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I'm a bit confused about repo settlement conventions, and let's say repos on US Treasuries (USTs).

USTs settle $T+1$ where $T$ is the trade date. So if today is Wed 3/8/17 and I execute a trade with someone to buy a UST, then that UST will be available in my securities account on 3/9/17 and cash to cover the purchase in theirs on 3/9/17 as well.

With this settlement lag of 1 day, it stands to reason that a one day repo agreement on a UST must work as follows: you negotiate with a repo dealer to borrow cash and post the UST as collateral sometime on day $T$. On day $T+1$ collateral and cash settle in the respective accounts, and on that same day (at some point before close of business) instructions are made to execute the unwind of the repo. That is, on $T+1$ the reverse transactions are ordered (the cash receiver remits cash back plus interest and the collateral receiver remits the UST back to the customer initiating the repo) and at the beginning of $T+2$ the unwind is settled, and thus the repo.

Viewed another way, on day $T_0$ quoted overnight repo rates are more like 1-day forward overnight rates. That is, we could express them as $R_{t_{0}}^{[t_1, t_2)}$ (read: repo rate observed at time $t_0=0$ corresponding to accrual period $[t_1, t_2)$).

To summarize and generalize a bit, if collateral underlying a repo settles on a lag of $\delta$ days, then a repo negotiated on day $T_0$ will settle on day $T_{\delta}$ (where transfers effecting the repo are executed before close of business on the trade date $T_0$) and the reverse repo will settle on $T_{2\delta}$ (where transfers effecting the repo are executed before close of business on $T_{\delta}$). Then the repo rate quoted at $t_0$ is $R_{t_0}^{t_0+\delta, t_0+2\delta}$. In particular, the rate is a $\delta$-forward rate of tenor $\delta$ (conclusion: you can't have a repo of term less than $\delta$ where $\delta$ is the settlement lag for the collateral.) $\delta=3$ comes to mind for equities.

Can someone with experience in repo markets/trading help clarify this for me? Does collateral post immediately by special wire for repos and other overnight collateralized transactions? One thing that occurred to me: maybe settlement is ignored and it's just the trade/execution dates that are considered---but this seems unlikely since this could lead to serious risk and clearing issues and since one repo is usually part of a long sequence of repos between multiple counterparties, one "bad faith" repo transaction (i.e., taking advantage of the fact that people will operate under the assumption that the collateral will clear later on when the lag is up) could cause a lot of disruption.

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It's confusing because US Treasury securities (USTs) don't actually have to settle $T+1$. Depositories, or non-depositories with an account at a clearing bank, can settle Treasuries on a gross delivery-versus-payment basis over the Fedwire Securities Service in real-time (i.e., $T+0$), which is what is done for same-day start bilateral repos backed by USTs.

The $T+1$ settlement convention for USTs comes from the widespread use of the Fixed Income Clearing Corporation Government Securities Division (FICC GSD) for settlement. FICC GSD netting members' transactions each day are netted down prior to determining their delivery obligations. This cycle of daily settlement on a net basis significantly reduces transaction costs, particularly for broker-dealers, whose securities inflows closely match their outflows. However, because it runs on a daily cycle, settlement via this facility has to happen on a T+1 basis.

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