I was going through some reports but having hard time with the jargon. When I google them online I came across the page: http://volcurve.blogspot.com/2007/10/carry-and-roll-down-back-to-basics.html

Unfortunately it is not updated anymore. I am having hard time to understand definitions in the link above. For example:

• Upfront Carry: For a 10-year receive fixed swap, the 1 year carry is the net present value of a 10-year swap less the net present value of a 9-year swap starting 1 year from now.

Does this mean Upfront Carry Return is equal to 10Y Swap Fixed Rate (SFR) - 1Y9Y Forward Swap Fixed Rate? If not, please tell me what is it?

• Upfront roll-down: For a 10-year receive fixed swap, the 1 year roll-down is the net present value of a 10-year swap and less net present value of a 9-year swap today. Same for this. Is Upfront Roll Down Return equal to 10Y SFR - 9Y SFR?

And complete other story is:

• Actual Vol-adjusted Running Carry & Running Roll-down: 1Y Running Carry divided by the actual volatility of the 1Y rate over the past 1 year. Is 1Y rate the reference rate in floating rate or 1Y swap rate or something else?

Cheers!

• In my experience carry, roll-down, running and upfront are all terms that are misused, not understood, bastardised and inconsistent. My opinion is that someone who doesn't define it, or can't when asked, doesn't really know what they are writing/talking about. There are lots of questions on QF that discuss this and the nature of the degree of questions demonstrates my opinion. It is often best just to try and guess what the author's definition is from context.
– Attack68
Commented Feb 5, 2019 at 19:57

Further to my comment the link you posted contains useless information.

**Upfront Carry**: For a 10-year receive fixed swap, the 1 year carry is the net present value of a 10-year swap less the net present value of a 9-year swap starting 1 year from now.

What is net present value (npv) given there is no mention of rates. Let's assume that the 0Y10Y swap is valued relative to mid market so its NPV is zero, and the 1Y9Y is valued relative to the 10Y mid-market rate. A simple mathematical calculation shows that the author is equating upfront carry to the present value of the cashflows receivable in the first year of the 10Y swap.

**Running Carry**: the Upfront Carry divided by the PV01 of the forward starting 9-year swap.

So if the upfront carry was something you genuinely believed to be a useful means of assigning value to a trade consideration running carry normalises that metric by factoring risk.