Fixed Income Securities and Interest Rate Products
The Fixed Income Securities and Interest Rate Products domain tests pricing, risk measurement, and the instruments used to hedge or take rate exposure. Expect calculations: clean versus dirty price, yield to maturity, duration-based sensitivity, and identification of curve and spread risk.
Pricing fundamentals
- Price is the present value of coupons and principal discounted at the yield. Coupon above yield gives a premium; below gives a discount.
- Clean (quoted) price = dirty (present value) price − accrued interest, where accrued = coupon × days accrued / days in the period.
- Yield to maturity assumes reinvestment at the YTM and full payment. Yield to call, yield to worst and current yield answer different questions.
Risk measures
- Macaulay duration is the present-value-weighted time to cash flows; modified duration = Macaulay / (1 + y/m) and approximates percentage price change per 1% yield move.
- Convexity is the second-order term: positive convexity means gains exceed losses for equal yield moves.
- Spread risk separates credit spread from the benchmark government curve; unhedged currency is an additional risk for non-domestic issuers.
Instruments
- Money market: T-bills, commercial paper, CDs, repo. Repo is a secured loan, and the haircut protects the cash lender.
- Interest rate swaps exchange fixed for floating; a payer swap gains when rates rise. FRAs, bond and short-rate futures, caps and floors complete the toolkit.
Worked example
A position has market value 10,000,000 and modified duration 6.5. Yields rise 50 bp. Approximate change = −6.5 × 0.005 × 10,000,000 = −325,000. With convexity of 60, the second-order adjustment is +0.5 × 60 × 0.005² × 10,000,000 = +7,500, so the estimated loss is 317,500. The asymmetry matters: a 50 bp fall gains slightly more than 317,500.
Traps
- Quoting a price without saying clean or dirty, or discounting coupons at the coupon rate.
- Mixing basis points and decimals: 50 bp is 0.005, not 0.5.
- Assuming a zero-coupon bond has no rate risk - it has the highest duration for its maturity.
- Reading spread widening as a fall in the risk-free curve; they are separate drivers.
- Ignoring reinvestment risk embedded in a YTM quotation.