Fixed Income Analysis
Prices, Yields, and Risk
Fixed income questions reward precision about conventions. Bond price is the present value of coupons and principal at the yield to maturity; price and yield move inversely, and the relationship is convex. Duration measures first-order price sensitivity, and modified duration times the yield change approximates the percentage price change; convexity corrects the estimate for larger moves. Know the distinctions among Macaulay, modified, and effective duration, and when effective duration is required (bonds with embedded options).
Term Structure and Spreads
Spot, forward, and par rates must be mutually consistent; a forward rate can be derived from the spot curve, and the expectation, liquidity preference, and market segmentation theories explain curve shape. Credit analysis covers the four Cs, spread decomposition into credit, liquidity, and tax components, and the recovery-adjusted expected loss. Securitization questions test prepayment risk, tranching, and the difference between agency and non-agency structures.
Worked Example
A bond has modified duration of 6.5 and convexity of 80. If yields fall 50 basis points, the duration estimate is +3.25%; adding convexity of 0.5 × 80 × 0.005² = 0.10% gives +3.35%. Rule of thumb: duration alone understates gains and overstates losses, and the gap widens with the size of the yield change.