Why Fixed Income Is Hard
Fixed Income accounts for 11–14% of the CFA Level I exam, placing it among the three highest-weighted topic areas alongside FSA and Equity. Candidates consistently rank it among the most difficult topics in candidate surveys, and for good reason.
The difficulty is not conceptual complexity in isolation. The individual concepts (bond pricing, yield measures, duration) are learnable. The difficulty is that Fixed Income requires mathematical precision, layered concepts where each topic builds on the previous one, and the ability to execute calculations correctly under time pressure. A candidate who understands duration qualitatively but cannot calculate modified duration from financial data will lose points on exam questions that require that calculation.
This guide breaks down the key areas, explains where candidates typically struggle, and describes how to build the preparation that translates to exam-day accuracy.
The Core Building Blocks: Bond Pricing
The foundation of Fixed Income is bond pricing: given a bond's cash flows (coupon payments and principal), discount those cash flows at the appropriate yield to arrive at the bond's price. The formula is straightforward in principle:
$$P = \sum_{t=1}^{n} \frac{C}{(1+r)^t} + \frac{FV}{(1+r)^n}$$
Where P is price, C is the coupon payment, r is the periodic required yield, n is the number of periods, and FV is the face value.
In practice, exam questions present bond characteristics (coupon rate, face value, maturity, required yield) and ask you to calculate the price, or present a price and ask you to solve for the yield. Both types require calculator fluency. The TI BA II Plus can solve bond pricing directly using the TVM worksheet (N, I/Y, PV, PMT, FV), and practising until this is automatic is a prerequisite for Fixed Income performance.
Common exam variations on bond pricing include:
- Accrued interest: Between coupon payment dates, the buyer of a bond pays accrued interest to compensate the seller for the coupon portion earned during the holding period. Questions ask you to calculate the full price (dirty price) versus the quoted price (clean price).
- Premium and discount bonds: When the required yield is below the coupon rate, the bond prices above par (premium). When the required yield is above the coupon rate, the bond prices below par (discount). Understanding why this is true and being able to calculate the price in both cases is straightforward but regularly tested.
- Zero-coupon bonds: Bonds that pay no coupons and return only the face value at maturity. Pricing is a simplified version of the general formula.
Yield Measures
The CFA curriculum covers several yield measures, each appropriate for different analytical purposes. Candidates often confuse them or know the definitions without understanding when to use each.
Yield to maturity (YTM) is the internal rate of return of a bond's cash flows at its current market price. It assumes coupons are reinvested at the YTM, which is an assumption that is rarely exactly true in practice but is the standard yield measure for most contexts.
Current yield is annual coupon payment divided by bond price. It measures income return without accounting for capital gains or losses as the bond approaches maturity. It is a simplified measure, not a complete return measure.
Yield to call (YTC) applies to callable bonds. If the issuer has the right to call the bond before maturity at a specified price (the call price), the YTC calculates the return assuming the bond is called at the earliest possible call date. For bonds trading at a premium, YTC is typically below YTM, because the issuer would prefer to call an above-par bond and refinance at a lower coupon.
Yield spread measures include the nominal spread (YTM of a bond minus YTM of a benchmark Treasury of similar maturity), the Z-spread (the constant spread added to each spot rate in the benchmark curve that makes the discounted cash flows equal to the bond price), and the option-adjusted spread (OAS), which adjusts for embedded options. Level I covers these conceptually; Level II requires deeper calculation.
The exam frequently presents a set of yield measures and asks you to rank them or identify which is most appropriate for a given analytical purpose. Understanding what each measure does and does not capture is the key.
Duration and Convexity
Duration and convexity are the most calculation-heavy section of Level I Fixed Income and the area that generates the most wrong answers.
Macaulay duration is the weighted average time to receive a bond's cash flows, where the weights are the present values of the cash flows as a proportion of the bond's total price. It measures the average timing of cash flows in years.
Modified duration is Macaulay duration divided by (1 + periodic yield). It is an approximation for the percentage price change of a bond given a small change in yield:
$$%\Delta P \approx -D_{mod} \times \Delta y$$
Where D_mod is modified duration and Δy is the change in yield. A bond with modified duration of 5 will decrease in price by approximately 5% if yields rise by 1 percentage point (100 basis points).
Dollar duration (also called DV01 or price value of a basis point) is the dollar change in price for a 1 basis point (0.01%) change in yield. It is used when you need the absolute dollar impact of a yield change rather than the percentage impact.
