Bond characteristics and valuation: ratings, yields, duration, credit spreads, calls, convertibles and DCF

A bond is a stack of promised payments. Nearly every bond question on the exam asks what happens to the value of those promises when market rates, the issuer's credit or the calendar changes.

A bond is a loan from your client to an issuer. The issuer promises interest, called the coupon, plus face value, called par, at maturity. Par is usually $1,000. A coupon bond pays interest usually every six months, so a 6% bond pays $30 twice a year.

So what are those promises worth today? Under discounted cash flow (DCF) valuation, a bond's value is the present value of its coupons and par discounted at the current market yield. The market yield is the return investors demand today from similar bonds.

$$P = \sum_{t=1}^{2n} \frac{C/2}{(1 + y/2)^{t}} + \frac{1{,}000}{(1 + y/2)^{2n}}$$

Here $C$ is the annual coupon in dollars, $y$ the market yield and $n$ the years to maturity. Three results follow:

• Par: A bond trades at par when its coupon equals the market yield.
• Premium: It trades at a premium when the coupon is higher, because buyers pay extra for an above-market coupon.

Common mistakes

• Calling a BB+ or Ba1 bond investment grade. The line is BBB- or Baa3, so both are high-yield.
• Quoting yield to call automatically for a premium callable bond. The quote is yield to worst, which is occasionally YTM.
• Using Macaulay duration as the price change. A 15-year zero at 4% loses about 14.7% per point, not 15%.

Bottom line

• A bond's price is the present value of its coupons and par at the market yield: par when coupon equals yield, premium when coupon is higher, discount when lower; prices move opposite to rates and drift to par.
• Premium bond yields rank nominal > current > YTM > YTC; a discount bond reverses the order; the quoted yield is YTW, the lowest of YTC and YTM.
• Macaulay duration is the weighted average time to cash flows (a zero's equals its maturity); modified duration, Macaulay ÷ (1 + y/2), is the percentage price change per one-point yield move and rises with longer maturity, lower coupon and lower...
• Investment grade is BBB- or Baa3 and above; the credit spread is yield over a same-maturity Treasury, wider for low ratings and in recessions; a downgrade raises yield and cuts price.

Exam shortcut

Open every bond question by comparing the coupon with the market yield. That tells you premium or discount, and the yield ranking follows. If a stem asks which yield a callable bond is quoted at, choose yield to worst. For price changes, multiply modified duration by the yield change in points; given only Macaulay duration, the right answer is slightly smaller.

The full lesson (about 3,495 words, 23 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

• B7

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