Understanding Repurchase Agreements in Excel Formulas

A repurchase agreement, or repo, is a short-term transaction in which one party sells a security to another party and agrees to buy it back later at a higher price. The difference between the sale price and the repurchase price is the interest paid on the loan, also known as the repo rate. The security serves as collateral for the loan.

Repos are used by financial institutions to raise cash quickly, manage liquidity, and finance their operations. They are also a common tool of central bank open market operations, which aim to regulate the money supply and interest rates in the economy.

Repos can be classified into different types based on the term, the collateral, and the counterparty involved. Some common types of repos are:

• Overnight repo: A repo that matures the next business day.
• Term repo: A repo that has a specified maturity date, usually longer than one day.
• Open repo: A repo that has no fixed maturity date, but can be terminated by either party at any time.
• Tri-party repo: A repo that involves a third-party agent, such as a clearing house, that manages the collateral and ensures the settlement of the transaction.
• Delivery repo: A repo that requires the transfer of the collateral from the seller to the buyer.
• Hold-in-custody repo: A repo that allows the seller to retain the custody of the collateral, subject to certain conditions and safeguards.

Repos are generally considered safe investments because they are backed by high-quality collateral, such as government securities. However, they also entail some risks, such as:

• Credit risk: The risk that the counterparty will default on the repurchase agreement and fail to return the cash or the collateral.
• Liquidity risk: The risk that the market for the collateral will dry up and make it difficult to sell or value the security.
• Market risk: The risk that the value of the collateral will fluctuate due to changes in interest rates, exchange rates, or other market factors.
• Operational risk: The risk that the transaction will be delayed or disrupted due to technical, legal, or administrative issues.

Basic Theory:

A Repurchase Agreement is a financial transaction where one party sells securities to another with a commitment to repurchase them at a specified price on a future date. Essentially, it is a short-term collateralized loan. The party selling the securities is the borrower, and the one purchasing them is the lender.

Procedures:

1. Agreement Terms: The borrower and lender agree on terms such as the collateral (securities), interest rate (repo rate), and maturity date.
2. Initial Trade: The borrower sells the securities to the lender and receives cash.
3. Interest Payments: The borrower pays interest on the cash borrowed.
4. Repurchase: On the agreed-upon date, the borrower repurchases the securities at the previously agreed-upon price.

Excel Formulas:

1. Initial Cash Received (Selling Securities):
   =PV(Rate, Nper, PMT, FV)
   where Rate is the repo rate, Nper is the number of periods, PMT is the interest payment, and FV is the future value.
2. Interest Payment:
   =IPMT(Rate, Per, Nper, PV, FV, Type)
   where Per is the period for which you want to calculate the interest payment.
3. Repurchase Price:
   =FV(Rate, Nper, PMT, PV)
   where PMT is the interest payment, PV is the present value, and FV is the future value.

Explanation:

Let’s consider a scenario where Company A borrows $1,000,000 from Bank B at a repo rate of 3% for a 30-day period. The interest payment is due at the end of the term.

1. Initial Cash Received (Selling Securities):
   =PV(3%, 30/365, 0, -1000000)
   The result is the initial cash received, which is $1,000,000.
2. Interest Payment (for 30 days):
   =IPMT(3%, 30, 30/365, -1000000)
   The result is the interest payment, let’s say $7,500.
3. Repurchase Price:
   =FV(3%, 30/365, -7500, -1000000)
   The result is the repurchase price, which is $1,007,500.

Result:

At the end of the 30-day period, Company A repurchases the securities for $1,007,500, including the interest payment.

Other Approaches:

1. Using RATE Function:
   Instead of using PV, IPMT, and FV separately, you can use the RATE function to calculate the repo rate.
2. Scenario Analysis:
   Perform sensitivity analysis by changing variables such as repo rate, collateral value, or maturity period to understand the impact on the transaction.