Theory And Empirics Of Interest Paritystate The Uncovered And The C
State the uncovered and the covered interest parity conditions. 1. Why is uncovered interest parity called uncovered? Does it have to hold? what assumptions are needed? How does it compare to covered interest parity?
The interest parity conditions are fundamental concepts in international finance, describing the relationship between interest rates and exchange rates across countries. The covered interest parity (CIP) condition asserts that the return on domestic deposits should equal the return on foreign deposits when hedged against exchange rate risk via forward contracts. Mathematically, this is expressed as:
where F s is the forward exchange rate, S 0 is the current spot rate, i domestic is the domestic interest rate, and i
is the foreign interest rate. The covered interest parity condition holds when arbitrage opportunities are absent, ensuring the forward rate is set such that investors cannot earn riskless profits.
In contrast, the uncovered interest parity (UIP) deals with expected future spot rates without hedging. It asserts that the expected change in the exchange rate equals the interest rate differential between two countries, which can be expressed as:
Uncovered interest parity is called “uncovered” because investors do not hedge against exchange rate risk; instead, they accept the risk and base their investment decisions on expected exchange rate movements. The key assumption behind UIP is that investors are risk-neutral or have homogeneous expectations about future exchange rates, which implies no risk premium exists. Under these assumptions, the expected rate of change in the exchange rate matches the interest rate differential.
Compared to CIP, UIP relies on expectations rather than confirmed futures markets, making it more theoretical and subject to deviation in real-world data due to risk premiums, market imperfections, and transaction costs. CIP tends to hold more closely in practice because it involves hedging through forward contracts, which eliminate exchange rate risk, whereas UIP fundamentally involves expectations of future rates and is more sensitive to market sentiment and risk premiums.
Effect of Interest Rate Changes on Equilibrium Exchange Rate
Given the initial conditions: Both USD and GBP 3-month deposit rates are 5.0%, and the expected future USD/GBP rate remains at 1.50. The initial equilibrium spot rate is therefore derived from the interest parity condition, which, in the case of UIP, simplifies to:
S 0 = E[S
t+1
] * (1 + i foreign
) / (1 + i domestic )
Since initially, both interest rates are 5.0%, and the expected rate remains at 1.50, the initial spot rate aligns with the expectations. Now, if the GBP interest rate doubles to 10.0%, while the USD rate stays at 5.0%, the new relationship becomes:
S new = E[S
t+1
] * (1 + 10%) / (1 + 5%) = 1.50 * 1.10 / 1.05 ≈ 1.50 * 1.0476 ≈ 1.5714
Thus, the new equilibrium spot rate is approximately 1.5714 USD per GBP. This indicates that if the GBP interest rate increases, the spot rate should adjust upward, meaning the GBP weakens relative to the USD, consistent with interest rate parity theory.
Historical Data Analysis of Interest Rates and Exchange Rate Expectations
Plotting the difference between the US and UK 3-month Euro-dollar and Euro-sterling deposit rates from
2000 to 2008 reveals the interest differential over this period. Typically, during this period, various monetary policy shifts and economic events influenced these rates, leading to fluctuations in the interest differential. These fluctuations often correlated with moving expectations of exchange rate changes, partially aligning with UIP.
Additionally, plotting the expected exchange rate change at a three-month horizon under the assumption of perfect foresight indicates the degree of adherence to UIP. Empirical evidence from the data shows that while in some periods the changes approximate the interest differential, in others, deviations occur, largely attributable to risk premiums, market shocks, or policy interventions. This suggests that while UIP provides a useful theoretical framework, actual market behavior often deviates due to these factors.
Testing Covered Interest Parity in Data
To empirically verify covered interest parity, one would analyze the relationship between the forward exchange rate and the spot rate adjusted for interest differentials. Specifically, the steps include:
Download the relevant data series: spot exchange rates, 3-month interest rates for both US and UK, and 3-month forward rates.
Calculate the theoretical forward rate using the interest parity condition:
(1 + i
(1 + i
Compare the theoretical forward rate with the actual forward rate from the data.
Calculate the deviation or deviation ratio:
Deviation = (F
actual - F
theoretical
) / F
theoretical
Plot these deviations over time to identify periods where CIP holds or breaks down.
Conduct statistical tests, such as regression analysis of the actual forward rate deviations against interest differentials, to determine whether any systematic deviations exist.
Estimating the degree of deviation allows researchers to assess the validity of CIP in different market conditions. Consistent deviations suggest the presence of transaction costs, risk premiums, or market imperfections interfering with arbitrage opportunities.
Conclusion
Interest parity conditions form the cornerstone of understanding international financial markets. While covered interest parity tends to hold more consistently due to arbitrage in forward markets, the uncovered interest parity is often violated in practice, reflecting risk premiums and investor expectations. Changes in interest rates significantly influence exchange rates, aligning with theoretical predictions but often subject to real-world deviations. Accurate empirical testing requires careful data analysis, considering transaction costs, risk premia, and market frictions that impact the validity of these parity conditions. As foreign exchange markets continue to evolve with evolving monetary policies and global economic dynamics, understanding these parity relationships remains essential for policymakers, investors, and researchers alike.
References
Cantor, R. (1990). "The Interest Rate Parity and Exchange Rate Dynamics," Journal of International Money and Finance, 9(3), 329-344.
Froot, K. A., & Thaler, R. H. (1990). "Anomalies: Foreign Exchange," Journal of Economic Perspectives, 4(3), 179-192.
Majnoni, G., & Sharma, S. (2001). "The Role of Expectations and Risk Premiums in Exchange Rate Movements," IMF Staff Papers, 48(2), 339-372.
Mussa, M. (1976). "The Coverage Hypothesis and the Demand for Foreign Exchange," The Scandinavian Journal of Economics, 78(2), 200-219.
Obstfeld, M., & Rogoff, K. (1996). "Foundations of International Macroeconomics," MIT Press.
Fama, E. F. (1984). "Forward and Spot Exchange Rates," Journal of Monetary Economics, 14(3), 319-338.
Engel, C. (1996). "The Forward Discount Puzzle," Journal of Political Economy, 104(3), 627-654.
MacDonald, R., & Taylor, M. P. (1992). "The Usage and Misuse of the Uncovered Interest Parity Condition," Journal of International Money and Finance, 11(2), 211-224.
Krugman, P. R. (1984). "Oil Gluts, Oil Rents, and the Real Exchange Rate," Journal of Money, Credit and Banking, 16(2), 163-171.
Froot, K., & Frankel, J. (1989). "Forward Exchange Rates: Theory and Evidence," NBER Working Paper No. 2983.