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Show how repo use can give rise to counterparty risk and to liquidity risk.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Repurchase Agreements and Financing · FRM2.LTR.13.c

The idea

Repo creates two linked risks. Counterparty risk is the chance that a party defaults while the other holds an exposure. The cash lender is exposed if the borrower defaults and the collateral, once sold, brings in less than the cash plus accrued interest owed. The haircut and daily variation margin are the protection. The borrower is also exposed, because it has posted collateral worth more than the cash received and may not get the excess back if the lender fails. Liquidity risk sits mainly with the borrower. Short-dated repo funds longer-dated assets, so lenders can refuse to roll the funding, raise haircuts, or demand more margin as collateral prices fall, forcing asset sales. The key point is that protections for the lender, such as higher haircuts and margin calls, transfer stress into the borrower's liquidity needs.

Formulas

Repo lender's loss when the borrower defaults

Loss = Cash × (1 + Rate × Days ÷ 360) − Proceeds

Cash
the cash lent
Rate
the repo rate, annualised
Days
days of interest accrued up to the default
Proceeds
what the collateral raises when sold

A loss arises only if the collateral falls by more than the haircut cushion. Leaving out the accrued interest understates the loss.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a repo, under what condition does the cash lender suffer a credit loss?

  1. The borrower defaults and the collateral sells for less than the cash plus interest owed. - correct
  2. The borrower defaults and the collateral raises more than the cash lent plus accrued interest.Why not: The lender is made whole and must return any surplus, so there is no loss.
  3. The borrower repays the cash and interest on time but the collateral has fallen in value.Why not: If the borrower performs, the collateral is returned and its fall in value does not affect the lender.
  4. The repo rate rises after the trade is agreed.Why not: The repo rate is fixed for a term repo, and a change in market rates is not a default loss.

The lender's exposure is the cash plus interest owed less the value the collateral can be sold for. Over-collateralisation through the haircut covers this unless the collateral falls by more than the haircut.

A harder one

A dealer finances USD 500 million of securities in repo, with a haircut of 2% (cash = MV x (1 - haircut)). In a stressed market, lenders raise the haircut to 6% on the same collateral value. The additional cash the dealer must find to keep the position is closest to:

  1. USD 30.0 millionWhy not: Applies the whole new haircut of 6% as the shortfall, forgetting the 2% haircut already funded.
  2. USD 10.0 millionWhy not: Applies the old 2% haircut rather than the 4 percentage point increase.
  3. USD 18.5 millionWhy not: Treats the haircut as a margin (cash = MV / (1 + haircut)) which does not match the stated convention.
  4. USD 20.0 million - correct

Cash falls from 500 x 0.98 = 490 to 500 x 0.94 = 470, a shortfall of USD 20 million (500 x 4%). The borrower must fund it from other sources or sell assets.

The hardest tier

A repo lender advanced USD 120 million against collateral worth USD 125 million (a 4% haircut) for 30 days at 5% (actual/360). The borrower defaults at maturity, and the lender sells the collateral after a 6% price decline. The lender's loss is closest to:

  1. USD 2.5 millionWhy not: Compares the collateral proceeds with the cash lent and omits the interest owed.
  2. USD 7.5 millionWhy not: Takes 6% of the collateral value as the loss and ignores the cushion from over-collateralisation.
  3. USD 7.2 millionWhy not: Takes 6% of the cash lent as the loss and ignores both the haircut cushion and the interest.
  4. USD 3.0 million - correct

Owed = 120 x (1 + 0.05 x 30/360) = 120.5 million. Proceeds = 125 x 0.94 = 117.5 million. Loss = 3.0 million, so the 4% haircut covered only part of the 6% fall.

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