Repo Valuation with Daily Collateral and Changing Repo Rates
Summary
The document addresses how to value an existing repurchase agreement before maturity when market repo rates have changed. Its central point is that, in a repo with daily collateral adjustment to preserve the agreed haircut, changes in the bond’s market value alter the quantity of collateral posted rather than the cash lent. Under that setup, the bond price at the valuation date does not directly determine the repo’s value.
Instead, the value is driven by the difference between the original repo rate and the prevailing rate for the remaining term, expressed as the present value of the rate difference over that period. The answer illustrates this with a small change in the spread over a benchmark rate. The discussion is brief and does not derive a full valuation formula or cover details such as payment conventions, discounting assumptions, margin frequency, or nonstandard collateral terms. Its conclusion therefore depends on the stated daily collateralization arrangement.
Key ideas
- Daily collateral adjustments maintain the haircut by changing the bond quantity posted.
- With that arrangement, bond market value affects collateral and risk, rather than directly setting repo value.
- The existing repo’s value depends on how its contracted rate compares with the current rate for the remaining term.
- The answer frames valuation as the present value of the rate difference over the unexpired period.
- The conclusion depends on daily collateral management and may not apply unchanged to other repo terms.
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# Valuation of a REPO
# Valuation of a REPO
I thought I had a pretty good grasp on how to calculate this but I'm getting questioned on it and just want to be sure I'm not getting it mixed up. In my notation you enter into the repo contract at $t=t_0$ and exchange a cash nominal, C, for bonds where C is determined by $C=B_{t_0} (1-HC)$ where HC is the haircut, e.g. 2%. The maturity of the repo is at $t_2$
The way I view it is that the present value of the repo at $t_1$ would be the value of the cash leg up to $t_2$ minus the cost of closing out the repo by entering into an opposite repo agreement from $t_1$ to $t_2$. The value of the cashleg of the reverse repo at that point would be $B_{t_1} (1-HC)$ and you get interest at the prevailing repo rate at the time that may be different from that of the first repo. I have put the calculations below. Is this correct? I am asking because I am being told by industry professionals that the value of the bond at the time doesn't affect the present value, only the risk. As a side note, if I am doing this correctly should you also discount this value from $t_2$ to $t_1$ to get the PV?
\begin{equation} PV = C_{t_2} - B_{t_1} (1 - HC) \exp{(r_2(t_2-t_1))} \end{equation} \begin{equation} C_{t_2} = C_{t_0} \exp{(r_1(t_2-t_0))} = B_{t_0} (1-HC) \exp{(r_1 (t_2-t_0))} \end{equation}
C = Cash leg value
B = Bond leg value
HC = haircut
PV = present value
$r_i$ = prevailing repo rate at time $t_i$
## Answer by dm63 (score 2, accepted)
https://quant.stackexchange.com/a/53928
As you have been advised, the value of the bond at $t_1$ is not relevant. This is because in any repo, the amount of bonds posted changes on a daily basis to maintain the haircut at the correct level. The amount of cash lent in the repo does not change. Hence , what matters is how the repo rate has changed from $t_0$ to $t_1$. For example , if the initial repo was at Fed Funds+ 25 and now it is Fed Funds + 20, the value of the repo is now the PV of 5bp over the remaining life of the repo.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.