Convexity accounts for the fact that the duration approximation is not precise for large yield changes. The actual price-yield relationship is curved (convex), not linear, and duration gives the slope of the tangent to that curve at the current yield. For large yield changes, convexity adds an additional term:
$$%\Delta P \approx -D_{mod} \times \Delta y + \frac{1}{2} \times Convexity \times (\Delta y)^2$$
Convexity is always positive for plain (option-free) bonds, which means the actual price rise when yields fall is greater than duration predicts, and the actual price fall when yields rise is smaller than duration predicts. Positive convexity is a desirable bond property.
Callable bonds have negative convexity at low yields (when the call option is near the money), because the issuer's option to call limits the price appreciation the bond can experience as yields fall. Fixed Income practice questions include both calculation and conceptual questions on duration and convexity.
The Yield Curve
The yield curve (term structure of interest rates) relates yields on similar-risk bonds to their maturities. The normal yield curve slopes upward (longer maturities have higher yields). Inverted yield curves (longer maturities have lower yields) are associated with recession expectations. Flat or humped curves appear during transition periods.
Three theories explain the yield curve shape:
Pure expectations theory holds that the forward rates implied by the yield curve are unbiased predictors of future short-term rates. An upward-sloping curve implies markets expect short-term rates to rise.
Liquidity preference theory holds that investors require a premium for holding longer-term bonds (because they are less liquid and carry more interest rate risk). The yield curve incorporates both rate expectations and a liquidity premium.
Market segmentation theory holds that different investor groups (pension funds, insurance companies, banks) prefer specific maturity segments and that supply and demand within each segment determines yields, with limited crossover between segments.
Level I questions on yield curve theory typically ask you to identify which theory explains a given yield curve shape or which prediction each theory makes about the forward rate versus the expected future spot rate.
Credit Analysis
Credit analysis covers the assessment of a bond issuer's ability to service its debt. Level I introduces the four Cs of credit analysis: capacity (financial ability to repay), character (management quality and willingness to repay), collateral (assets backing the debt), and covenants (contractual provisions protecting bondholders).
Credit ratings from agencies (Moody's, S&P, Fitch) provide a summary assessment. Investment grade is Baa3/BBB- and above; speculative grade (high yield or junk) is below that threshold. Rating transitions and their effect on bond prices are regularly tested.
Credit spreads represent the additional yield investors require for bearing credit risk versus a comparable-maturity risk-free benchmark. The credit spread reflects the market's aggregate assessment of default probability and recovery rate. When credit quality deteriorates, spreads widen (the bond price falls relative to the risk-free benchmark).
The exam also tests the relationship between a bond's seniority in the capital structure and its recovery rate in default. Senior secured creditors recover first; subordinated unsecured debt recovers last. The recovery rate affects the loss given default, which is one component of expected credit loss.
Studying Fixed Income Effectively
Start with bond pricing calculations. Before reading about duration or credit analysis, make sure you can price bonds and solve for yield correctly on your calculator. Duration and convexity calculations build on bond pricing; if you are not comfortable with the foundation, the later material is harder to learn.
Practise duration calculations extensively. Modified duration and convexity calculations appear on almost every exam. Run through examples that ask you to calculate the percentage price change for a given yield change, and check whether convexity is positive or negative given the bond's embedded options. Fixed Income practice questions cover these calculation types systematically.
Use the TVM worksheet consistently. For bond pricing, N is number of periods, I/Y is the periodic yield (annual yield divided by periods per year), PV is the price (typically negative as it is a cash outflow), PMT is the coupon payment, and FV is the face value. The most common calculator error is using annual figures without dividing by the coupon frequency. Semiannual bonds divide the coupon rate and yield by 2 and double the number of periods.
Connect the concepts. Fixed Income is more interconnected than most candidates realise. Understanding why a callable bond has negative convexity requires understanding how option value affects the bond price, which requires understanding how yield changes affect prices. If you study each subtopic in isolation, you will struggle with questions that require connecting two or three concepts.
Review wrong answers carefully. Fixed Income wrong answers almost always trace to a specific conceptual error (confusing Macaulay and modified duration, misidentifying the sign of convexity for callable bonds) or a calculation error (using annual yield where periodic yield is required). Identifying the specific error for each wrong answer prevents the same mistake from recurring.
Fixed Income is hard, and preparing it properly requires more focused effort than some other topic areas. Candidates who invest that effort and practise the calculations until they are reliable consistently find that Fixed Income becomes one of the more manageable high-weight topics on exam day.