates across countries, if left unchecked, would quickly lead to arbitrage opportunities. As such, the theory evolved to explain how capital flows would move to exploit these differences until the market reached an equilibrium where such opportunities were eliminated. Reuven Glick, in a 1999 economic letter from the Federal Reserve Bank of San Francisco, described how the interest rate parity condition acts as a "benchmark" for short-run exchange rate movements and how closely related domestic and foreign interest rates are through this mechanism.⁴

Key Takeaways

Term interest rate parity posits that the interest rate differential between two currencies should equal the percentage difference between their forward and spot exchange rates for a specific term.
It is a no-arbitrage condition, meaning it suggests that perfectly informed investors cannot make risk-free profits by exploiting interest rate and exchange rate differences across countries for a given maturity.
The principle is crucial for the pricing of forward exchange rate contracts in the foreign exchange market.
Deviations from term interest rate parity, while theoretically fleeting, can occur in practice due to factors like transaction costs, capital controls, and market imperfections.

Formula and Calculation

Term interest rate parity can be expressed by the following formula:

\frac{F_t}{S_t} = \frac{1 + i_d \cdot \frac{T}{360}}{1 + i_f \cdot \frac{T}{360}}

Where:

(F_t) = Forward exchange rate for a period (T)
(S_t) = Current spot exchange rate
(i_d) = Domestic risk-free rate (annualized)
(i_f) = Foreign risk-free rate (annualized)
(T) = Time to maturity of the forward contract in days (often adjusted for a 360-day year in currency markets)

This formula indicates that the ratio of the forward rate to the spot rate is equivalent to the ratio of the domestic interest rate factor to the foreign interest rate factor over the specified term. The domestic interest rate and foreign interest rate combine to form the interest rate differential.

Interpreting the Term Interest Rate Parity

Interpreting term interest rate parity involves understanding that the forward exchange rate is not simply a prediction of the future spot rate, but rather a rate that ensures no arbitrage opportunities exist given current interest rates. If the forward rate implied by the interest rate differential is different from the actual market forward rate, then an arbitrage opportunity would theoretically exist. For instance, if the domestic interest rate is higher than the foreign interest rate, the domestic currency is expected to depreciate in the forward market relative to the foreign currency. This depreciation ensures that an investor gains no advantage by borrowing in the low-interest-rate foreign currency, converting it to the high-interest-rate domestic currency, and investing it, as any higher interest earnings would be offset by the cost of converting back at an unfavorable forward rate.

Hypothetical Example

Consider an investor in the United States looking at investment opportunities in Japan.
Assume the following:

Current Spot Exchange Rate (USD/JPY): 1 USD = 150 JPY
U.S. 3-month (90-day) interest rate: 5.0% per annum
Japan 3-month (90-day) interest rate: 0.5% per annum

Using the Term Interest Rate Parity formula to find the implied 3-month forward rate:

\frac{F_{90}}{150} = \frac{1 + 0.05 \cdot \frac{90}{360}}{1 + 0.005 \cdot \frac{90}{360}} \\ \frac{F_{90}}{150} = \frac{1 + 0.05 \cdot 0.25}{1 + 0.005 \cdot 0.25} \\ \frac{F_{90}}{150} = \frac{1 + 0.0125}{1 + 0.00125} \\ \frac{F_{90}}{150} = \frac{1.0125}{1.00125} \\ F_{90} = 150 \cdot \frac{1.0125}{1.00125} \\ F_{90} \approx 150 \cdot 1.01123 \\ F_{90} \approx 151.68 \text{ JPY/USD}

The implied 3-month forward rate is approximately 151.68 JPY per USD. This indicates that, to prevent arbitrage opportunities, the USD is expected to be more expensive in the future, effectively compensating for the higher U.S. interest rate.

