Interest Rate Differentials and Currency Values

Why Interest Rates and Currency Values Move Together

An interest-rate change can alter the relative appeal of domestic and foreign assets. Investors who want to buy a domestic asset may first need to acquire the domestic currency, changing demand in the foreign-exchange market. But the effect on the spot exchange rate depends not only on the current interest rates: investors also consider the exchange rate they expect in the future. Separating those immediate and expected effects is essential for interpreting a currency movement.

The analysis here uses uncovered interest rate parity (UIP), the benchmark relation between interest rates and expected exchange-rate changes when investors compare unhedged assets. It gives a conditional prediction, not a guarantee that every rate increase will strengthen a currency. Expectations, risk, and market conditions matter.

Definition: Let $E_t$ denote the spot exchange rate at time $t$, quoted as domestic-currency units per one unit of foreign currency. An increase in $E_t$ means the foreign currency costs more domestic currency, so the domestic currency has depreciated. A decrease in $E_t$ means the domestic currency has appreciated. Let $E^e_{t+1}$ be the exchange rate expected for the end of the period.

For example, if $E_t=1.25$ dollars per foreign-currency unit, one unit of foreign currency costs $1.25. If the quote rises to 1.30, the foreign currency has strengthened relative to the dollar; equivalently, the dollar has depreciated. Keeping the quotation convention visible prevents many sign errors.

Uncovered Interest Rate Parity

Suppose a domestic investor can choose between a one-period domestic asset paying the effective rate $i$ and a comparable foreign asset paying the effective rate $i^*$. The foreign asset is uncovered: the investor does not lock in a future conversion rate with a forward contract. Assume for the benchmark calculation that the assets have the same maturity, investors compare expected returns, capital can move freely, and there are no transaction costs, taxes, or risk-premium differences.

A domestic investor who puts one unit of domestic currency into the domestic asset has $1+i$ units at the end of the period. If instead the investor converts that unit into foreign currency at $E_t$, invests at $i^*$, and converts the expected proceeds back at $E^e_{t+1}$, the expected domestic-currency amount is $(1+i^*)E^e_{t+1}/E_t$. Under UIP, these expected gross returns are equal.

1+i=(1+i^*)\frac{E^e_{t+1}}{E_t}

Solving for today’s spot rate gives a useful form for comparative calculations:

E_t=E^e_{t+1}\frac{1+i^*}{1+i}

Interpretation: Holding the expected future exchange rate and the foreign interest rate fixed, a higher domestic interest rate implies a lower spot $E_t$: the domestic currency appreciates immediately. Holding the expected future exchange rate and the domestic rate fixed, a higher foreign interest rate implies a higher spot $E_t$: the domestic currency depreciates immediately.

The result follows from the return comparison. If the domestic rate rises while $E_t$ and the expected future rate stay fixed, the domestic asset would offer a higher return. Investors would then prefer it under the benchmark assumptions. The spot exchange rate must adjust so that the foreign asset’s expected return is again competitive. With the quote used here, that adjustment is a fall in $E_t$: foreign currency costs fewer domestic units today, while the expected future conversion rate is held constant.

Deriving the Expected Currency Movement

UIP can also be rearranged to show what expected exchange-rate movement is associated with a given interest-rate differential. Divide the parity equation by $1+i^*$, then subtract 1:

\frac{E^e_{t+1}}{E_t} =\frac{1+i}{1+i^*}

\frac{E^e_{t+1}-E_t}{E_t} =\frac{i-i^*}{1+i^*}

The left side is the expected percentage change in the domestic-currency price of foreign currency. If $i>i^*$, it is positive: UIP implies expected depreciation of the domestic currency over the period. For small interest rates, the exact expression is often approximated by $i-i^*$, but the exact formula should be used when rates are not negligible or a precise result is required.

This expected depreciation is not a contradiction of the immediate appreciation that can follow a rise in the domestic interest rate. If the expected future exchange rate is unchanged, a higher domestic rate lowers the current spot rate. Starting from that stronger spot value, the currency can then be expected to depreciate toward the unchanged future value. UIP links the current price to the expected future price; it does not say the currency must move in the same direction at every date.

Worked Example: A Domestic Rate Increase With the Future Expectation Held Fixed

A hypothetical investor compares one-year assets in two countries. The foreign interest rate is 4%, and the expected exchange rate one year ahead is 1.20 domestic-currency units per foreign-currency unit. The domestic rate rises from 3% to 6%. Use UIP to find the spot exchange rate before and after the increase, and determine the immediate currency movement.

Method. Use $E_t=E^e_{t+1}(1+i^*)/(1+i)$, with effective annual rates and the same one-year horizon. The expected future rate remains 1.20.

