# How do repos introduce leverage?

#### kchristo

##### Member
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I have heard that repos can be used to gain leverage, particularly within hedge funds. However, if repo sellers (who borrow cash) have to post collateral, and the value of collateral is reduced via a haircut, wouldn't this in effect be the opposite of leverage? i.e. repo sellers would be getting in cash less than the full market value of their securities, when the objective is to get more cash?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
This is interesting, isn't it? At first glance, the repo does seem like anti-leverage. A repo is secured borrowing, so instead of (say) me borrowing unsecured cash from you, I secure the borrowing with cash by giving you collateral to hold. That doesn't seem like leverage to me, either. Except that we normally learn the repo in terms of the bilateral relationship between the trader (who maybe delivers collateral in the near leg) and the repo dealer (who lends cash in the near leg).

But in practice hedge funds, in the near leg, conduct two simultaneous transactions: they buy the collateral (e.g., bond) in the open market and fund this purchase by borrowing the cash in a repo (in the repo, the hedge fund is the lending a security in order to borrow cash). Without a haircut (or practical constraints), their leverage goes to infinity. If the collateral has a value of $100 and the haircut is 20%, the dealer provides 80% or$80 of the purchase price. If the repo interest is 1%, the leverage is something like 5x (to be super simple without agonizing over definition of leverage) as the return on capital = 1%/20% = 5%. The leverage is the same leverage the fund would get in straight-up borrowing to buy the collateral. Hope that helps!

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#### kchristo

##### Member
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Hi @David Harper CFA FRM , thank you for the explanation - this seems to really clear things up. The concept I'm hung up on is that if a hedge fund has securities to use as collateral in a repo (for example, treasuries), why not just sell those, get the cash, and use that to fund the purchase? Then they wouldn't have to go through the trouble of rolling the repo or being forced to sell the asset (that the purchased with the cash from the repo) in the case that the repo comes due?

Also I'm a bit confused as to how the leverage would be 5x, would that just ($100 of securities)/($20 haircut)?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @kchristo Sure, your hedge fund can do that. But your hedge fund starts with collateral on the balance sheet (funded by debt/equity on the liabilities side). It sells the collateral which doesn't change the size of the balance sheet: cash replaces collateral. Then buy something back to collateral. Leverage (aka, debt to equity, debt to assets) is unchanged. My hedge didn't start with anything funded and it effectively borrowed; leverage is (generally) adding debt to fund more assets.

If the bond costs $100, but the haircut is 20%, then dealer (cash lender) provides$80 (80%). Say the bond's coupon is 6.0% and the bank charges only 2.0% repo interest such that cost of funds (COF) on the borrowing = 2.0% * $80 =$1.60. The dollar spread = (6% * $100) -$1.60 = $4.40 or 4.40% of the$100 bond. But the hedge fund's return is $4.40 /$20.0 = 22.0% which is 5x the 4.40% simply because 100/20 = 5x. Please do not get me wrong: there are flavors and nuances, I just used a dead simple rule of thumb (forgetting frictions etc) that 20% haircut is borrowing 80% and so the leverage is 1/20% = 5x. Hope that helps,

#### kchristo

##### Member
Subscriber
This helps very much, thank you David!

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