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Use the following information on government bond yields for Questions 1-5. Time Period Rate “0y1y” 4%...

Use the following information on government bond yields for Questions 1-5.

Time Period Rate

“0y1y” 4%

“0y2y” 5%

“0y3y” 6%

“0y4y” 7%

“0y5y” 8%

4. You are considering the purchase of a government bond that will pay you $1000 in exactly 5 years. Given the rates in the table above, what do you expect the bond’s value to be in exactly 1 year?

Solutions

Expert Solution

To value the government bond 1 year from now we need to compute the 4 year Forward rate 1 year from now

(1 + 5 year spot rate)5 = (1 + 1 year spot rate) * (1 + forward rate)4

(1 + 8%)5 = (1 + 4%) * (1 + forward rate)4

(1 + forward rate)4 = (1 + 8%)5 / (1 + 4%)

(1 + forward rate)4 = 1.4128

(1 + forward rate) = 1.090238

forward rate = 9.0238%

4 year Forward rate 1 year from now = 9.0238%

Value of the Government Bond exactly 1 year from now = Payment in 5 years / (1 + 4 year Forward rate 1 year from now)4

Value of the Government Bond exactly 1 year from now = $1000 / (1 + 9.0238%)4

Value of the Government Bond exactly 1 year from now = $707.81

jeff jeffy answered 2 years ago
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