Estimating a Bond’s Richness from Repo Specialness
Summary
A bond that trades special in the repo market can be financed at a rate below general collateral (GC). That financing advantage can support a higher bond price, or equivalently a lower yield, than would prevail without specialness. The document estimates the effect by comparing forward pricing under the issue’s special repo rate with pricing under the GC rate.
Its historical example assumes the bond will cease being special in three months. It uses the special repo rate to derive a forward price, then solves for the spot price consistent with that forward price at the higher GC rate. The resulting implied yield is compared with the quoted yield to estimate the richness attributable to specialness. This is an illustrative calculation using a particular bond, date, and assumed horizon; the estimate depends on those inputs and does not establish a general relationship for every bond or repo market.
Key ideas
- Repo specialness can lower a bond’s financing cost relative to the general collateral rate.
- A lower financing cost can make a bond richer in price and lower in yield.
- Compare forward pricing under special and general collateral financing to estimate the effect.
- The estimate depends on the assumed time until specialness ends and the market inputs used.
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Full text
# How do you quantify the impact on bond if it becomes special?
# How do you quantify the impact on bond if it becomes special?
If the bond is trading at 5% and it becomes special, how do you quantify the impact this has on the bond? Or am I misunderstanding the concept of specialness?
## Answer by Helin (score 4, accepted)
https://quant.stackexchange.com/a/36120
I'll use a real life example back from the early 2000s, since the specialness effect was much more pronounced.
Back on Feb 14, 2001, the 10-year on-the-run note (5s of Feb 15, 2011) traded at a yield of 5.121% / price of 99.062. We assume that the bond will lose its specialness in three months, so we reference the 3-month forward market for clues.
On this day, this issue's 3-month repo rate was 3.14%, so the 3-month forward price is simply: $$ 99.062 \times \left(1 + 3.14\% \times \frac{89}{360}\right) - 1.230 = 98.602, $$ where 1.230 was the accrued interest as of the forward settlement date.
The general collateral repo rate on the same day was over 200 bp higher at 5.19%. If the bond weren't trading special and had to be financed at GC, the forward price calculated above would imply a spot price as follows: $$ P \times \left(1 + 5.19\% \times \frac{89}{360}\right) - 1.230 = 98.602. $$ So without repo advantage, the bond's price should be $P = 98.567$, or a yield of 5.18%. This is 6 bp higher than the quoted yield of 5.12%, indicating that specialness richened the bond by 6 bp.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.