Exchange Rates and Cross-Border Capital Flows

Why Interest Rates Are Not the Whole Return

An investor comparing a domestic asset with a foreign asset must consider more than the interest rates each pays. The foreign asset’s value is ultimately converted back into the investor’s domestic currency, so the exchange rate at that time also affects the result. A foreign asset can pay a higher interest rate yet produce a lower domestic-currency return if its currency loses enough value.

This comparison helps explain why interest-rate differences and expectations about currencies can influence cross-border investment. It does not, by itself, predict a certain exchange-rate movement or guarantee that investors will move their funds. Perceived risk, transaction costs, liquidity, and other features of the assets also matter.

Definition: Let $E_t$ denote the exchange rate at time $t$, quoted as units of domestic currency per one unit of foreign currency. An increase in $E_t$ means the foreign currency has appreciated against the domestic currency; a decrease means it has depreciated. For a one-period investment, $i_D$ is the domestic asset’s interest rate and $i_F$ is the foreign asset’s interest rate. When both rates apply over the same period, the foreign asset’s gross domestic-currency return is $(1+i_F)(E_1/E_0)$.

This comparison assumes the investor starts with domestic currency, converts it at $E_0$, invests for one period at a known foreign interest rate, and converts the proceeds back at $E_1$. It also assumes the assets have the same investment horizon and that taxes, transaction costs, credit losses, and restrictions on moving funds are absent. If these assumptions do not hold, the investor must account for the relevant differences separately.

Deriving the Domestic-Currency Return

The conversion formula follows from keeping track of the units of currency. Suppose an investor begins with $W$ units of domestic currency. At $E_0$ domestic currency per foreign unit, the investor can buy $W/E_0$ foreign currency units. After one period, that amount earns interest at $i_F$. The resulting foreign currency is then converted back into domestic currency at $E_1$.

\begin{aligned} \text{Initial foreign currency} &= \frac{W}{E_0},\\ \text{Foreign currency after investment} &= \frac{W}{E_0}(1+i_F),\\ \text{Domestic currency after conversion} &= \frac{W}{E_0}(1+i_F)E_1,\\ \text{Gross domestic-currency return} &= \frac{W(1+i_F)E_1/E_0}{W} =(1+i_F)\frac{E_1}{E_0}. \end{aligned}

Subtracting 1 from the gross return gives the net return. The formula combines the interest earned abroad with the currency conversion effect; these effects multiply rather than simply add. For modest rates, adding the foreign interest rate and the percentage change in $E$ can be a rough approximation, but the product is the exact result under the stated assumptions.

R_F^D=(1+i_F)\frac{E_1}{E_0}-1

If the future exchange rate is uncertain, $E_1$ is a random variable. With a fixed foreign interest rate and a fixed initial exchange rate, expected domestic-currency return is $(1+i_F)\mathbb{E}[E_1]/E_0-1$. This expected return is not a guaranteed outcome: the realized exchange rate may differ from its expected value. The domestic asset’s one-period return in this simple comparison is $i_D$.

Important distinction: A higher foreign interest rate does not necessarily mean a higher return for a domestic investor. Compare the domestic return $i_D$ with the foreign return after converting into domestic currency. If the exchange rate is uncertain, also distinguish expected return from the return that will actually be realized.

Worked Comparisons

Worked Example: A Lower Foreign Yield With Expected Currency Appreciation

A domestic investor has $10,000 to invest for one year. A domestic deposit pays 6%. A comparable foreign deposit pays 4%. The current exchange rate is $E_0=1.20$ domestic dollars per foreign unit, and the investor expects $E_1=1.23$. Ignoring risk and transaction costs, compare the expected domestic-currency returns and ending values.

Method and assumptions. Both interest rates are annual rates for the same one-year period. The investor can exchange currency at the stated rates, and the foreign deposit pays its stated rate without default.

Step 1: Interpret the exchange-rate movement. The quote rises from 1.20 to 1.23 domestic dollars per foreign unit. Its percentage change is $(1.23-1.20)/1.20=0.025$, or 2.5%. The foreign currency is expected to appreciate.

Step 2: Calculate the domestic investment. Its ending value is $10{,}000(1.06)=\$10{,}600$, a return of 6%.

Step 3: Convert, invest, and convert back. The initial foreign currency purchased is $\$10{,}000/1.20=8{,}333.333\ldots$ foreign units. After interest, the balance is $8{,}333.333\ldots(1.04)=8{,}666.666\ldots$ foreign units. Converting at 1.23 gives $8{,}666.666\ldots(1.23)=\$10{,}660$.

Step 4: Compare returns. The foreign investment’s domestic-currency return is $(10{,}660-10{,}000)/10{,}000=0.066$, or 6.6%. It exceeds the domestic return by 0.6 percentage points. The same result follows from $1.04(1.23/1.20)-1=0.066$.

