Repurchase Agreements (Repos)

Repurchase agreements, commonly known as repos, serve as a secured method for short-term borrowing and lending. These transactions consist of a seller committing to repurchase a security at a predefined price on a future date. This operation essentially allows the seller to obtain a short-term loan collateralized by the security.

The repo transaction starts with the sale of a security and ends with its repurchase. For instance, consider a US five-year Treasury note trading at $150 million. If it’s sold today (t=0) under a 45-day repo term at an annual interest rate (repo rate) of 0.5%, the repurchase price after 45 days would be calculated as illustrated below.

Assuming that there are 360 days in a year:

$$ 150\times\left[1+\left(0.5\%\times\frac{45}{360}\right)\right]=\$150.094 \text{ million} $$

The security seller effectively gets a short-term loan, collateralized by the US Treasury note. Repos can range from overnight to term repos, which have maturities longer than a day. The most common collateral is highly liquid bonds with minimal credit risk, such as sovereign bonds. A general collateral repo transaction allows a range of securities as eligible collateral.

Features and Calculations

Repos may require collateral in excess of the cash exchanged, termed as initial margin.

$$ \text{Initial margin}=\frac{\text{Initial security price}}{\text{Initial purchase price}} $$

A loan that’s backed entirely by collateral has a 100% initial margin. If the margin is greater than this, it indicates that there’s even more collateral provided initially. You can think of this extra collateral as a “haircut” or reduction to the loan in comparison to the starting value of the collateral. Belo is the equation representing this concept.

$$
\text{Haircut} =\frac{\left(\text{Initial Security Price} – \text{Purchase Price at the start}\right)}{\text{Initial Security Price}} $$

Repos adapt to fluctuations in collateral value by allowing those involved in the contract to either ask for more collateral or give back some of what they’ve already provided. This ensures that the security interest remains consistent with the originally agreed-upon margin terms. This fluctuating margin payment, known as the variation margin, measures the gap between the currently required margin and the value of the security at a specific time, which is represented in the following equation:

$$ \begin{align*} \text{Variation margin} = & (\text{Initial margin} \times \text{Purchase price at time t}) \\ – & \text{Security Price at time t}. \end{align*} $$

Uses of Repos

1. Financing Securities: Institutions that trade or hold securities, such as banks, often use the repo market to finance their security ownership. It enables them to manage their cash flow efficiently without selling the asset.
2. Secured Lending: From the buyer’s perspective, a repo transaction is an opportunity to lend funds on a short-term basis with the added security of collateral, thus minimizing default risk.
3. Short Selling: Some entities utilize repos to borrow securities for short selling, a strategy where the borrower believes the asset price will decrease.

Benefits of Repos

1. Liquidity: Repos provide immediate liquidity, making them invaluable for institutions requiring short-term funds.
2. Security: Repos are collateralized, meaning the default risk is lower compared to unsecured loans.
3. Flexibility: With durations ranging from overnight to longer-term, repos can cater to diverse liquidity needs.
4. Central Bank Operations: Central banks use the repo market as a tool for implementing monetary policy, allowing them to manage liquidity in the banking system.

Risks Associated with Repos

1. Default Risk: Despite being secured, there remains a risk of default. If a party fails to meet its obligations, the other party might suffer losses, especially if the collateral’s value has depreciated.
2. Collateral Risk: The quality, liquidity, and value of the collateral can fluctuate. If a party defaults, the other might find it challenging to liquidate the collateral at the expected value.
3. Margining risk: It’s crucial to ensure accurate and prompt valuation of collateral and the transfer of variation margin. This helps prevent collateral deficiencies if there’s a need to liquidate after a default. Moreover, unfavorable market situations might lead to significant shifts in collateral’s value, amplifying margin requirements and prompting more liquidations among traders.
4. Legal risk: This pertains to the enforceability of rights within a repurchase agreement.
5. Netting and settlement risk: This involves the capability of those involved in a repo contract to either offset the duties of a party that hasn’t defaulted and to claim either collateral or cash as a trade settlement.

Risk Management

Repo market players often involve a third party for risk management. Direct transactions between two entities are termed bilateral repos. On the other hand, triparty repos involve a third-party agent agreed upon by both main parties. The triparty agent, such as a custodian, oversees the transaction, including cash, securities, collateral valuation, and safekeeping. Triparty agents enable cost efficiencies, larger collateral pools, and access to multiple counterparties. Although the repo market is stable, it poses significant rollover and liquidity risks, especially during adverse conditions. Financial institutions must weigh the affordability of repo funding against the flexibility of pricier long-term financing methods. While repo transactions are collateralized, they’ve led to significant losses during crises due to over-reliance on repo financing by some firms.

Question #1

Assume that today (t=0), the current US ten-year Treasury note trades at a price equal to the bond’s face value of USD150,000,000. The security buyer takes delivery of the US Treasury note today and pays the security seller a purchase price based on an initial margin of 104%. The repo haircut is closest to:

1. 0.00%.
2. 3.85%.
3. 4.00%.

Solution

The face value of the US ten-year Treasury note = USD150,000,000.

Initial margin =104%.

Now, the “Purchase Price” can be found using the formula:

$$ \begin{align*} { \text{Purchase Price} } & =\frac{{\text{Security price}}}{{ \text{Initial Margin} }} \\
{\text{Purchase Price} } &=\frac{ \text{USD } 150,000,000}{1.04}=\text{USD } 144,230,769.23 \end{align*} $$

Now, the repo haircut is defined as:

$$ {\text {Haircut} }=\left(\frac{\text{Initial Security Price} {-\text{Purchase Price} }}{\text{Initial Security Price}}\right)\times100\% $$

Inserting our values:

$$ {\text{Haircut} }=\left(\frac{{\text {USD } }150,000,000-{ \text{USD } }144,230,769.23}{{ \text{USD } }150,000,000}\right)\times100\%=3.85\% $$

Question #2Which of the following best describes the primary use of a repurchase agreement (repo) in the context of financial institutions?

1. Hedging against exchange rate fluctuations.
2. Financing their security ownership.
3. Securing long-term funding for capital expenditure.

Solution

The correct answer is B.

Financial institutions often use the repo market to finance their security ownership, which enables them to manage their cash flow efficiently without selling the asset.

A is incorrect: Hedging against exchange rate fluctuations is not the primary use of repos.

C is incorrect: Repurchase agreements are primarily for short-term funding, not long-term capital expenditure.

Question #3

What are the inherent risks associated with repurchase agreements?

1. Inflation risk, currency risk, and equity risk.
2. Default risk, collateral risk, and legal risk.
3. Commodities risk, strategic risk, and liquidity risk.

Solution

The correct answer is B.

Repos come with risks such as default risk (if a party fails to meet its obligations), collateral risk (related to the quality, liquidity, and value of the collateral), and legal risk (related to the enforceability of rights within a repurchase agreement).

A is incorrect: Inflation risk, currency risk, and equity risk are more general market risks and not specifically inherent to repos.

C is incorrect: While liquidity risk is a concern for the repo market, commodities risk and strategic risk aren’t primary risks associated with repurchase agreements.