# Carry and roll (upfront vs running)

I am still confused regarding the differences between upfront and running. If two bonds have a spread of 50bp, does that equate to 50bp in total return over the course of the year or do I have to multiply 50bp by the duration effect.

Sometimes I mix up the two and don't know which space I'm in.

For example, a 10-year bond currently has a DV01 of roughly 9. Then "1 bp running" for this bond is equivalent to "9 bp upfront". If the notional amount is \$100 million, then the total dollar risk is$9 \text{ bps} \times \text{100 million} = \$90,000$.
Carry and roll for bonds/swaps are usually quoted in "bps running" terms over a specified horizon. If a bond's RD&C (rolldown + carry) is $x$ bps running over 3 months, it means that your expected P&L from carry and roll will be $x \text{ bp} \times \text{PV01}$ over three months. Continuing with our 10-year bond example, its RD&C is currently about 4.4 bps running, or 39.6 bps upfront, or \$396,000 for 100 million notional. Note that we don't usually annualize carry and roll statistics when we report them, so these are expected P&L over the specified horizon (3 months in this case). Also note that bps running is bond specific, "1 bp running" would equate to "$x$bp upfront" depending on a bond's risk. So the simple yield spread between two bonds is neither bps running nor bps upfront. Typically we'd calculate the carry/roll for each bond and then take the difference. The result would be considered a "bps running" concept and you'd implement a spread trade in a DV01-neutral way (i.e., you'd scale the notionals on the two bonds so that their DV01s are identical). Let's use a real life example: 10-year bond yield closed at 2.17% today while 30-year bond yield closed at 2.75%, a yield spread of 58 bp. If we implement a duration-neutral spread trade (say short 2.27 units of 10-year bond against each unit of 30-year bond), the 3-month carry of the trade would be$1.9-2.7 = -0.8$bp running and the 3-month rolldown is$0.1 - 1.7 = -1.6\$ bp running.