A Positive Carry Primer

May 30th, 2008 7:37 am | by John Jansen |

Several readers have requested a discussion of positive carry and the ride down the yield curve.I will assume a par bond of $1mm and no accrued interest.

I will use the approximately the same set of facts I used in my closing commentary yesterday. That is, the current 2 year note with a 2 5/8 coupon.

I will use a term repo rate to September 30th of 1.60 percent.

The repo begins on June 2 and matures on September 30. That looks to be 121 days.

So the repo calculation is( $1mm X .016 ) divided by 360 days times 121 days. That works out to $5377 and means that if you own the bond and financed the bond for the 121 day period at 1.60 percent you had a cost of $5377.

However, as the owner of the bond you are accruing that 2.625 percent coupon over that same period. So you earned ($1,000,000 X..02625) divided by 365 times 121 day. That works out to $8702 accrued interest for the 121 days.

$8702 minus $5377 equals $3325 of POSITIVE CARRY for each $1 million bonds.

For purposes of this discussion and simplicity I am going to arbitrarily reduce the $3325 to $3125. That is because bonds trade in increments of $312.50 per million bonds. So my arbitrary $3125 is equal to 10/32 on the $1mm par bonds.

That 1/32 increment has a value in basis points of yield. The yield value of that 1/32 increment is 1.7 basis points. So in my example the 10/32 is equal to 17 basis points. So, ceteris paribus, if I buy the bond today at a yield of 2.625 percent (par) and finance it under the set of circumstances presented here, I have a cushion of 17 basis points. So if the yield on the bond on Sept 30 is approximately 2.79 percent I have a break even transaction. There is one more step to complete the analysis.

There is one other consideration and that is the steepness of the yield curve.

Over the term of this transaction the note that we own will slide down the curve and finish as a 20 month note rather than the 24 month note at which it began. We assume that the shape of the yield curve will be the same at the end of the 120 day repo as it is at the start. At the close of business yesterday that 4 months was worth about 12 basis points. So all other things being equal the 2.625 yield today will be approximately a 2.50 percent yield on September 30.

I add those 12 basis points of yield to the 17 basis points which I earned in the financing leg of the transaction and my breakeven is now 29 basis points.

So under that set of assumptions I can buy the 2 year note today at 2.625 percent and breakeven on September 30th if the yield on the 2 year note is less than 2.915 percent. (2.625 plus the 29 basis point cushion).

If you believe that the FOMC is about to embark on a policy of serial tightenings, that is a very bad trade. If you think that the Federal Reserve is on hold and that the funds rate will be 2 percent for the rest of our natural lives it is a fair bet. And if you believe that we are in the midst of a protracted slowdown and that the FOMC will be forced to cut rates again sooner rather than later then it is a great bet.

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  1. 9 Responses to “A Positive Carry Primer”

  2. By greg on May 30, 2008 | Reply

    Nice example. That clarifys it very well. Is term repo (gc) out to Sept trading as low as 1.6%?

  3. By John Jansen on May 30, 2008 | Reply

    The rate on this security was 1.60 yesterday. so that was a real world example.

    Seprately, the basic repo trade is overnight. There is also an market in “term” repo. I guess that is anything beyond one day. In your comment you seem to equate term with GC. GC is general collateral. It is stuff for which there is no special demand.

    The stuff for which there is special demand is called appropriately “special ” repo.

    What makes something special? Well , if the entire worls shorts the 2 year note versus the long end that creates extra demand for the issue in repo as those who are short need to make delivery. So special collateral will trade at a spread rich to GC.

    If you are short the security you have in hand funds from that sale.The speialness arises because you are willing to earn a lower rate of interest on that money in order to make delivery of the security.

    So in a sense the specialness of an issue can be determined by the extent to which it trades through GC.

  4. By Dave on May 30, 2008 | Reply

    I liked this article a lot. As one of the few technical bond blog out there it would be great if you do more posts on the mechanics of the bond markets as I think they would be very helpful to a lot of us (at least me). I read every post you write.

    Thanks,
    Dave

  5. By hh on May 30, 2008 | Reply

    thank you for the elaboration on the calculations.

    successful trading and market endeavors require a great amount of tacit knowledge lacking in most books and financial literature. i am grateful to see an experienced practitioner, like yourself, donating time to fill in some of the void.

    sincerely,

  6. By John Jansen on May 30, 2008 | Reply

    Thanks for the compliments. If anyone has any thoughts on other bond market topics they wish to see discussed let me know and I will think about doing a longer explanatory piece.

    i will not make an uneqivocal statement that i will because I spend so much time on this already that I have to ration my time. Today was easy because the topic isrelatively simple and i felt that it would be a quiet market which would allow me the luxury to prepare this piece.

  7. By Adan Lerma on May 30, 2008 | Reply

    john, i feel like i got a decent handle on the subject, extremely interesting

    my main question is re: “That 1/32 increment has a value in basis points of yield. The yield value of that 1/32 increment is 1.7 basis points.”

    is every 1/32 worth 1.7 basis points on all bonds, or just on this, the two yr note?

    if not, how would one find out what each 1/32 is worth for the 4 3/8 30 yr?

    saw in another post you were heading out w/your wife, have a great time! respond whenever 🙂

    thank you much

  8. By jck on Jun 1, 2008 | Reply

    “is term repo (gc) out to Sept trading as low as 1.6%?”

    no way near it, either for term or o/n.
    o/n is trading above fed funds (’tis not supposed to happen)

  9. By John Jansen on Jun 1, 2008 | Reply

    The term repo (1.60) on the 2 year note to September 30 which I used in my calculation was the rate on that issue at the time of the writing.

  10. By John Jansen on Jun 1, 2008 | Reply

    According to my usually reliable sources!!

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