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Sorry if this question is a little too basic but what determines repo rates? Not like "they are OTC transactions so they are determined directly between counterparties" but like what is the way you would approach calculations?

Take a bond priced $100$ at time $t=0$. Basic examples would say that party A lends party B the bond in exchange for $100$ now and repurchase the bond at $98$ later, for a repo margin of $2$. But how did $2$ arise; how did part B decide the appropriate return for this transaction was $2$? For example, is it because the risk-free is at $2\%$ so that's the return you would earn from investing the $100$, and therefore you're NPV zero in this transaction? How does the bond coupon tie into the calculation, since as a bond lender I assume you're receiving coupons?

Add on the scenario of an environment of rising yields like recently. Repo rates were observed to go down (at least for my region). Why did it go down? I tried to explain it with this made up theory: party B is going to be buying back a bond for $98$ that may only be worth $96$ after the selloff. Therefore he doesn't want to pay such a large haircut of $2$.

Can someone demonstrate with an example plz.

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Haircuts will be determined the same way any margin is determined - asset vol plus adjustments for other risk factors like liquidity risk. See https://www.cmegroup.com/clearing/risk-management/span-overview.html for an example.

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If you are an asset manager with a large amount of cash at hand there are typically 3 options you encounter with managing that cash:

  1. Lend the cash unsecured to a financial institution

Unsecured lending takes place but it should not be the go to action for large sums because it exposes a large amount of credit risk. You can mitigate this by lending to multiple institutions. The advantage here is that you will secure the best lending rates (running the largest risk). The lending tenor is typically negotiable but if you commit to a term that you lose some flexibility with respect to liquidity.

  1. Buy Assets - typically government bonds

If you buy an asset you have the advantage that the term is indefinite and you maintain liquidity control. You are however exposed to market risk but this can be minimised by buying the shortest dated bonds. The disadvantage is that if you succeed in minimising all the risks you typically end up with the lowest yield.

  1. Action a reverse-repo, or collateralised lending transaction

You commit your cash in exchange for collateral, which limits your credit exposure. You have committed the cash for term so you lose liquidity, especially if the collateral is not rehypothecatable. Since this is so closely linked to item 2) the two prices form a stable relationship. If one becomes much more advantageous that the other non-arbitrage arguments serve to bring the prices back inline.

Since a repo is a collateralised lending transaction, the lender does not want to suffer loss through devalued collateral based on market movements so the margin/haircut is volatility adjusted. Practical considerations like risk classifications and market practice/standard will also factor in the determination of the haircut.

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    $\begingroup$ Investing excess cash in an MMF is also common. Likely the MMF ends up doing 1, 2 or 3, of course! $\endgroup$ – user42108 Mar 4 at 23:16
  • $\begingroup$ A money market fund is a security, i.e. it is 2) buying assets. $\endgroup$ – Attack68 Mar 5 at 6:47
  • $\begingroup$ Indeed. Prime MMFs might buy financial CP which is the equivalent of 1), and they might participate in repo, hence my answer. As you probably know, the share of MMFs participating in CP seems to have gone down due to tight CP/bill spreads, so less of 1) and more of 2) since last March. $\endgroup$ – user42108 Mar 5 at 17:45

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