Check and common mistake. The foreign investment earns 4% in foreign currency, but the appreciated currency raises its domestic-currency return to 6.6%. Comparing 4% directly with 6% would omit the conversion effect and reach the wrong conclusion. The ending value and return agree: $\$10{,}000(1.066)=\$10{,}660$.

Worked Example: A Higher Foreign Yield Despite Expected Currency Depreciation

An investor begins with $20,000. A domestic asset pays 4% over one year, while a foreign asset pays 7%. The current quote is $E_0=2.00$ domestic units per foreign unit, and the expected future quote is $E_1=1.95$. Under the same no-risk and no-transaction-cost assumptions, determine which has the higher expected domestic-currency return.

Method and assumptions. Use the conversion formula for the foreign investment. The expected exchange rate is below the current quote, so the foreign currency is expected to depreciate.

Step 1: Calculate the currency change. The percentage change is $(1.95-2.00)/2.00=-0.025$, or -2.5%. This is an expected depreciation of the foreign currency, not an appreciation.

Step 2: Calculate the domestic alternative. The ending value is $\$20{,}000(1.04)=\$20{,}800$, for a 4% return.

Step 3: Calculate the foreign alternative. The investor initially buys $\$20{,}000/2.00=10{,}000$ foreign units. These grow to $10{,}000(1.07)=10{,}700$ foreign units. At the expected exchange rate, they are worth $10{,}700(1.95)=\$20{,}865$.

Step 4: Compare. The foreign return is $(20{,}865-20{,}000)/20{,}000=0.04325$, or 4.325%. Equivalently, $1.07(1.95/2.00)-1=1.07(0.975)-1=0.04325$. Its expected return exceeds the domestic return by 0.325 percentage points.

Check and common mistake. The foreign yield is higher, and the expected currency depreciation reduces—but does not eliminate—the advantage. Calling the currency movement an appreciation because the foreign asset’s return remains above 4% confuses the asset return with the exchange-rate movement. The expected ending value checks: $\$20{,}000(1.04325)=\$20{,}865$.

How Perceived Risk Changes the Comparison

Expected returns alone do not describe the whole investment decision. A foreign asset may expose an investor to uncertainty about its currency, the borrower’s ability to pay, the ease of selling the asset, or restrictions on transferring funds. Investors may require compensation for bearing risks they dislike. As a result, two assets with the same expected return need not be equally attractive, and a higher expected return need not lead every investor to choose the foreign asset.

There is no single risk adjustment that applies to every investor or asset. To make the effect transparent, the next example uses a deliberately simple decision rule: subtract a stated risk charge, measured in percentage points, from expected return. This is a comparison device for the hypothetical investor, not a universal pricing formula. In real decisions, risk may affect investors differently and may not be summarized by one number.

Worked Example: A Risk Charge Reverses the Expected-Return Ranking

A fund can invest $2 million in a domestic asset paying 4% or in a foreign asset paying 6%. The current exchange rate is $E_0=1.25$ domestic units per foreign unit, and the expected rate in one year is $E_1=1.24$. The fund’s investment committee assigns the foreign asset a risk charge of 1.5 percentage points. Under the stated decision rule, compare the risk-adjusted scores and identify the preferred asset.

Method and assumptions. First calculate the foreign asset’s expected return in domestic currency. Then subtract the committee’s stated risk charge and compare the resulting score with the domestic return. Ignore fees and taxes.

Step 1: Identify the currency movement. The percentage change in the quote is $(1.24-1.25)/1.25=-0.008$, or -0.8%. The foreign currency is expected to depreciate slightly.

Step 2: Calculate the foreign expected return. The gross domestic-currency return is $1.06(1.24/1.25)=1.06(0.992)=1.05152$. The expected return is therefore $1.05152-1=0.05152$, or 5.152%.

Step 3: Apply the committee’s risk charge. The risk-adjusted score is $5.152\%-1.5\%=3.652\%$. The domestic asset’s score is 4%, since no domestic risk charge is specified.

Step 4: Decide under this rule. Because 3.652% is less than 4%, the committee prefers the domestic asset according to its stated rule, even though the foreign asset has the higher expected return before adjustment.

Check and common mistake. Subtracting 1.5 percentage points gives 3.652%, not 3.652 percentage points below the domestic return and not a 1.5% reduction of the foreign return. The comparison is $3.652\%<4\%$. Treating the foreign asset’s expected return as sufficient to determine the choice would ignore the risk assumption in the problem.

From Portfolio Choices to Currency Flows

When a domestic investor buys a foreign asset, the investor generally sells domestic currency and buys foreign currency to pay for it. That transaction increases demand for foreign currency and supplies domestic currency in the foreign-exchange market. A foreign investor buying a domestic asset generally makes the opposite currency transaction. These are the payment-side mechanics of an investment decision; the actual route may differ if the investor already holds the required currency or uses an intermediary.

