Lesson 1 of 5 · 14 min

Periodicity and converting annual yields

A quoted annual yield means nothing until you know how many times a year it compounds, so convert yields to the same periodicity before you compare them.

In short

  • Periodicity = the number of compounding periods per year assumed in an annual yield. It normally matches the coupon frequency.
  • A semiannual bond basis yield (semiannual bond equivalent yield) is the yield per half-year × 2. Do not confuse it with the yield per semiannual period.
  • An effective annual rate (EAR) has a periodicity of 1: (1+APRm/m)m−1(1 + APR_m/m)^m - 1.
  • Convert between periodicities with (1+APRm/m)m=(1+APRn/n)n(1 + APR_m/m)^m = (1 + APR_n/n)^n.
  • More frequent compounding ↔ lower stated annual rate for the same return. With negative yields, more frequent compounding gives a more negative rate.
  • A zero-coupon bond has no coupons, so the periodicity of its yield is a free choice; any one can be converted to any other.

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Periodicity and converting annual yields · Yield and Yield Spread Measures for Fixed-Rate Bonds