Fixed income security as portfolio of zero coupon bonds?

CFA Level II Fixed Income
#1

In the text, it shows that:

Using the arbitrage-free approach, any fixed-income security should be thought of as a package or portfolio of zero-coupon bonds

Could someone clarify this conceptually? Eg. How’s a premium bond a portfolio of zero-coupon (discount) bonds?

#2

Suppose that you have a 4-year, annual-pay, 6% coupon, $1,000 par bond with a YTM of 5%. It’s equivalent to a portfolio comprising:

  • A 1-year, $60 par zero coupon bond
  • A 2-year, $60 par zero coupon bond
  • A 3-year, $60 par zero coupon bond
  • A 4-year, $1,060 par zero coupon bond

If, instead, your original bond has a YTM of 7%, it’s equivalent to . . . wait a minute! . . . the same portfolio of zeros!