Uncovered Interest Rate Parity: Risks and Returns
Uncovered Interest Rate Parity (UIP): Actors and Exchange Rate Risk
Exchange Rate Strategies and Returns
Uncovered Interest Rate Parity (UIP) states that the expected returns on investments are subject to potential variations in exchange rates. Let’s examine two strategies:
- Buying domestic treasury plans:
- Return (Rb) = (1 + R), where R is the domestic interest rate.
- Buying foreign treasury plans:
- Initial return: Rb = 1/S * (1 + Re), where S is the spot exchange rate and Re is the foreign interest rate.
- Converting back to domestic currency: 1/S * (1 + Re) implies ^S/S * (1 + Re), where ^S is the expected future exchange rate.
The problem is the lack of information on the spot exchange rate at the end of the investment period. Investors have an *expectation* of the future exchange rate, denoted as ^S. Therefore, the expected return in domestic currency from the foreign investment is ^S/S * (1 + Re).
It’s crucial to remember that investment abroad is conditioned by exchange rate evolution. The investor is not covered in the market and term risk. No result is secured with certain performance in domestic currency.
UIP Equilibrium Condition
The equilibrium condition in UIP is:
Rb = (1 + R) = ^S/S * (1 + Re)
We can also derive the equilibrium condition through the rate of currency appreciation (or depreciation/discount):
- Assuming the investor considers a difference between the estimated exchange rate and the actual exchange rate: %X = (^S – S)/S
- Then: ^S/S = 1 + X
- Substituting: (1 + R) = (1 + Re) * (1 + X)
- Simplifying: R = Re + X
This final equation represents the uncovered interest rate parity. It’s a case of the “law of one price,” which states that under certain conditions, the same price must prevail across markets for identical assets. By analogy, in the international monetary market, financial assets with the same characteristics (liquidity, risk, etc.) must provide the same performance.
Empirical Evidence of UIP
Empirical testing of UIP is difficult because the expected future exchange rate (^S) is not directly observed. A common approximation is to use the forward rate (Fr), which represents the rate of appreciation/depreciation of a currency or the forward premium/discount.
- If ^S is approximated by Fr, then UIP becomes: R = Re + Fr
- Therefore X = Fr
Risk Aversion and Risk Premium
If we abandon the assumption of risk neutrality and assume investors are risk-averse, we must add a risk premium (P). In this case, uncovered investments introduce a risk premium. If the risk of foreign investments increases or decreases, the portfolio’s return should be higher or lower than the domestic investment pool.
The difference between the expected rate of appreciation/depreciation (X) and the forward rate must equal the risk premium:
X = F + P, and R = Re + X – P (where P is the risk premium)
The equilibrium condition is modified as follows:
- If P > 0: Uncovered investment abroad increases the risk of the asset portfolio. The expected yield must be *higher* than the domestic profitability to compensate investors for taking more risk.
- If P < 0: Uncovered investment abroad *reduces* the risk of the asset portfolio. The expected yield can be *lower* than domestic investments to compensate.
Challenges in Determining the Risk Premium
Empirically approximating the equation using the forward rate (Fr) presents the problem that the risk premium (P) is not easy to determine. There is intense debate on the factors determining the risk premium. One element that might affect the risk premium is the variability of returns on foreign investments compared to domestic investments. *Ceteris paribus*, if the variability of returns from domestic investments increases, the risk premium is expected to increase.