Question

Suppose that two-year interest rates are 3.65% in the U.S and 0.06% in Japan. The current exchange rate is 12.07 yen per dollar. Suppose that one year later interest rates are 3% in both countries, while the value of the yen has appreciated to 115 yen per dollar.

a) A person from the U.S invested in a U.S two-year zero-coupon bond at the start of the period and sold it after one year. What was the return?

b) A person from Japan bought dollar, invested them in the two-year U.S zerocoupon bond, and then sold it after one year. What was the return?

Answer 1

The current exchange rate is mistakenly written as 12.07 yen per dollar. It should be either 120.7 yen per dollar or 120 yen per dollar. I am solving here for 120.7 yen per dollar,

a) Purchase price of the two year zero coupon bond (assuming face/par value of $1000)

= 1000/1.0365^2 = $930.81

Selling price after one year (when interest rate is 3%)

= 1000/1.03 = $970.87

Return to investor = (970.87-930.81)/930.81 = 0.043041 or 4.3041%

b) Amount in Yen required to buy $930.81 = $930.81 * 120.70 Yen/$ = 112348.86 Yen

Amount in Yen realised after sellng the bond = $970.87* 115 Yen/$ = 111650.49 Yen

Return to investor = (111650.49 - 112348.86)/112348.86 = -0.006216 or -0.6216%