Foreign Exchange Markets and Rates of Return

Learning Objective

1. Learn how to apply numerical values for exchange rates and interest rates to the rate of return formulas to determine the best international investment.

Use the data in the tables below to calculate in which country it would have been best to purchase a one-year interest-bearing asset.

Example 1

Consider the following data for interest rates and exchange rates in the United States and Britain:

We imagine that the decision is to be made in $2004$, looking forward into $2005$. However, we calculate this in hindsight after we know what the $2005$ exchange rate is. Thus we plug in the $2005$ rate for the expected exchange rate and use the $2004$ rate as the current spot rate. Thus the ex-post (i.e., after the fact) rate of return on British deposits is given by

$R o R_{£}=0.0483+(1+0.0483) \frac{1.75-1.96}{1.96}$

which simplifies to

$RoR_£ = 0.0483 + (1 + 0.0483)(−0.1071) = −0.064$ or $−6.4 \%$.

A negative rate of return means that the investor would have lost money (in dollar terms) by purchasing the British asset.

Since $RoR_$ = 2.37 \% > RoR_£ = −6.4 \%$, the investor seeking the highest rate of return should have deposited her money in the U.S. account.

Example 2

Consider the following data for interest rates and exchange rates in the United States and Japan.

Again, imagine that the decision is to be made in $2004$, looking forward into $2005$. However, we calculate this in hindsight after we know what the $2005$ exchange is. Thus we plug in the $2005$ rate for the expected exchange rate and use the $2004$ rate as the current spot rate. Note also that the interest rate in Japan really was $0.02$ percent. It was virtually zero.

Before calculating the rate of return, it is necessary to convert the exchange rate to the yen equivalent rather than the dollar equivalent. Thus

$E_{\$ / ¥}^{04}=\frac{1}{104}=0.0096$  and $E_{\$ / ¥}^{05}=\frac{1}{120}=0.0083$

Now, the ex-post (i.e., after the fact) rate of return on Japanese deposits is given by

$R o R_{¥}=0.0002+(1+0.0002) \frac{0.0083-0.0096}{0.0096}$

which simplifies to

$RoR_¥ − 0.0002 + (1 + 0.0002)(−0.1354) = −0.1352$ or $−13.52 \%$.

A negative rate of return means that the investor would have lost money (in dollar terms) by purchasing the Japanese asset.

Since $RoR_$ = 2.37 \% > RoR_¥ = −13.52 \%$, the investor seeking the highest rate of return should have deposited his money in the U.S. account.

Example 3

Consider the following data for interest rates and exchange rates in the United States and South Korea. Note that South Korean currency is in won (W).

As in the preceding examples, the decision is to be made in $2004$, looking forward to $2005$. However, since the previous year interest rate is not listed, we use the current short-term interest rate. Before calculating the rate of return, it is necessary to convert the exchange rate to the won equivalent rather than the dollar equivalent. Thus

$E_{\$ / \mathrm{w}}^{04}=\frac{1}{1059}=0.000944$ and $E_{\$ / \mathrm{w}}^{05}=\frac{1}{1026}=0.000975$

Now, the ex-post (i.e., after the fact) rate of return on Italian deposits is given by

$R o R_{\mathrm{W}}=0.0404+(1+0.0404) \frac{0.000975-0.000944}{0.000944}$

which simplifies to

$RoR_W = 0.0404 + (1 + 0.0404)(0.0328) = 0.0746$ or $+7.46 \%$.

In this case, the positive rate of return means an investor would have made money (in dollar terms) by purchasing the South Korean asset.

Also, since $RoR_$ = 2.37$ percent < $RoR_W = 7.46$ percent, the investor seeking the highest rate of return should have deposited his money in the South Korean account.

Key Takeaway

• An investor should choose the deposit or asset that promises the highest expected rate of return assuming equivalent risk and liquidity characteristics.