Calculating Rate of Returns on International Investments (2024)

Learning Objective

1. Learn how to calculate the rate of return (RoR) for a domestic deposit and a foreign deposit.

U.S. Rate of Return

The rate of return on the U.S. CD is simply the interest rate on that deposit. More formally,

RoR_$ = i_$.

This is because the interest rate describes the percentage increase in the value of the deposit over the course of the year. It is also simple because there is no need to convert currencies.

British Rate of Return

The rate of return on the British CD is more difficult to determine. If a U.S. investor, with dollars, wants to invest in the British CD, she must first exchange dollars for pounds on the spot market and then use the British pound (£) to purchase the British CD. After one year, she must convert pounds back to dollars at the exchange rate that prevails then. The rate of return on that investment is the percentage change in dollar value during the year. To calculate this we can follow the procedure below.

Suppose the investor has P dollars to invest (P for principal).

Step 1: Convert the dollars to pounds.

$\frac{P}{E_{\text{\$/£}}}$ is the number of pounds the investor will have at the beginning of the year.

Step 2: Purchase the British CD and earn interest in pounds during the year.

$\frac{P}{E_{\text{\$/£}}}(1+i_{\text{£}})$ is the number of pounds the investor will have at the end of the year. The first term in parentheses returns the principal. The second term is the interest payment.

Step 3: Convert the principal plus interest back into dollars in one year.

$\frac{P}{E_{\text{\$/£}}}(1+i_{\text{£}})E_{\text{\$/£}}^e$ is the number of dollars the investor can expect to have at the end of the year.

The rate of return in dollar terms from this British investment can be found by calculating the expected percentage change in the value of the investor’s dollar assets over the year, as shown below:

$$Ro{R}_{\text{£}}=\frac{\frac{P}{E_{\text{\$/£}}}(1+i_{\text{£}})E_{\text{\$/£}}^{\text{e}}-P}{P}\text{.}$$

After factoring out the P, this reduces to

$$Ro{R}_{\text{£}}=\frac{E_{\text{\$/£}}^{\text{e}}}{E_{\text{\$/£}}}(1+i_{\text{£}})-1.$$

Thus the rate of return on the foreign investment is more complicated because the set of transactions is more complicated. For the U.S. investment, the depositor simply deposits the dollars and earns dollar interest at the rate given by the interest rate. However, for the foreign deposit, the investor must first convert currency, then deposit the money abroad earning interest in foreign currency units, and finally reconvert the currency back to dollars. The rate of return depends not only on the foreign interest rate but also on the spot exchange rate and the expected exchange rate one year in the future.

Note that according to the formula, the rate of return on the foreign deposit is positively related to changes in the foreign interest rate and the expected foreign currency value and negatively related to the spot foreign currency value.