Fixed Income Characteristics

Quick Answer

Bond prices and yields move in opposite directions. For a discount bond the yield ladder climbs (nominal < current yield < yield to maturity < yield to call); for a premium bond it dips in reverse. Duration measures price sensitivity to rate changes; longer maturity, lower coupon, and lower yield all raise it. Credit ratings gate at investment grade.

Everything in the unit on one sheet: yields, the see-saw, the ladder, duration, ratings, and risk.

Which One-Liners Win Points?

  • Bond prices and interest rates move in OPPOSITE directions. Rates up, prices down. The single most important fixed income idea.
  • Premium = coupon above market rate (price over par); discount = coupon below market rate (price under par); par = coupon equals market rate.
  • Premium bonds amortize toward par (built-in principal loss, offset by the high coupon); discount bonds accrete toward par (built-in price gain if the issuer pays). Every bond converges to par at maturity.
  • Higher coupon = LOWER duration = less price volatility (cash comes back sooner). Counterintuitive but tested.
  • A zero-coupon bond's duration EQUALS its maturity (maximum sensitivity); a coupon bond's duration is always less than its maturity.
  • Zero-coupon bonds have the HIGHEST interest rate risk but ZERO reinvestment risk (no coupons to reinvest). Treasury STRIPS and zero-coupon corporates owe phantom income tax yearly, so they fit tax-deferred accounts. A T-bill matures in a year or less, so its discount is ordinary income at sale or maturity.
  • Investment-grade cutoff = BBB-/Baa3 and above; below that is high-yield (junk). Many fiduciary, pension, and insurance accounts may hold investment grade only.
  • Interest rate risk and reinvestment risk are INVERSELY related. Duration matching (immunization) balances the two.
  • Yield to worst (YTW) is always the LOWEST of yield to maturity (YTM), yield to call (YTC), or any yield to a put date.
  • Callable bonds benefit issuers, who call when rates fall; price compression near the call price is negative convexity.
  • OID and market discount below 0.25% per full year to maturity are de minimis and treated as zero. So de minimis OID is not accreted annually as ordinary income, and de minimis market discount produces capital gain instead of ordinary income at sale or maturity.
  • Quotation conventions differ by instrument: corporates and term/dollar munis as a percentage of par, Treasury notes/bonds and agencies in 32nds, T-bills on a discount yield basis, muni serial bonds in yield terms. "Offered on a 5.5 basis" quotes YTM, not price; compare that basis to the coupon for premium/discount/par.
  • Accrued interest is added to the quoted price at settlement: the buyer pays the seller for interest since the last coupon, and recovers it in the next full coupon.
  • Moody's bottoms out at C; only S&P and Fitch use D. C is Moody's lowest grade and already means "typically in default."

Which Numbers Matter Most?

  • Nominal (coupon) yield = annual coupon / par value, fixed at issuance.
  • Current yield = annual coupon / market price. Example: $50 / $900 = 5.56%.
  • YTM = annualized return if held to maturity, coupons reinvested at the YTM rate.
  • YTC = annualized return if called at the first call date, using the call price and years to call.

Yield-to-price map: YTM > coupon → discount, YTM < coupon → premium, YTM = coupon → par. The ladder itself is below.

Key formulas:

Taxable Equivalent Yield (TEY)=Tax-exempt Yield1−Marginal Tax Rate\text{Taxable Equivalent Yield (TEY)} = \frac{\text{Tax-exempt Yield}}{1 - \text{Marginal Tax Rate}} Price Change≈−Duration×Change in Yield\text{Price Change} \approx -\text{Duration} \times \text{Change in Yield} Credit Spread=Corporate Bond Yield−Treasury Yield\text{Credit Spread} = \text{Corporate Bond Yield} - \text{Treasury Yield}

Duration drivers: longer maturity, lower coupon, and lower yield all raise duration. A bond with duration 7 loses roughly 7% if rates rise 1%.

What Are the Memory Aids for Price, Yield, and the Ladder?

Rates and prices sit on a see-saw. One end up always means the other end down.

Read the ladder by the comparison signs, not by left-to-right order:

  • Discount bond: yields climb: Nominal < Current < YTM < YTC
  • Premium bond: yields dip: Nominal > Current > YTM > YTC
  • Par bond: yields stay flat: Nominal = Current = YTM

Which Gotchas Trip Students Up?

  • Yield ordering flips by price. Mixing up the direction is the classic trap.
  • For premium callable bonds, use YTC, not YTM, as the relevant yield; the issuer will likely call.
  • Modified duration ignores embedded options. Callable bonds need effective duration, which is SHORTER because the call compresses the bond's life when rates fall.
  • Downgrade = price falls, yield rises; upgrade = price rises, yield falls. A drop from BBB to BB ("fallen angel") can force institutional selling and a sharp decline.
  • During a recession, credit spreads WIDEN even if Treasury yields fall, so corporate prices can drop while Treasury prices rise. Rate moves are not spread moves.
  • Ratings measure credit risk only (default likelihood), NOT interest rate, liquidity, or market risk.

One-Breath Recap

Bond prices and yields see-saw in opposite directions: coupon above market rate means a premium (price over par, amortized down), coupon below means a discount (price under par, accreted up), and every bond converges to par at maturity. The yield ladder climbs for discounts (nominal, then current yield, then yield to maturity, then yield to call) and dips in reverse for premiums, with yield to worst always the lowest; use yield to call on premium callable bonds. Duration measures rate sensitivity (roughly the percent price move per 1% rate change), rising with longer maturity, lower coupon, and lower yield, and equaling maturity for zeros; use effective duration when a call is embedded. Ratings gate at investment grade (BBB-/Baa3), spreads widen in recessions, and interest rate risk trades off inversely against reinvestment risk, balanced by immunization.

Need more than the recap? Read the full Fixed Income Characteristics unit.