Numerical Examples Using the Rate of Return Formula

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. These numbers were taken from the December 17, 2005 issue of the Economist.

Example 1:. Consider the following data for interest rates and exchange rates in the US and Britain.

i_$	2.37% per year
i_£	4.83% per year
E_£⁰⁴	1.96 $/_£
E_$/£⁰⁵	1.75 $/_£

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 2005exchange rate is. Thus, we plug in the 05 rate for the expected exchange rate and use the 04 rate as the current spot rate. Thus, the ex-post (i.e. after the fact) rate of return on British deposits is given by,

which simplifies to

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 their money in the US account.

Example 2: Consider the following data for interest rates and exchange rates in the US and Japan.

i_$	2.37% per year
i_¥	0.02% per year
E_$/¥⁰⁴	104 ¥/$
E_$/¥⁰⁵	120 ¥/$

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 05 rate for the expected exchange rate and use the 04 rate as the current spot rate. Note also that the interest rate in Japan REALLY was 0.02%!!! 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,

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

which simplifies to

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 their money in the US account.

Example 3: Consider the following data for interest rates and exchange rates in the US and South Korea. Note that South Korean currency is in won (W).

i_$	2.37% per year
i_W	4.04% per year
E_$/W⁰⁴	1059 W/$
E_$/W⁰⁵	1026 W/$

As before the decision is to be made in 1996, looking forward into 1997. However, since the year-ago 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,

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

which simplifies to

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% < RoR_W = 7.46% the investor seeking the highest rate of return should have deposited their money in the South Korean account.

International Finance Theory and Policy - Chapter 20-2: Last Updated on 12/29/05