A swap dealer takes the fixed side of a $200 million 5-year interest rate swap, paying Secured Overnight Financing Rate (SOFR) and receiving 4.2% fixed. The dealer's book is now exposed to rate moves until it can offset with another counterparty or hedge in the futures market. Treasury bond futures are the standard hedging tool, and the conversion factor mechanic is what most candidates get wrong on the FRM. Pricing the deliverable bond, matching hedge sensitivity and tracing each swap cash flow are connected applications of the same discounting principles.
Day count rules tell you what fraction of a year falls between two dates. Get this wrong and your interest accrual is off by a few percent, material on multi-million-dollar trades.
T-bills quote yields on a discount basis with Actual/360. A T-bill quoted at 4.5% discount and 90 days to maturity has price . The bond-equivalent yield is higher because it uses a 365-day denominator and the discount is paid on $98.875, not $100.
Common mistakes
- Confusing clean and dirty prices in delivery cost. Delivery cost = quoted price - (futures × CF). The quoted price is clean; the buyer separately pays accrued interest. Trap: a candidate uses dirty for both sides and miscalculates which bond is CTD.
- Picking CTD from a slogan alone. Above the 6% conversion-factor benchmark, high-duration deliverables tend to be favored; below it, low-duration deliverables tend to be favored. Confirm the result with carry-adjusted costs. Curve shape and repo specialness can outweigh the yield-level tendency.
- Treating swap notional like exchanged principal. Plain-vanilla rate swap notional is never exchanged; only interest payments. Currency swaps DO exchange principal. Trap: a question asks "what does the dealer post as collateral on a $100M IR swap on day 1?" Initial market value may be zero, but required initial margin can be material.
Bottom line
- Treasury futures define an eligible delivery basket for each contract. Conversion factor (CF) scales prices to a 6% benchmark; CF > 1 when coupon > 6%, CF < 1 when coupon < 6%.
- Cheapest-to-deliver (CTD): minimize quoted bond price - (futures × CF). Low coupon, long maturity (high duration) favored when yields > 6%; high coupon, short maturity favored when yields < 6%.
- Duration-based hedge ratio: . Assumes a linear, parallel-shift, stable-CTD world.
- Plain-vanilla swap: exchange fixed for floating (typically SOFR) on notional. Principal is never exchanged.
Exam shortcut
When a swap valuation question lands, decide: do you have a yield curve in hand, or forward rates? Curve → two-bond method (faster). Forward rates → FRA method. Both must give the same answer; if they don't, your arithmetic is wrong. The trap is forgetting the floating leg includes the next-coupon-plus-notional discounted to now (not par).
The full lesson (about 6,040 words, 40 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
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