A fund is short a bond future settling at 98.00 and must choose what to deliver: bond A at 101.20 with conversion factor 1.0300, B at 96.50 with 0.9850, C at 104.80 with 1.0700. Which is cheapest to deliver, and how could that change if yields rise sharply?

Bond C is cheapest to deliver: it costs 104.80 and earns an invoice of 104.86, a gain of 0.06 per 100. Bond B gains only 0.03 and bond A costs 0.26. On Rs 200 crore, C beats A by about Rs 0.64 crore. B and C are almost tied, and B falls faster when yields rise, so a rise of under one basis point would make B the bond to deliver.

A buyer who promised to accept any of three rice varieties, at a fixed price adjusted by a quality factor, will be handed whichever variety is cheapest for the seller after the adjustment. The short in a bond future chooses which bond to deliver, receives the futures price times that bond's conversion factorA number set by the exchange that scales the futures price for each deliverable bond, so that bonds with different coupons and maturities can be delivered against one contract., and pays the bond's market price to source it. The cost of delivering is price minus futures price times factor, per 100 of face. The lower that number, the better for the short.

Work each one. A: 101.20 minus 98.00 times 1.0300, which is 101.20 minus 100.94, +0.26. B: 96.50 minus 96.53, -0.03. C: 104.80 minus 104.86, -0.06. C is cheapest, and the lowest price, B, is not, because its low factor also shrinks what the short is paid. On Rs 200 crore of face, delivering C instead of A is worth 0.32 per 100, about Rs 0.64 crore. A negative cost on the delivery day means the short earns by buying the bond and delivering it; in a market with active arbitrage that gap would be closed, so seeing one is a sign the futures price is a touch rich against bond C.

Divide each price by its factor and the ranking is the same, because cost is factor times (price over factor minus 98). Price over factor is the number to watch, and it moves with each bond's duration: the long-duration bond falls fastest when yields rise, so it tends to become cheapest to deliver. Bond B has a modified duration of 8.8, bond C only 4.2. Using durations as a straight-line guide, a 100 basis point rise takes B's price over factor to about 89.35 and C's to 93.83, so B becomes cheapest by a wide margin. A 100 point fall leaves C cheapest at 102.06. The two lines cross at a rise of only about 0.6 basis point, which is the real lesson: B and C are close, and the short's choice is live.

This is why the short's right to choose is valuable and why the futures price sits a little below where a single-bond calculation would put it: the long must accept whichever bond suits the short, and the short can switch as markets move. The conversion factors are built from a notional coupon; when market yields are above that coupon, long-duration, low-coupon bonds tend to be cheapest, and below it, short, high-coupon bonds do. The limit of the duration guide is convexity and curve shape: a steepening that cheapens long bonds more than short ones would push B ahead faster than a parallel shift. Check the exchange's contract terms for the current deliverable basket and factors rather than relying on these illustrative ones.