calculating spread

CFA Level II Fixed Income
#1

“Swap rates are very useful in the valuation of bonds. I would like you to use the information in Exhibit 2 to value a bond, issued by AAA-rated European Supranational Bank (ESB), maturing in 3.86 years, with a coupon rate of 2.86% paid annually. Dealers are quoting the bond flat to swaps. Simple Interpolation can be used to perform this calculation”

EXHIBIT 2 - YIELD MEAURES AT VARIOUS MATURITIES

MATURITY (YEARS) 1 2 3 4 5

OFF THE RUN BOND YIELD (%) 0.25 0.32 0.46 0.57 0.66

ON THE RUN BOND YIELD (%) 0.21 0.27 0.41 0.5 0.59

SWAP RATE (%) 0.81 0.89 1.05 1.16 1.27

Based on the data, the spread the market is expecting for the credit and liquidity component of the yield to maturity for the ESB bond is closest to :

A 1.14

B 0.59

C 0.66

1 Like
#2

anyone knows how to calculate this?

#3

You have to use interpolation to calculate the yield and swap rate, then to can find the spread.

Since the bond matures in 3.86 years, you combine the yield for a 3 year bond + the difference between a 4 year and 3 year bond multiplied by 0.86 years to capture the yield after year 3.

0.41 + 0.86 * (0.5 - 0.41) = 0.4874

Do the same thing for the swap rates.

1.05 + 0.86 * (1.16 - 1.05) = 1.1446

Swap Rate - Yield = Swap Spread

1.1446 - 0.4874 = 0.6572 or 0.66 rounded

#4

thanks!

#5

So why do i need this swap spread to pricing the bond if i already have the interpolated yield?