Fixed Income and Derivatives
Domain 7 - Fixed Income and Derivatives
This domain tests bond pricing, yield measures, duration and convexity, credit risk, and the pricing of forwards, futures, and options. Questions often require a price-change estimate or an arbitrage or parity check.
Core rules
- Bond price: The present value of coupons and principal at the yield to maturity. Price and yield move inversely.
- Duration: Macaulay duration is a weighted average time; modified duration measures percentage price sensitivity to a small yield change. Convexity improves the estimate for larger changes.
- Credit: Yield spread compensates for credit, liquidity, and tax differences. A widening spread lowers price.
- Forwards and futures: Forward price reflects spot, carry, and convenience yield. Futures are marked to market daily.
- Options: Call value rises with volatility and underlying price; put value rises with volatility and falls with underlying price. Parity links calls, puts, spot, and the risk-free rate.
Worked example
A bond portfolio has modified duration of 6 and convexity of 40. Yields rise by 50 basis points, or 0.005. The duration effect is -6 × 0.005 = -0.030, or -3.0%. The convexity adjustment is 0.5 × 40 × (0.005)^2 = 0.0005, or +0.05%. The estimated price change is -2.95%. On a 100 million portfolio, the expected loss is about 2.95 million. The positive convexity adjustment means the actual loss should be slightly smaller than the duration-only estimate. For a large yield move, the duration-only estimate would be less accurate.
Traps that cost marks
- Confusing Macaulay duration with modified duration.
- Quoting clean price when the question asks for cash paid, which includes accrued interest.
- Ignoring day-count conventions in accrued interest.
- Treating an option premium as the same as its payoff.
- Forgetting that futures profits and losses are settled daily.