Question

1.A semi-annual pay floating-rate note pays a coupon of Libor + 60 bps, with exactly three years to maturity. If the required margin is 40 bps and Libor is quoted today at 1.20% then the value of the bond is closest to:

A. 99.42

B. 100.58

C. 102.332.

The following details (all annual equivalent) are collected from Treasury securities: Years to maturitySpot rate

2.0 1.0%

4.0 1.5%

6.0 2.0%

8.0 2.5%

Which of the following rates is closest to the two-year forward rate six years from now (i.e. the “6y2y” rate)?

A 2.0%

B 3.0%

C 4.0%

Answer 1

1)

No of periods = 3 years * 2 = 6 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (LIBOR + 60 bps / 2) * $100

Coupon per period = ((1.2% + 0.6%) / 2) * $100

Coupon per period = $0.9

YTM = LIBOR + Required margin

YTM = LIBOR + 40bps

YTM = 1.2% + 0.4%

YTM = 1.6%

We assume all the coupon in the future to be based on LIBOR + 60 bps

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

Bond Price = $0.9 / (1 + 1.6% / 2)¹ + $0.9 / (1 + 1.6% / 2)² + ...+ $0.9 / (1 + 1.6% / 2)⁶ + $100 / (1 + 1.6% / 2)⁶

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $0.9 * (1 - (1 + 1.6% / 2)^-6) / (1.6% / 2) + $100 / (1 + 1.6% / 2)⁶

Bond Price = $5.25 + $95.33

Bond Price = $100.58

2)

(1 + 8 year spot rate)⁸ = (1 + 6 year spot rate)⁶ * (1 + 2 year forward rate 6 years from now)²

(1 + 2.5%)⁸ = (1 + 2%)⁶ * (1 + 2 year forward rate 6 years from now)²

(1 + 2 year forward rate 6 years from now)² =  (1 + 2.5%)⁸ / (1 + 2%)⁶

(1 + 2 year forward rate 6 years from now)² = 1.081907

(1 + 2 year forward rate 6 years from now) = 1.081907

(1 + 2 year forward rate 6 years from now) = 1.040148

2 year forward rate 6 years from now = 4.0148% or 4.0%