Yield and Yield Spread Measures for Fixed-Rate Bonds

A bond's "yield" is not one number. The same cash flows produce different yields depending on how you compound, what you discount against, and which spread you quote. The exam tests whether you can convert between these conventions cleanly.

A stated annual rate must always travel with its compounding frequency, called the periodicity. A 6% rate compounded semi-annually is not the same return as 6% compounded monthly. You calculate the annual yield on a common periodicity before you compare two quotes, because more compounding periods squeeze more growth out of the same stated rate.

$$\left(1 + \frac{r_m}{m}\right)^{m} = \left(1 + \frac{r_n}{n}\right)^{n}$$

KEY: US bonds quote yields with semi-annual periodicity (the "bond equivalent yield" or BEY). European bonds typically quote annual. To compare a US Treasury YTM to a Bund YTM, convert one to match the other.

The effective annual yield (EAY) sets $n = 1$, giving the once-a-year compounded equivalent. EAY always exceeds the stated rate when periodicity is greater than 1.

Common mistakes

• Comparing yields across different periodicities directly. A 6% semi-annual yield is richer than a 6% annual yield. Compounded twice a year, 6% grows to an effective $(1.03)^{2} - 1 = 0.0609$, or 6.09%, against 6.00% for the annual quote. Put the other way, a 6% annual yield equals only a 5.91% semi-annual bond equivalent yield.
• Treating current yield as YTM. Current yield ignores the pull-to-par on premium or discount bonds. A premium bond's current yield overstates total return; a discount bond's current yield understates it. Trap: reporting 4.063% for the Example 2 bond when its YTM is 4.35%.
• Reporting the periodic rate as the YTM. The calculator returns 2.175% per half-year in Example 2. Trap: selecting 2.175% instead of the 4.35% annualized YTM.

Bottom line

• Periodicity must accompany every rate: an 8% semi-annual bond equivalent yield is not 8% annual. Convert via $(1 + r_m/m)^m = (1 + r_n/n)^n$
• Effective annual yield always exceeds the stated rate whenever periodicity is greater than 1, because interest compounds on interest within the year
• Current yield ignores capital gain or loss and reinvestment; YTM captures both under hold-to-maturity and assumes reinvestment at YTM
• Simple yield = (coupon plus discount accretion, or minus premium amortization, straight-line) / price

Exam shortcut

For periodicity conversion, equate effective annual factors, never just multiply or divide rates by frequency. For YTM, solve I/Y on the TVM keys and multiply by the periodicity before you pick an answer. For YTW on a callable bond, compute YTM and the yield to every call date given, then pick the smallest; a later call can be the minimum.

The full lesson (about 3,556 words, 24 min read) adds 11 worked examples, all 7 common mistakes, a self-check, free in the app.

Learning objectives

• yield measures fixed-rate bonds

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