Debt Yields and Pricing

The whole unit on one sheet: the four yields and their ordering, the inverse price-yield relationship, accrued interest, ratings, taxes, and volatility.

The Four Yields (Plus Two)

• Nominal (coupon) yield: annual coupon / par ($1,000). Fixed at issuance; never changes when rates move.
• Current yield (CY): annual coupon / current market price. Ignores any gain or loss at maturity.
• Yield to maturity (YTM): total annualized return if held to maturity; includes the capital gain (discount) or loss (premium) and time value. The most comprehensive measure; also called the bond's basis.
• Yield to call (YTC): return if called at the first call date, using the call price and call date.
• Yield to worst (YTW): the lowest of YTM and YTC across every call date; the most conservative measure.
• Discount yield: money market instruments (Treasury bills, commercial paper); uses face value and a 360-day year, so it understates true return.

The One-Liners That Win Points

• Nominal yield never changes after issuance. When rates rise, only the market price moves.
• Prices and yields move in opposite directions. Rates up, existing prices down; rates down, prices up.
• Discount bond: CY is higher than nominal. Premium bond: CY is lower than nominal. At par, all yields are equal.
• Callable premium bond = quote on a YTC basis (issuer will likely call and refinance). Callable discount bond = quote on a YTM basis (unlikely to be called).
• For a premium bond, YTC is lower than YTM; for a discount bond, YTC is higher than YTM.
• Most volatile = longest maturity AND lowest coupon. A 30-year zero-coupon bond is the most volatile fixed-income instrument.
• Investment grade = BBB-/Baa3 and above. BB+/Ba1 and below is non-investment grade (junk).

Numbers to Lock In

Memory Aid: Day-Count by Issuer

Corporate and Municipal use 30/360. Government uses actual/actual.

Top Gotchas

• If asked what happens to nominal yield when rates rise, the answer is nothing; only price changes.
• A bond's price always converges toward par as maturity approaches, discount rising and premium falling; at maturity every bond is worth $1,000.
• Government bonds are quoted in 32nds, not decimals: 99-16 means 99 and 16/32 = $995.00, not $99.16. Municipal bonds are typically quoted on a yield basis.
• Use the wrong day-count method and your accrued-interest answer is slightly off, and that wrong answer is usually one of the choices. The buyer pays accrued interest to the seller at settlement.
• Bonds trade flat (no accrued interest) when in default, income (adjustment) bonds, or zero-coupon.
• A downgrade from BBB- to BB+ crosses the investment-grade line and can cause a disproportionately large price drop as institutions are forced to sell. Credit spreads widen in bad times, narrow in good times.
• Original Issue Discount (OID) is taxed as ordinary income annually (phantom income), raising cost basis to par by maturity; zeros suit tax-deferred accounts. Market discount at maturity is ordinary income, not capital gain.
• Premium amortization is elective for taxable bonds but mandatory for municipals. For OID bonds, compute gain or loss on the adjusted basis (original price plus accreted OID).

One-Breath Recap

Memorize the yield order first: on a discount bond yield to call leads and nominal trails, and on a premium bond that order reverses. Then remember prices and yields move opposite, every bond pulls to par at maturity, the longest low-coupon bond swings the most, and discounts and premiums each carry their own tax treatment. Nail the ordering and the pricing logic and this unit answers itself.

Need more than the recap? This is a condensed summary. If it is not enough, read the full Debt Yields and Pricing unit for the complete lesson.