Use the same data in the table above to answer the following questions. a) What

Question

Use the same data in the table above to answer the following questions.
a) What is the the forward rate F(1,1), i.e. the rate that applies to transaction starting in one year and continue for an additional year?

b) Assume that the 3-year forward rate F(2, 1) is 5.7%. This is today's rate that applies to borrowing and lending starting two years from today, for one additional year. Can you price of a 3-year government bond with 5% coupon paid annually and face value equal to $1000?
If you can, state the price and any assumption you need to make to compute it. If you cannot compute the price, state what is missing. (Hint: write the time line and see which rate do you need to price the bond.)

Explanation / Answer

forward rate F(1,1), i.e. the rate that applies to transaction starting in one year and continue for an additional year would be using the formula

1+f1 = 1+r1

(1+f1)(1+f2) = (1+r2)2

(1+f1)(1+f2)(1+f3) = (1+r3)3

1+f1=1+1.9

f1=1.9

(1+f1)(1+f2)=(1+r2)2

(1+1.9)(1+f2)=(1+2.5)2

2.9(1+f2)=(3.5)2

2.9(1+f2)=12.25

f2=3.22

(1+f1)(1+f2)(1+f3) = (1+r3)3

=(2.9)(4.22)(1+f3)=(1+4.4)3

12.24(1+f3)=157.46

f3=11.86%%

3)the price for the 3yr bond cannot be calculated as the spot rate is not given

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