Quick Answer
Bond prices move inversely to yields, and duration measures that sensitivity. A zero-coupon bond's duration equals its maturity; a coupon bond's is always less. Discount bonds run coupon rate below current yield below yield to maturity, and premium bonds reverse it. Yield to call sits outside that fixed order, set by the call terms.
The whole unit on one sheet: what moves a bond's price, the yield measures and their ordering, convertible math, credit spreads, and discounted cash flow.
Which One-Liners Win Points?
- Bond prices move inversely to interest rates. When the required yield rises, the present value of future cash flows falls, so the price falls.
- Duration measures price sensitivity to a 1% rate change, expressed in years. Higher coupon lowers duration; longer maturity raises it.
- Zero-coupon bonds carry the highest rate sensitivity of any bond of the same maturity, and no reinvestment risk (no coupons to reinvest).
- Callable bonds pay higher yields to compensate for call risk; issuers call when rates fall. Near the call price a callable bond stops rising: negative convexity.
- Premium means the coupon rate is above market yield (price above par); discount means the reverse. Both converge to par at maturity (pull to par).
- Municipal interest is generally federal-tax-exempt and can be triple tax-exempt in your home state; Treasury interest is federally taxable but state-exempt; corporate interest is fully taxable.
- Yield to maturity (YTM) is the most comprehensive measure and assumes every coupon is reinvested at the YTM rate.
Which Formulas Must You Reproduce?
- Current Yield = Annual Coupon / Current Market Price
- Conversion Ratio = Par Value / Conversion Price
- Conversion Value (Parity) = Conversion Ratio x Current Stock Price
- Credit Spread = Corporate Yield - Comparable-Maturity Treasury Yield
How Does the Yield Hierarchy Work?
- Discount bonds: Coupon Rate < Current Yield < YTM. The measures rise as they get more comprehensive.
- Premium bonds: Coupon Rate > Current Yield > YTM. The measures fall.
- Par bonds: all three are equal.
- Tie-breaker: ask whether the capital gain (discount) or loss (premium) at maturity helps or hurts total return.
- Yield to call is not part of this hierarchy. Its position depends on the assumed call date and call price. For a premium callable bond it is generally the lowest measure, but "generally" is not "always."
Which Numbers Matter Most?
| Item | Value |
|---|---|
| Duration price move | approx 1% price change per 1% rate change per year of duration |
| Example: 5-year-duration bond, rates up 1% | loses approximately 5% of value |
| Zero-coupon duration | equals maturity |
| Coupon-bond duration | less than maturity |
| Investment-grade line | Baa3 / BBB- and above |
| Par value (standard) | $1,000 |
What Are the Three Decision Rules?
- Convertible: convert when conversion value exceeds the bond's market price; otherwise hold. At a ratio of 40 with the stock at $30, conversion value is $1,200, so convert against a $1,100 bond and hold against a $1,300 bond.
- Discounted cash flow: buy when DCF value exceeds market price, avoid when it falls short. The discount rate is the required yield, so a higher required yield produces a lower present value.
- Credit spread: a wider spread signals higher perceived risk. Spreads narrow in expansion, widen in recession, and widen sharply in a crisis as money flees to Treasuries.
Which Gotchas Trip Students Up?
- Duration is not maturity. Only zero-coupon bonds have duration equal to maturity; a 10-year 6% coupon bond has a duration well below 10 years.
- Current yield ignores the gain or loss at maturity and the time value of money. It is income return only.
- The muni exemption covers interest only. Sell any bond, including a muni, at a profit and the capital gain is still taxable.
- A muni does not belong in a retirement account. Tax shelters do not stack, and a traditional account turns the exempt interest into ordinary income on withdrawal. The same reasoning bars munis for a pension plan or a charitable foundation.
- A debenture is just an unsecured bond. Liquidation runs secured bonds, unsecured debentures, subordinated debentures, preferred stock, common stock.
- Credit spreads widen in bad times, which feels backward: in good times risky bonds look safer, so the extra yield demanded shrinks.
- Liquidity ranks Treasuries, agencies, investment-grade corporates, municipals, then high-yield corporates. Less liquid bonds must pay more.
One-Breath Recap
Bond prices move inversely to yields, and duration measures that sensitivity: a zero-coupon bond's duration equals its maturity while a coupon bond's is always less, and higher coupons or shorter maturities cut duration. Know the yield hierarchy cold, because it flips by pricing: coupon rate below current yield below yield to maturity for discount bonds, the reverse for premiums, all three equal at par. Yield to call sits outside that fixed order, because the assumed call terms decide where it lands. Municipal interest is generally tax-exempt, Treasuries are state-exempt only, and corporates are fully taxable, so a municipal bond earns its exemption only in a taxable account, never inside a retirement plan. Credit spreads widen in stress. Convertibles turn on conversion ratio times stock price versus the bond's market price.
Need more than the recap? Read the full Fixed Income Valuation unit.