Question

A 2%, 3-year US Treasury is selling at 100.25 . The 5% , 3-year IBM is selling at 100.65. Both bonds pay interest semi-annually. The G-spread in basis points on the IBM bond is closest to

		a. 264 bps.
		b. 285 bps.
		c. 300 bps
		d. 345 bps
		e. 435 bps

A 3-year floating-rate note pays 6-month Libor plus 140 bps. The floater is priced at 97 per 100 of par value. Current 6-month Libor is 1.00%. Assume a 30/360 day-count convention and evenly spaced periods. The discount margin for the floater in basis points is closest to:

		a. 218 bps.
		b. 246 bps.
		c. 342 bps.
		d. 180 bps.
		e. 239 bps.

Answer 1

A)

Let us compute the Yield to Maturity(YTM) of US Treasury

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 = (2% / 2) * $100

Coupon per period = $1

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

$100.25 = $1 / (1 + YTM / 2)¹ + $1 / (1 + YTM / 2)² + ...+ $1 / (1 + YTM / 2)⁶ + $100 / (1 + YTM / 2)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 1, FV = 100, PV = -100.25

CPT --> I/Y = 0.9569

YTM = 2 * I/Y

YTM = 2 * 0.9569%

YTM of US Treasury = 1.9139% or 1.91%

Let us compute the Yield to Maturity(YTM) of IBM

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 = (5% / 2) * $100

Coupon per period = $2.5

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

$100.65 = $2.5 / (1 + YTM / 2)¹ + $2.5 / (1 + YTM / 2)² + ...+ $2.5 / (1 + YTM / 2)⁶ + $100 / (1 + YTM / 2)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 2.5, FV = 100, PV = -100.65

CPT --> I/Y = 2.3825

YTM = 2 * I/Y

YTM = 2 * 2.3825%

YTM of IBM = 4.7649% or 4.76%

G-spread = YTM of IBM - YTM of US Treasury

G-spread = 4.76% - 1.91%

G-spread = 2.85% or 285 bps

B)

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 + 140 bps) / 2) * $100

Coupon per period = ((1% + 1.4%) / 2) * $100

Coupon per period = $1.2

We assume all the coupons shall be 6 month LIBOR + 140 bps paid semi-annually

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

$100.25 = $1.2 / (1 + YTM / 2)¹ + $1.2 / (1 + YTM / 2)² + ...+ $1.2 / (1 + YTM / 2)⁶ + $100 / (1 + YTM / 2)⁶

Using Texas Instruments BA 2 plus calculator

SET N = 6, PMT = 1.2, FV = 100, PV = -97

CPT --> I/Y = 1.7307

YTM = 2 * I/Y

YTM = 2 * 1.7307%

YTM = 3.4614% or  3.46%

YTM = LIBOR + Discount margin

3.46% = 1% + Discount margin

Discount margin = 2.46% or 246 bps