Fixed Income Valuation

The whole unit on one sheet: the characteristics that move a bond's price, the four yield measures and their ordering, convertible math, credit spreads, and discounted cash flow valuation.

The One-Liners That Win Points

• Bond prices move inversely to interest rates: when the required yield (the discount rate) rises, the present value of future cash flows falls, so the price falls.
• Duration measures a bond's price sensitivity to a 1% change in interest rates, expressed in years. Higher duration equals greater price volatility.
• A zero-coupon bond's duration equals its maturity; a coupon-paying bond's duration is always LESS than its maturity (earlier cash flows pull it in).
• Higher coupon rate lowers duration; longer maturity raises duration; higher yield slightly lowers duration.
• Callable bonds carry higher coupons to compensate for call (reinvestment) risk; issuers call when rates FALL to refinance cheaper.
• When rates drop, a callable bond's price stops rising near its call price: negative convexity.
• Zero-coupon bonds have the HIGHEST interest rate sensitivity and NO reinvestment risk (no coupons to reinvest).
• Premium means coupon rate is above market yield (price above par); discount means coupon rate is below market yield (price below par); prices converge to par at maturity (pull to par).
• Municipal bond interest is generally federal-tax-exempt; a muni bought in your home state can be triple tax-exempt; the exemption covers interest only, NOT capital gains.
• Treasury interest is federally taxable but exempt from state and local tax; corporate interest is fully taxable at all levels.
• Yield to maturity (YTM) is the most comprehensive yield measure; it assumes all coupons are reinvested at the YTM rate.
• Yield to call (YTC) matters most for premium callable bonds and is generally LOWER than YTM for them.

Formulas to Reproduce Exactly

• Current Yield = Annual Coupon Payment / Current Market Price
• Conversion Ratio = Par Value / Conversion Price
• Conversion Value (Parity) = Conversion Ratio x Current Stock Price
• Credit Spread = Yield on a corporate bond - Yield on a comparable-maturity Treasury

The Yield Hierarchy (memorize the direction)

• Discount bonds (price below par): Coupon Rate < Current Yield < YTM < YTC (measures rise as they get more comprehensive)
• Premium bonds (price above par): Coupon Rate > Current Yield > YTM > YTC (measures fall)
• Par bonds (price equals par): Coupon Rate = Current Yield = YTM = YTC (all equal)
• Tie-breaker: ask whether the capital gain (discount) or loss (premium) at maturity helps or hurts total return.

Numbers to Lock In

Convertible Decision Rule

• Conversion value greater than bond market price: conversion is attractive (stock worth more than the bond).
• Conversion value less than bond market price: hold the bond.
• Conversion value equals bond market price: at parity, indifferent.
• Worked example: conversion ratio 40, stock at $30 gives conversion value 40 x $30 = $1,200; convert if the bond trades at $1,100, hold if it trades at $1,300.

Credit Spread and the Economy

• Wider spread signals higher perceived credit risk; narrower spread signals lower risk.
• Spreads narrow in growth/expansion (investors confident), widen in recession/uncertainty, and widen sharply in a financial crisis (flight to quality into Treasuries).

Discounted Cash Flow Decision Rule

• DCF value greater than market price: bond is undervalued, buy.
• DCF value less than market price: bond is overvalued, avoid or sell.
• DCF value equals market price: fairly valued, neutral.
• The discount rate is the required yield; a higher required yield produces a lower present value (the inverse price-yield relationship in math form).

Top Gotchas

• 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 capital gains or losses at maturity and the time value of money; it is income return only, so for a discount bond current yield is above the coupon rate, and for a premium bond it is below.
• The muni tax exemption is on interest only: sell any bond, including a muni, at a profit and the capital gain is still taxable.
• A debenture is just an unsecured bond; in liquidation it sits behind secured bondholders (secured bonds, then unsecured debentures, then subordinated debentures, then preferred stock, then common stock).
• Credit spreads widen in bad times, narrow in good times, which feels backward to some students: in good times risky bonds look less risky, so the extra yield demanded shrinks.

Liquidity Hierarchy (Most to Least Liquid)

• Treasuries, then agency bonds (Fannie Mae, Freddie Mac), then investment-grade corporates, then municipals, then high-yield corporates.
• Less liquid bonds must offer HIGHER yields to compensate for the difficulty of selling.

One-Breath Recap

Bond prices move inversely to yields, and duration is how you measure 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 four yield measures cold, because the hierarchy flips by pricing (Coupon Rate less than Current Yield less than yield to maturity less than yield to call for discount bonds, and the reverse for premiums, all equal at par). Tax treatment separates munis (interest generally exempt, capital gains still taxed) from Treasuries (state-exempt only) from corporates (fully taxable), while credit spreads widen in stress and narrow in growth. Convertibles turn on conversion ratio (par over conversion price) times stock price versus the bond's market price, and discounted cash flow says buy when intrinsic value tops the market price. Nail those relationships and this valuation unit answers itself.

Need more than the recap? This is a condensed summary. If it is not enough, read the full Fixed Income Valuation unit for the complete lesson.