A 5 year bond yields 3.20% while the 4 year point yields 3.00%. In a year the bond will have duration 3.8, funding costs 2.00%, and the curve is unchanged. What is the one year excess return, and what parallel yield rise breaks even?

A 5 year bond yields 3.20% while the 4 year point yields 3.00%. In a year the bond will have duration 3.8, funding costs 2.00%, and the curve is unchanged. What is the one year excess return, and what parallel yield rise breaks even?

Approach: Separate the return into the coupon carry and the price gain from sliding down a static curve, then subtract funding and convert the remainder into a yield move using duration.

1.96%. On an unchanged curve the bond earns its 3.20% yield as carry and rolls down to the 4 year point where the yield is 20 basis points lower, gaining duration times that move, 3.8*0.0020 = 0.76%. Total return is 3.96%, so the excess over 2.00% funding is 1.96%. The breakeven parallel rise is the move that removes it, 1.96/3.8 = 51.6 basis points, so the position survives anything short of half a point of selling across the curve. Two assumptions carry the result. The roll assumes the curve shape holds, so a steepening centred on the 4 year point removes it directly, and the funding rate has to be termed out, since a repo rate that follows the front end higher takes away the carry at the same moment the price loss arrives.

Follow-up: How does the breakeven change if the 4 year point yields 3.15% rather than 3.00%?

Key concepts: carry, roll-down, breakeven yield, funding.