Introduction

Dollar roll transactions are a crucial aspect of the mortgage-backed securities (MBS) market, often utilized by investors and market participants to manage their exposure and optimize their portfolios. A dollar roll involves the sale of an MBS with an agreement to repurchase a similar MBS at a future date, typically within a short span of time. This transaction effectively enables the investor to finance their MBS holdings by leveraging their existing securities. Understanding the mechanics of dollar roll transactions and valuing them is essential for participants in the MBS market.

Dollar Roll Transaction Mechanics

A dollar roll transaction begins with an investor selling an MBS for a certain period, let’s say “T”, and simultaneously agreeing to repurchase the same or a similar MBS at a later date, “T+1”. The attractiveness of a dollar roll lies in the financing advantage it offers. The investor receives cash from the initial sale that can be reinvested at a potentially higher short-term rate, while also committing to repurchase the MBS at a future date.

Valuation of Dollar Roll Transactions

The valuation of a dollar roll transaction involves calculating the implied financing rate, which represents the difference between the initial selling price of the MBS and the lower repurchase price. This rate essentially indicates the implied interest rate at which the investor is able to borrow funds in the market for the duration of the transaction.

Formula for Implied Financing Rate (IFR)

The formula to calculate Implied Financing Rate (IFR) is given by:

$$\text{Implied Financing Rate (IFR) = } \frac{\text{Purchase Price at T+1- Sale Price at T}}{\text{ Sale Price at T}} \times \frac{360}{\text{Number of Days between T and T+1}}$$

Where:

• Purchase Price at $T+1$ is the repurchase price at the future date $T+1$.
• Sale Price at $T$ is the initial selling price at the date $T$.
• Number of Days between $T$ and $T+1$ represents the time span of the dollar roll transaction.

Example: Suppose an investor sells an MBS for USD 1,000,000$ today (T) and agrees to repurchase the same MBS for USD 1,005,000 in 30 days (T+1). The number of days between T and T+1 is 30 days.

$$\text{Implied Financing Rate (IFR) = } \frac{( 1,005,000- 1,000,000)}{\text{ 1,000,000}} \times \frac{360}{30}$$

This implies that the investor can effectively borrow funds at an annualized rate of $6 \%$ for the 30-day period through the dollar roll transaction.