If many investors revise their expected returns or risk assessments in the same direction, their transactions can contribute to a change in currency demand and supply. For example, a perceived improvement in the prospective return on domestic assets may attract foreign investment, increasing demand for domestic currency as investors acquire it to make purchases. This does not establish the size or even the final direction of an exchange-rate change: other buyers and sellers may respond, and expectations may already be reflected in prices.

These cross-border asset transactions are financial flows. As the earlier material on balance-of-payments accounts explains, financial flows are recorded alongside the current account and related external transactions. A financial outflow does not, on its own, show that a country has an unsustainable external position or that its currency must depreciate. It describes a transaction during a period; it is not the same thing as the accumulated stock of foreign assets and liabilities.

A useful analysis keeps three questions separate: What is the asset’s expected return in the investor’s own currency? What risks or costs change the investor’s assessment? What currency transaction is needed to make the investment? Answering them in that order prevents a common error: inferring the attractiveness of an asset from its stated interest rate alone.

Common Exam Traps

Reversing the exchange-rate quote. With domestic currency per foreign unit, a rise in $E$ is foreign-currency appreciation. Always use the quote’s stated units before labeling the movement.
Comparing unlike returns. A foreign interest rate is earned in foreign currency. Convert the investment proceeds back before comparing with the domestic return.
Adding instead of multiplying. The exact gross return is $(1+i_F)(E_1/E_0)$, not $1+i_F+(E_1-E_0)/E_0$. The additive expression omits the interaction between interest and currency change.
Treating an expectation as a guarantee. An expected future exchange rate is not necessarily the realized rate. Uncertainty can matter even when expected returns are equal.
Ignoring the risk assumption. A risk-adjusted comparison depends on the stated investor or decision rule. Do not invent a risk charge or assume every investor evaluates risk identically.

Key takeaway: For an investor starting with domestic currency, the foreign asset’s one-period domestic-currency return depends on both its interest rate and the exchange-rate ratio $E_1/E_0$. Expected returns can influence cross-border asset demand, while perceived risk can change the comparison. The associated currency transactions help trace financial flows, but they do not alone determine the exchange rate.

Check Your Understanding

For each problem, use the stated domestic-per-foreign exchange-rate quote. Assume one-year investments unless otherwise stated, and ignore costs and risk except where specified.

A domestic deposit pays 3%, while a foreign deposit pays 5%. The current exchange rate is $E_0=4.00$ domestic units per foreign unit, and the expected rate in one year is $E_1=4.08$. Calculate the foreign investment’s expected domestic-currency return, identify the currency movement, and state the return advantage over the domestic deposit. (Answer: The foreign currency is expected to appreciate by 2%; foreign return $=1.05(4.08/4.00)-1=7.1\%$, an advantage of 4.1 percentage points.)
A domestic asset pays 6%, and a foreign asset pays 9%. The exchange rate is expected to fall from $E_0=0.80$ to $E_1=0.76$ domestic units per foreign unit. Which asset has the higher expected domestic-currency return, and by how much? (Answer: The foreign currency is expected to depreciate by 5%; foreign return $=1.09(0.76/0.80)-1=3.55\%$, so the domestic asset is higher by 2.45 percentage points.)
An investor has $500,000. A domestic asset pays 4%; a foreign asset pays 5%. The exchange rate is $E_0=1.60$ domestic units per foreign unit and is expected to be $E_1=1.62$. Calculate the foreign asset’s expected ending value in domestic currency and compare its return with the domestic asset. (Answer: Initial foreign balance $=500{,}000/1.60=312{,}500$; after interest $=328{,}125$ foreign units; expected ending value $=328{,}125(1.62)=\$531{,}562.50$. Its return is 6.3125%, or 2.3125 percentage points above the domestic return.)
A domestic asset pays 4.5%. A foreign asset pays 7%, with $E_0=2.50$ and expected $E_1=2.45$ domestic units per foreign unit. An investor subtracts a risk charge of 1 percentage point from the foreign expected return and applies no charge to the domestic asset. Which asset has the higher score under this rule? What if the foreign risk charge falls to 0.2 percentage points? (Answer: The foreign expected return is $1.07(2.45/2.50)-1=4.86\%$. With a 1-point charge its score is 3.86%, below 4.5%; with a 0.2-point charge its score is 4.66%, above 4.5%.)
A domestic pension fund converts $12 million into foreign currency at $E_0=1.50$ domestic units per foreign unit and uses all of it to buy foreign bonds. How many foreign currency units does it acquire, and what currency transactions accompany the purchase? Do these facts alone determine the later exchange rate? (Answer: It acquires $\$12{,}000{,}000/1.50=8{,}000{,}000$ foreign units; the transaction supplies domestic currency and demands foreign currency. No; other market transactions and responses also affect the exchange rate.)

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