Say I'm interested in a trade that wants to execute a 10s/20s steepener
This is done via a receiver leg on the 10s and a payer leg on 20s
Look at the following example (the figures are all indicative)
I understand the basic logic of the trade, that we are long the short end and short the long end, because the fixed cashflows we receive on the short-end become more valuable if demand spikes and yields fall. On the long-end, paying fixed cashflows is advantageous when prices fall and subsequently yields rise.
But how is my carry on 6months, a year or 5 years calculated?
Would it simply be $500,000\times0,04\times\frac{6}{12}-1,000,000\times0,02\times\frac{6}{12}$ for the $6m$ carry, for example?
Furthermore, why would the PV01 of the receiver leg be positive? The way I understand PV01: If market yields move up a point, then what is the change in PVs of the cashflows. If this is the definition, then my PV01 on the receiver leg should be negative because my present value would decrease?
This may be a trivial trade but it is my first time seeing this and I'd be interested to hear how carry etc. is calculated, and how the notionals are changed to ensure that such swaps with different tenors are indeed initially "fair", i.e. have an NPV of $0$