Carry and Pull to Par of a bond

Question

I am of the understanding the true carry of a bond is yield - repo rate. And not simply coupon + repo cost because this doesn’t include pull to par.

Please could someone explain why yield - repo rate is the real carry? ie why it is equivalent to

coupon  + financing cost + pull to par ?

Secondly, where does the idea of a bonds carry = forward yield - spot yield tie into all of this?

Thanks

Answer 1

I disagree with your definition of carry. Carry is the difference between the cash an investment throws off less the cost to finance it. I would argue a zero coupon bond has zero or negative carry (depending if you finance it or not). The yield to maturity is capturing the price appreciation you’d expect as you roll closer to maturity. It’s a bit of a grey area but I wouldn’t consider that carry (instead it’s price appreciation). I’d prefer current yield for calculating carry, but even then it depends on the bond. I doubt distressed debt traders would include future coupons in carry when there is substantial doubt those coupons will ever be paid. Those bonds often trade “dirty”, i.e. without any accrued to reflect that doubt. Distressed debt with 20%+ yields definitely doesn’t have 20%+ “carry”.

As to your second question, don’t think it applies because disagree with using yield to maturity to calculate carry in the first place.

Answer 2

I'd say coupon - repo is strictly cash flow and coupon + pull to par + rolldown - repo is the "carry", most often referenced in fixed income especially in liquid rates. We could replace coupon and pull to par with yield to maturity. You can see carry referenced as % total return or in bps which is "carry" in dollars divided by duration.

Answer 3

"where does the idea of a bonds carry = forward yield - spot yield tie into all of this?"

I'd refer to that as rolldown rather than carry.