Forward rates

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  • 0y1y 0.80%
  • 1y1y 1.12%
  • 2y1y 3.94%
  • 3y1y 3.28%
  • 4y1y 3.14%
Q) The value per 100 of par value of a two-year, 3.5% coupon bond, with interest payments paid annually, is closest to:
  • A. 101.58
  • B. 105.01
  • C. 105.82
Answer: B
3.5/1.0080 + 103.50/(1.0080 x 1.0112) = 3.47 + 101.54 = 105.01
Does anyone know why we multiply the 1 year spot rate to the 2 year spot to discount the 103.50?
I would have just discounted the 103.50 by 1.0112?
 
You need to discount the 2nd year cash flow by the 2 yr spot rate.
The second year spot rate is equivalent to the 1 yr spot rate multiplied by the 1 yr forward rate in 1 yr:
r(0,1) = 1 yr spot rate starting today
r(0,2) = 2 yr spot rate starting today
f(1,2) = 1 yr forward rate starting in yr 1 and ending in yr 2
Then:
(1+r(0,2))^2 = (1+r(0,1))(1+f(1,2))
So you can either discount the 2nd yr cash flow by the LHS or by the RHS.
 
You’re not multiplying the one-year spot rate by the 2-year spot rate.
You’re multiplying (1 + s1)(1 + 1y1y): you’re compounding the one-year spot rate with the 1-year forward rate starting one year from now.
Dividing 103.50 by 1.0112 discounts it from two years hence to one year hence. Discounting it again by 1.0080 discounts it from one year hence to today.
(1 + s1)(1 + 1y1y) = (1 + s2)²
 
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