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28. Suppose you purchase a 10-year, AAA-rated Swiss bond for par that is paying an annual...

28. Suppose you purchase a 10-year, AAA-rated Swiss bond for par that is paying an annual coupon of 6 percent. The bond has a face value of 1,000 Swiss francs (SF). The spot rate at the time of purchase is SF1.15/$. At the end of the year, the bond is downgraded to AA and the yield increases to 8 percent. In addition, the SF appreciates to SF1.05/$.

  1. What is the loss or gain to a Swiss investor who holds this bond for a year? What portion of this loss or gain is due to foreign exchange risk? What portion is due to interest rate risk?
  1. What is the loss or gain to a U.S. investor who holds this bond for a year? What portion of this loss or gain is due to foreign exchange risk? What portion is due to interest rate risk?
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Answer #1

The investor has 3 types of gains from his bond investment. They are intetest income, change in price (due to interest rate risk) and foreign exchange gain/loss.

(A) For Swiss Investor

1. Interest Income = SF1,000 x 6% = SF60

2. Price of bond at end of year 1

= Coupon x PVIFA(8%,9yrs) + Face value x PVIF(8%,9yrs)

= SF60 x 6.246888 + SF1,000 x 0.50025

= SF875.06

Loss due to interest rate risk = SF1,000 - SF875.06

= SF124.94

There will be no foreign currency risk gain or loss, as the investor is trading in only one Currency.

Total Income including Interest = SF60 - SF124.94

= -SF64.94 (i.e. loss)

(B) For US Investor

1. Interest income = SF60 x (1/1.05) = $57.14

(The exchange rate at end of year is taken)

(SF60 is takkem from Part A)

2. Interest rate risk gain or loss

We know that the interest rate risk loss is SF124.94. Converting this into dollars using year starting exchange rate will give $108.38 (SF124.94 x (1/1.15))

3. Foreign exchange risk gain or loss

Opening value of investment = SF1,000 x (1/1.15) = $869.57

Closing value of investment = SF875.06 x (1/1.05) = $833.39

Total loss = $869.57 - $833.39 = $34.18

Gain due to exchange risk = Interest rate risk loss - Total loss

= $108.38 - $34.18

= $74.2

Total Income including Interest income = $57.14 + $74.2 - $108.38

= $22.96

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