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.
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.
When you buy a coupon bond between coupon dates, you pay the seller for the accrued interest they earned. The clean price (or "quoted price") excludes accrued interest.
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 without considering yield level. CF was calibrated to 6% yield. At 4% yields, low-coupon long bonds are CTD; at 8% yields, high-coupon short bonds are CTD. Trap: a question states current yields are 8% and asks for CTD, listing four bonds. The answer is the high-coupon short bond, not the low-coupon long bond.
- 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?" The answer is "essentially nothing, only mark-to-market exposure plus initial margin." The wrong answer is...
Bottom line
- T-bond futures allow delivery of any bond with maturity > 15 years. 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). High coupon, short maturity favored when yields > 6%; low coupon, long 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 3,293 words, 22 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
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