# carry for a sovereign bond

For sovereign bond, I saw two carry calculations: one would be forward yield - spot yield, the other would be spot yield - repo rate. I would assume these 2 methods result in same or very close result. But that is not the case. Did I misunderstand something here?

For example, a 5 year bond with 5% coupon and 5% yield, current price = 100, say 4% repo rate, then the carry would be 5% - 4% = 1% based on the yield minus repo rate method. The 1 year forward price would be 99 (=100-(5-4)), and with the 5% coupon and 4 years to maturity, the 1 year forward yield would be 5.284%, then carry would be 5.284% - 5% = 0.284% (based on forward yield minus spot yield method). 1% versus 0.284%, this is quite different, right?

• Those should be very similar. Can you show your working ?
– dm63
Aug 30, 2019 at 10:50
• For example, a 5 year bond with 5% coupon and 5% yield, current price = 100, say 4% repo rate, then the carry would be 5% - 4% = 1% based on the yield minus repo rate method. The 1 year forward price would be 99 (=100-(5-4)), and with the 5% coupon and 4 years to maturity, the 1 year forward yield would be 5.284%, then carry would be 5.284% - 5% = 0.284% (based on forward yield minus spot yield method). 1% versus 0.284%, this is quite different, right? Sep 2, 2019 at 2:59

## 2 Answers

Ah, but the 0.284% ‘carry’ is expressed in units of yield on a 4yr bond. The value of this in upfront terms is approximately 4*0.284% which is in the same ballpark as the 1% number.

• Thank you, but both 1% and 0.284% looks like running bps to be (both are annual rate earned based on bond notional), so it seems already apple to apple comparison. Not sure why we need to convert 0.284% to 0.284%*4 here. Sep 2, 2019 at 3:54
• Because the 1% is applicable for a period of 1 year only (to make it apples to apples with the forward yield method)
– dm63
Sep 2, 2019 at 8:12

carry = OAS + rolldown. If you look just at the yields you miss considering the slope of the term structure