I read recently the following comment: "If the yield-curve is positively sloped (long-term interest-rates higher than short-term) then holding a bond position for future delivery actually produces a net income (rather than a net outgo)". I don't understand why this is the case.Is this a matter of "carry"?

Model a par value bond in a positive yield curve and negative yield curve environment.It is pretty easy to tell.Just remember the basics of bonds....as yields go up price goes down remember about discounting your cash flows too with coupon payments!

yes it is a function of the carry of bonds. After that it's a matter of cash and carry arbitrage principles. So because holding the bond, financing it and selling it forward shouldn't really result in an arbitrage then the carry of the bond is pretty much equivalent to:1. financing cost in an upward sloping yield curve implies that financing say a 2yr bond that yields 2% annually and costs you .25% to fund will result in a net profit to horizon. The opposite will be the case in a downward sloping yield curve.2. coupon interest3. m2m from the shortening of the bonds time to maturity. If the yield curve is upward sloping the bond will have a lower yield in time as it falls on a shorter part of the yield curve at horizon. In a downward sloping yield curve environment this will be a higher yield and will result in a m2m loss.if all these accruals result in a net loss then generally speaking the price of the future, or carry to expiration will be negative.

It's just like selling options. Produces income. Until it doesn't. Simple trade for simple minds.