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 price/yield see-saw, the yield ladder, duration, ratings, and bond risk.

The One-Liners That Win Points

  • Bond prices and interest rates move in OPPOSITE directions. Rates up, prices down (see-saw). This is 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 are amortized toward par (guaranteed principal loss offset by high coupon); discount bonds are accreted toward par (guaranteed gain). 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). They owe tax on phantom income every year, so they fit tax-deferred accounts.
  • Investment-grade cutoff = BBB-/Baa3 and above; below that is high-yield (junk). Many fiduciary, pension, and insurance accounts are restricted to 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.

Numbers to Lock In

  • Nominal (coupon) yield = annual coupon / par value (fixed at issuance).
  • Current yield = annual coupon / current market price. Example: $50 coupon on a bond at $900 = $50 / $900 = 5.56%.
  • Yield to maturity (YTM) = total annualized return if held to maturity with coupons reinvested at the YTM rate.
  • Yield to call (YTC) = total 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 yield ladder (heavily tested, memorize both directions):

  • Discount bond: Nominal < Current yield < YTM < YTC
  • Premium bond: Nominal > Current yield > YTM > YTC
  • Par bond: Nominal = Current yield = YTM

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 → higher duration; lower coupon → higher duration; lower yield → higher duration. A bond with duration 7 loses roughly 7% if rates rise 1%.

Memory Aid: See-Saw for the Price/Yield Inverse

Picture a see-saw with rates on one end and bond prices on the other. Rates go up, prices go down; rates go down, prices go up. The two ends always move in opposite directions.

Memory Aid: Discount Climbs, Premium Dips for the Yield Ladder

For a discount bond each successive yield measure climbs higher (Nominal → Current → YTM → YTC). For a premium bond each measure dips lower. Par sits flat.

Top Gotchas

  • Yield ordering flips by price. Discount bonds climb (Nominal < CY < YTM < YTC); premium bonds reverse. 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. For callable bonds you MUST use effective duration, which is SHORTER than modified duration because the call compresses the bond's life when rates fall.
  • Higher coupon lowers duration, not raises it. Earlier cash flow cuts sensitivity.
  • Downgrade = price falls, yield rises; upgrade = price rises, yield falls. A drop from BBB to BB ("falling 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. Do not confuse rate moves with 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 < current yield < yield to maturity < 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? This is a condensed summary. If it is not enough, read the full Fixed Income Characteristics unit for the complete lesson.