Question

In: Finance

Consider the following spot rate curve: 6-month spot rate: 4%. 12-month spot rate: 12%. 18-month spot...

Consider the following spot rate curve:

  • 6-month spot rate: 4%.
  • 12-month spot rate: 12%.
  • 18-month spot rate: 14%.

What is the forward rate for a 6-month zero coupon bond issued one year from today? Equivalently, the question asks for f12, where 1 time period consists of 6 months. Remember, like spot rates, forward rates are expressed as bond-equivalent yields.

Solutions

Expert Solution

Given that,

1-year spot rate r1 = 12%

18 month spot rate r1.5 = 14%

So, 6 month forward rate 1 year from now = 2*((((1+r1.5/3)^2)/((1+r1/2)^2)) - 1) = 2*((((1+0.14/2)^3)/((1+0.12/2)^2)) - 1)

=> 6 month forward rate 1 year from now = 18.06% or 0.1806


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