In page 34 of "Treasury Bond Basis" (Third Edition) by Burghardt et al, it says:
If the yield curve has a positive slope, carry for someone who is long bonds and short futures is positive. Every day that goes by is money in the bank. The implied repo rates simply confirm this.
Why is this the case?
Up to that point in the book, the implied repo rate (IRR) is defined (simple version) as:
IRR = (Futures Invoice Price / Bond Purchase Price - 1) x (360 / n)
where n is number of days to delivery.
It seems to be a function of coupon and actual term repo rate (i.e. carry), or at least it's not clear from this formula how the slope of yield curve impacts IRR.
E.g. if we have a bond with coupon=5% and meanwhile a negatively sloped yield curve with spot rate starting at 0%. Then carry should be actually positive, but using the conventional wisdom of looking at yield curve will say negative carry.