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CFA Level I · Study Guide

Fixed Income

11-14% of exam19 modulesDemanding
Overview

Fixed Income is one of the largest and most calculation-intensive topics at Level I (11–14%, 19 modules). It covers bond pricing, yield measures, duration, convexity, credit risk, and the term structure of interest rates. The topic consistently generates some of the hardest exam questions and disproportionately separates passing from failing candidates. Precision with formulas and an understanding of the price-yield relationship are essential.

Key Formulas

The formulas that appear most often

Bond Price (flat)
P = Σ [Ct / (1+r)^t] + [FV / (1+r)^N]
Ct = coupon payment; r = periodic required yield; N = total periods; semi-annual coupons common
Current Yield
CY = Annual Coupon / Price
Simpler than YTM; ignores capital gain/loss and reinvestment income
Macaulay Duration
D_mac = Σ [t × (Ct / (1+r)^t)] / P
Weighted average time to receive cash flows; units = years; zero-coupon bond: D_mac = maturity
Modified Duration
D_mod = D_mac / (1 + r/m)
m = compounding periods per year; measures % price change per unit change in yield
Price Change Approximation (Duration + Convexity)
ΔP/P ≈ −D_mod × Δy + ½ × Convexity × (Δy)²
Duration term is always negative for yield increase (price falls); convexity term is always positive
Dollar Duration (DV01)
DV01 = D_mod × P × 0.0001
Dollar value of a 1 bp (0.01%) change in yield; used for hedging
Yield Spread
OAS = Z-spread − Option Value
Z-spread = constant spread added to each spot rate to match market price; OAS removes option effect
High-Yield Exam Areas

What actually gets tested

1

Price-yield relationship: price and yield move inversely. Premium bond (coupon rate > YTM) → price > par → pulls to par at maturity. Discount bond (coupon rate < YTM) → price < par.

2

Duration rules: duration increases with maturity, decreases with coupon rate, decreases with yield, decreases with embedded put options, increases with embedded call options (for callable bonds, use effective duration).

3

Convexity: bonds with positive convexity outperform duration-only estimates for both price increases and price decreases. Callable bonds can have negative convexity at low yields.

4

Credit risk measures: know the difference between probability of default, loss given default, and expected loss. Investment-grade (BBB/Baa and above) vs. high-yield (below BBB). Credit spreads widen during recessions.

Common Mistakes

Where candidates lose marks

Confusing Macaulay duration (in years, weighted average time) with modified duration (in years, but a price sensitivity measure). Modified duration is used in the price change formula.

Getting the sign wrong on the duration price change: a yield increase causes a price decrease. ΔP/P ≈ −D_mod × Δy — the negative sign is built in.

Using nominal yield spreads instead of OAS to compare bonds with embedded options — a callable bond's nominal spread overstates the true credit spread because it does not separate out the call option value.

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