Practical Applications

Term interest rate parity serves as a theoretical foundation for various practical applications in international finance and investment. It is widely used by financial institutions, corporations, and investors for:

Currency Hedging: Corporations engaged in international trade use forward contracts to lock in future exchange rates for expected foreign currency revenues or expenses, mitigating foreign exchange risk. The pricing of these contracts is directly influenced by TIRP. Reuters has reported on how companies navigate currency hedging strategies amidst market volatility to protect their earnings.³
International Investment Decisions: Investors considering foreign bond markets or other yield-bearing financial market instruments analyze interest rate differentials and implied forward rates to determine the actual hedged return on a foreign investment, helping them compare the yield of domestic versus foreign assets.
Central Bank Operations: Central banks monitor the foreign exchange market closely, including adherence to interest rate parity conditions, as part of their monetary policy implementation and management of international capital flows. The Federal Reserve, for instance, engages in foreign currency operations as authorized by the Federal Open Market Committee, indirectly influencing exchange rates and interest rate relationships.²

Limitations and Criticisms

Despite its theoretical robustness as a no-arbitrage condition, term interest rate parity does not always hold perfectly in the real world. Several factors can lead to deviations:

Transaction Costs: The costs associated with actual foreign exchange transactions and borrowing/lending (e.g., bid-ask spreads, brokerage fees) can prevent infinitesimal arbitrage opportunities from being exploited, creating a "band of no-arbitrage" within which the parity can deviate.
Capital Controls: Government restrictions on the movement of capital across borders can inhibit the free flow of funds required for arbitrage, thereby breaking the parity condition.
Credit Risk and Liquidity Premiums: The interest rates used in the parity formula are typically risk-free rates (e.g., government bond yields). In reality, market participants face different borrowing and lending rates depending on their creditworthiness. Additionally, liquidity premiums can arise, especially during periods of financial stress. The Bank for International Settlements (BIS) has extensively documented the "covered interest parity lost" phenomenon, where persistent deviations, particularly since the 2008 financial crisis, have been observed due to factors like hedging demand and stricter bank balance sheet constraints.¹
Market Frictions: Imperfections like asymmetric information, differing tax treatments, and regulatory hurdles can also contribute to deviations.

Term Interest Rate Parity vs. Covered Interest Rate Parity

Term interest rate parity and Covered Interest Rate Parity are closely related, with TIRP essentially being a generalization of CIP.

Covered Interest Rate Parity (CIP)
Covered interest rate parity specifically refers to the condition where the interest rate differential between two currencies is exactly offset by the differential between their spot and forward exchange rates. This "covering" refers to the use of a forward contract to eliminate foreign exchange risk. CIP applies to a single, specific maturity period.

Term Interest Rate Parity (TIRP)
Term interest rate parity extends this concept across a range of maturities. It acknowledges that interest rate differentials (and thus implied forward premiums or discounts) can vary depending on the tenor of the loan or forward contract (e.g., 3-month, 6-month, 1-year). While CIP focuses on the condition holding for a covered transaction, TIRP considers the entire term structure of interest rates and how it relates to the term structure of forward exchange rates. In essence, TIRP describes how CIP should hold for all available maturities in the market.

Confusion often arises because both concepts deal with the same core idea of no-arbitrage between interest rate differentials and spot/forward exchange rate relationships. However, TIRP provides a more comprehensive framework by considering the time dimension and how these relationships hold across different future periods.

FAQs

What happens if term interest rate parity does not hold?

If term interest rate parity does not hold, it theoretically creates an arbitrage opportunity. An investor could exploit the discrepancy by borrowing in one currency, converting it, investing in another, and simultaneously entering a forward contract to convert it back, earning a risk-free profit. However, such opportunities are usually short-lived as market participants quickly act to close them, restoring parity.

Is term interest rate parity always observed in the real world?

No, while it is a powerful theoretical concept, perfect term interest rate parity is rarely observed in the real world due to transaction costs, capital controls, liquidity constraints, and credit risk. These market frictions create small, but sometimes persistent, deviations from parity.

How does central bank policy affect term interest rate parity?

Central bank interest rate policies directly influence the domestic and foreign interest rate differential components of the TIRP formula. Changes in policy rates can shift this differential, leading to immediate adjustments in spot and forward exchange rates to re-establish the parity condition, guiding currency market expectations.

What is the relationship between TIRP and uncovered interest rate parity?

Unlike term interest rate parity (or covered interest rate parity), Uncovered Interest Rate Parity (UIRP) is an unhedged condition. UIRP posits that the difference in interest rates between two countries should equal the expected future change in the spot exchange rate, without using a forward contract. This introduces an element of risk (forecast error), making UIRP a less reliable predictor than TIRP, which is based on a risk-free arbitrage condition.