Fixed Income covers bond characteristics, valuation, yield measures, interest rate risk (duration and convexity), credit analysis, and structured products. This is one of the most formula-intensive topics on the exam.
A bond is a debt instrument where the issuer promises to pay periodic interest (coupons) and return the principal (face value) at maturity. Key features include coupon rate, maturity date, par value, and currency. Bond types include government bonds, corporate bonds, zero-coupon bonds (sold at a discount, no periodic payments), floating-rate notes (coupon adjusts with reference rate), and inflation-linked bonds. Embedded options include callable bonds (issuer can redeem early) and putable bonds (holder can sell back early).
A bond's value is the present value of its expected future cash flows (coupons and principal) discounted at the required yield. When the coupon rate equals the market yield, the bond trades at par. When coupon > yield, it trades at a premium. When coupon < yield, it trades at a discount. As a bond approaches maturity, its price converges toward par value (pull to par). The relationship between price and yield is inverse and convex.
Yield to maturity (YTM) is the internal rate of return if the bond is held to maturity and all coupons are reinvested at the YTM. Current yield = Annual coupon / Current price. Yield to call (YTC) is the yield assuming the bond is called at the first call date. The yield spread is the difference between a bond's yield and a benchmark (typically government bonds). The spread compensates for credit risk, liquidity risk, and other factors.
Duration measures the sensitivity of a bond's price to changes in yield. Macaulay duration is the weighted average time to receive cash flows. Modified duration = Macaulay duration / (1 + yield/n). The price change approximation: %ΔP ≈ -ModDur × Δy. Convexity is the second-order measure that captures the curvature of the price-yield relationship. Including convexity: %ΔP ≈ -ModDur × Δy + ½ × Convexity × (Δy)². Longer maturity, lower coupon, and lower yield all increase duration.
Credit risk is the risk that the issuer will fail to make promised payments. Credit analysis evaluates the probability of default, loss given default, and expected loss. Credit ratings (AAA to D) are assigned by agencies like Moody's, S&P, and Fitch. Investment-grade bonds are rated BBB-/Baa3 or higher. Key credit metrics include interest coverage ratio, debt-to-EBITDA, and free cash flow to debt. Credit spreads widen during economic downturns and narrow during expansions.
Present value of coupon payments plus present value of face value at maturity.
Simple yield measure based on current income relative to price.
Measures approximate percentage price change for a 1% change in yield.
More accurate price change estimate including the convexity adjustment.
Additional yield investors demand for bearing credit risk above the risk-free rate.
Bonds are valued as the present value of future cash flows.
Measures of bond price sensitivity to interest rate changes.