Before the increase: $i=0.03$, $i^*=0.04$, and $E^e_{t+1}=1.20$.

$E_t=1.20(1.04)/(1.03)=1.248/1.03=1.211650$ domestic-currency units per foreign-currency unit.

After the increase: $i=0.06$, while $i^*=0.04$ and $E^e_{t+1}=1.20$ are unchanged.

$E_t=1.20(1.04)/(1.06)=1.248/1.06=1.177358$ domestic-currency units per foreign-currency unit.

The spot quote falls by $1.177358-1.211650=-0.034292$, or approximately $(-0.034292/1.211650)\times100=-2.83\%$. The domestic currency appreciates immediately. As a return check, investing one domestic-currency unit abroad gives an expected domestic amount of $1.04(1.20)/1.177358=1.06$, equal to the domestic asset’s gross return $1+0.06=1.06$.

Common mistake avoided: The expected future exchange rate is in the numerator of the foreign asset’s return, but solving for the current spot rate puts $1+i$ in the denominator. Reversing that ratio predicts the wrong direction.

Domestic and Foreign Rate Changes Have Different Signs

With $E_t$ quoted as domestic currency per foreign currency, a domestic rate increase and a foreign rate increase have opposite effects in the UIP spot-rate equation, provided the other rate and the expected future exchange rate are held fixed. A higher domestic yield makes domestic assets more attractive and is associated with a stronger domestic currency on impact. A higher foreign yield makes foreign assets more attractive and is associated with a weaker domestic currency on impact.

These are ceteris paribus comparisons: they isolate one rate change while holding the expected future exchange rate and the other interest rate constant. In an actual market, those conditions may not hold. A rate announcement may also change expectations about future rates, inflation, economic conditions, or risk. The net spot movement then reflects the combined changes.

Worked Example: A Foreign Rate Increase

A hypothetical one-year domestic asset pays 5%. The foreign rate rises from 2% to 4%. The expected exchange rate in one year remains 1.20 domestic-currency units per foreign-currency unit. Find the spot rate before and after the foreign rate increase, and calculate the percentage change in the spot quote.

Method. Apply the UIP spot-rate equation separately at each foreign rate; keep the domestic rate and expected future exchange rate fixed.

Before: $i=0.05$, $i^*=0.02$, so $E_t=1.20(1.02)/(1.05)=1.224/1.05=1.165714$.

After: $i=0.05$, $i^*=0.04$, so $E_t=1.20(1.04)/(1.05)=1.248/1.05=1.188571$.

The percentage change is $((1.188571-1.165714)/1.165714)\times100$, which is approximately 1.96%. The spot quote rises, so the domestic currency depreciates against the foreign currency. The parity check after the change is $(1.04)(1.20)/1.188571=1.05$, matching the domestic gross return.

Common mistake avoided: A rise in the foreign rate does not have the same sign as a rise in the domestic rate in this quotation convention. Check which country’s currency is in the numerator of the quote before identifying appreciation or depreciation.

Why the Expected Future Rate Can Change the Outcome

A rate change need not leave the expected future exchange rate unchanged. For example, investors may revise that expectation because they anticipate different future interest rates or other economic conditions. The spot rate is then determined by the changed combination $E^e_{t+1}(1+i^*)/(1+i)$. A stronger expected foreign currency raises the spot quote, while a higher domestic rate, on its own, lowers it. The two effects can offset one another or one can dominate.

Identify the quotation.
Here $E$ is domestic currency per foreign currency, so a rise in $E$ is a domestic depreciation.

List the changed inputs.
Record $i$, $i^*$, and $E^e_{t+1}$ before and after the news. Do not assume expectations are fixed unless the problem says so.

Calculate each spot rate.
Use $E_t=E^e_{t+1}(1+i^*)/(1+i)$ for each set of inputs.

Compare and interpret.
Compare the new quote with the old one, then translate its direction into appreciation or depreciation using the stated quotation.

Worked Example: A Rate Increase Alongside a Revised Expectation

In a hypothetical market, the domestic rate is initially 5%, the foreign rate is 3%, and the expected one-year exchange rate is 1.05 domestic-currency units per foreign-currency unit. New information raises the domestic rate to 7% and changes the expected future exchange rate to 1.08. The foreign rate remains 3%. Find the old and new spot rates and explain why the domestic currency’s response differs from the fixed-expectation case.

Method. Recalculate the UIP spot rate using all three inputs in each case. This accounts for the revised expectation rather than attributing the full movement to the interest-rate change.

Initially: $E_t=1.05(1.03)/(1.05)=1.0815/1.05=1.030000$.

After the news: $E_t=1.08(1.03)/(1.07)=1.1124/1.07=1.039626$.

