Fixed Income 1

All else being equal, the difference between the nominal spread and the Z-spread for a non-Treasury security will most likely be larger when the:

  1. yield curve is steep.
  2. security has a bullet maturity rather than an amortizing structure.
  3. yield curve is flat.

Answer is A

This is best explained by setting up an example in Excel.

can you send me the excel if I provide u my email id?

It’s better if you do it yourself.

Start with, say, a 5-year, annual-pay, 6% coupon bond. Suppose that Treasury spot rates are:

  • 1-year: 1%
  • 2-year: 2%
  • 3-year: 3%
  • 4-year: 4%
  • 5-year: 5%

Calculate the price:

  • Discount 60 at the 1-year spot rate for one period
  • Discount 60 at the 2-year spot rate for two periods
  • Discount 60 at the 3-year spot rate for three periods
  • Discount 60 at the 4-year spot rate for four periods
  • Discount 1,060 at the 5-year spot rate for five periods
  • Tot them up

Calculate the YTM for this bond using Excel’s IRR function; this assumes a flat yield curve.

Increase each spot rate by a spread of, say, 10 bps (0.1%) and do it all over again. Calculate the difference between this YTM and the original YTM. This is the spread for the flat yield curve. Is it greater than, equal to, or less than 10 bps (0.1%)?

If you do it correctly, you should get:

  • Price of the first bond: 1,053.81
  • YTM of the first bond: 4.7652%
  • Price of the second bond: 1,049.34
  • YTM of the second bond: 4.8647%