A 3-year bond yields 7.2% while the 2-year yields 6.8%, and the desk funds positions at 6.5%. What does holding the 3-year for a year earn in carry plus roll-down, in basis points, and what yield rise would wipe it out?

The year earns about 143 bps: 70 bps of carry and 73 bps of roll-down, Rs 2.85 crore on Rs 200 crore, and a rise of about 79 bps in the 2-year yield wipes it out. Carry is the 7.2% coupon less 6.5% funding. Roll-down is the 40 bps the bond sheds as it becomes a 2-year, times its duration of 1.81. Divide the total by that duration for the breakeven. It protects against a slow drift in yields, not a sharp move.

Think of a flat rented out on a mortgage: the rent minus the mortgage interest is the income, and if flats in that area drift up in value, the owner gains on top without doing anything. A bond bought with borrowed money earns the same two things: carryThe income a position earns while it is held, here the coupon minus the cost of funding it., the coupon less the funding cost, and roll-downThe price gain a bond earns as it ages toward a shorter, lower-yielding point on an upward-sloping curve, with the curve itself unchanged., the price gain from sliding to a lower yield as it ages. Carry is 7.2% minus 6.5%, 70 bps of price over the year. Roll-down needs the bond repriced: in a year it is a 2-year bond with a 7.2% coupon, and at the 2-year yield of 6.8% it is worth 100.725, a gain of 72.5 bps. The total is 142.5 bps, Rs 2.85 crore on Rs 200 crore, against which the desk puts up only margin.

The question is how far the 2-year yield can rise, from 6.8%, before the price loss equals 142.5 bps. Divide the total by the duration of the bond at the horizon: 142.5 / 1.81 = 79 bps, and solving exactly with the price formula gives 79 bps, so the 2-year yield can reach about 7.59% before the year is a loss. Use the duration at the end of the year, not today's 2.61, because the loss happens on a 2-year bond. The breakeven is generous: yields must rise about twice the roll-down the curve offers, and a market that expected that would not have an upward-sloping curve of this shape. That is also the warning. An upward slope is partly the market's forecast that yields will rise, so part of the roll-down is the market's own estimate of the loss you will take.

The 79 bps is a cushion over a full year, so it absorbs a slow drift. It says nothing about the path: a 79 bp rise in the first month shows a loss of about 2.1% on the mark before any carry has arrived, and a risk limit or a margin call can close the position before the year it was sized for. Nor does it cover funding risk: 6.5% is a rate for the year only if the desk actually locks a one-year term; rolling overnight funding reprices every day, and a rise in the policy rate squeezes carry from both sides, lifting the funding cost while pushing the 2-year yield up. The trade is a bet that the curve's slope overstates how fast rates will rise, and sizing it should start from the mark-to-market loss a one-month move can produce, not from the annual cushion.

State the simplifications. The bond is assumed to trade at par with annual coupons, so carry is exactly coupon minus funding; a premium or discount bond has a pull-to-par term as well. The 2-year yield in a year is today's 2-year yield only if the curve is unchanged, which is an assumption, not a forecast. And the duration approximation ignores convexity, which is why the exact breakeven differs by a basis point or so from the division.