The spot quote increases by $1.039626-1.030000=0.009626$. Relative to the initial quote, the increase is approximately $(0.009626/1.030000)\times100=0.93\%$. The domestic currency therefore depreciates on impact in this calculation. The higher domestic rate alone would have lowered the spot quote, but the higher expected future quote pushes the spot quote upward enough to more than offset that effect.

As a check, the new expected foreign-asset return in domestic currency is $1.03(1.08)/1.039626=1.07$, equal to the domestic gross return $1+0.07=1.07$. Common mistake avoided: attributing the net spot movement to the rate change alone when the expected future rate has also changed.

Immediate Market Response Versus Later Adjustment

An unanticipated rate change can affect asset demand as soon as market participants receive the information, not only on the date a new rate formally takes effect. If domestic assets are expected to yield more, investors may seek them and demand domestic currency. Under the simple UIP comparison, the spot rate moves immediately to a level consistent with the expected future rate and the new interest differential. The predicted appreciation is therefore a statement about the spot adjustment holding expectations and other conditions fixed.

Later, the expected future rate may itself change as new information arrives or as market participants revise their outlook. The exchange rate can then move again. The initial response and later movement need not have the same direction. UIP alone specifies a relationship among current rates, the expected future exchange rate, and interest rates; it does not provide a complete theory of how expectations evolve over time.

Important limitation: The clean UIP calculation assumes comparable assets and ignores risk-premium differences, transaction costs, taxes, restrictions on capital movement, and other market frictions. When investors require compensation for currency or asset risk, expected returns need not be equal. The UIP result is a benchmark conditional prediction, not a promise that a given interest-rate change will produce a particular spot movement.

Common Exam Traps

Inverting the quote. If the quote is domestic currency per foreign currency, a rise in the quote is domestic depreciation. The reverse convention would reverse that interpretation.
Reversing the interest-rate ratio. In the spot-rate formula, the foreign gross return $1+i^*$ is in the numerator and the domestic gross return $1+i$ is in the denominator.
Treating an approximation as exact. The exact expected percentage change is $(i-i^*)/(1+i^*)$, not simply $i-i^*$. The difference is usually small for low rates but can matter in a precise calculation.
Ignoring changed expectations. The ceteris paribus direction for a domestic rate increase does not determine the net movement if the expected future exchange rate also changes.
Confusing an immediate appreciation with expected future appreciation. With a fixed expected future exchange rate, a spot appreciation can coexist with expected depreciation over the period.

Key takeaway: Under the benchmark UIP assumptions, $E_t=E^e_{t+1}(1+i^*)/(1+i)$. A higher domestic rate lowers the spot quote when other inputs are fixed; a higher foreign rate or a higher expected future quote raises it. Always calculate the combined effect and interpret the result using the quotation convention.

Check Your Understanding

For each problem, use the stated domestic-currency-per-foreign-currency quote and the one-period UIP benchmark. Round percentages to two decimal places where needed.

A domestic asset pays 4%, a foreign asset pays 2%, and the expected future exchange rate is 1.08. Calculate the spot rate implied by UIP and state whether the domestic currency is expected to appreciate or depreciate over the period. (Answer: $E_t=1.08(1.02)/(1.04)=1.0592$; expected domestic-currency depreciation of about 1.96%.)
The domestic rate is 6%, the expected future exchange rate is 1.10, and the foreign rate rises from 3% to 5%. Calculate the spot quote before and after the change and its percentage change. (Answer: Before, $1.10(1.03)/(1.06)=1.0689$; after, $1.10(1.05)/(1.06)=1.0896$; the quote rises about 1.94%, so the domestic currency depreciates.)
Initially, $i=5\%$, $i^*=3\%$, and $E^e_{t+1}=1.05$. Then $i$ rises to 7%, $i^*$ stays at 3%, and $E^e_{t+1}$ rises to 1.08. Find both spot rates and the direction of the net change. (Answer: Initially $E_t=1.0300$; afterward $E_t=1.0396$; the spot quote rises, so the domestic currency depreciates.)
The current spot rate is 1.25, the domestic rate is 8%, and the foreign rate is 5%. Under UIP, calculate the expected future exchange rate and the exact expected percentage change in the quote. (Answer: $E^e_{t+1}=1.25(1.08)/(1.05)=1.2857$; expected depreciation is $(0.08-0.05)/(1.05)=2.86\%$.)
A domestic rate increases while the foreign rate is unchanged. An analyst claims that the domestic currency must appreciate, even though investors also raise their expected future exchange rate. Is the claim necessarily correct? State the calculation needed to decide. (Answer: No. Calculate the old and new $E_t=E^e_{t+1}(1+i^*)/(1+i)$; the net direction depends on the relative changes in the domestic rate and expected future exchange rate.)

What You'll Learn