Today we will start with very simple from the math point of view but also very important transaction in Fixed Income industry – Repurchase agreement or Repo. Here is the definition from Pietro Veronesi book:

A repurchase agreement (repo) is an agreement to sell some securities to another party and buy them back at a fixed date and for a fixed amount. The price at which the security is bought back is greater than the selling price and the difference implies an interest rate called the repo rate.

A reverse repo is the opposite transaction, namely, it is the purchase of the security for cash with the agreement to sell it back to the original owner at a predetermined price, determined, once again, by the repo rate.

Let’s calculate return on capital for trader in repo agreement:

Usually repo dealer gives something less than the market price of the security delivered by trader and the difference is called haircut.

If the bond price was price and dealer’s haircut rate was haircutRate then we can calculate haircut using the function:

let haircut (price, haircutRate) =

    price * haircutRate

If the dealer held the security during the number of days ndays, repo rate was annualRate and initial price of the security was buyPrice then the repo interest paid by trader will be:

let daysRate (ndays, annualRate) =

    days / 360.0 * annualRate

let repoInt ndays repoRate buyPrice haircut =

    let repoRateDays = daysRate (ndays, repoRate)

    (buyPrice - haircut) * repoRateDays

If trader will sell the security after ndays days at price sellPrice then return on capital for trader will be:

let repoROI sellPrice buyPrice days repoRate haircut =

    let rInt = repoInt days repoRate buyPrice haircut

    (sellPrice - buyPrice - rInt)/haircut

We could see that the position is highly leveraged and risky, because the trader put up the haircut as own capital.

The term of repo agreement is usually very short, mainly overnight. Repo rate is decided at the beginning of the agreement.

During the repo agreement’s time the trader earns the interest on the security (usually bond). If the interest earned is above repo interest then the trade implies positive carry (negative carry otherwise)

Next time we will take a look at reverse repo transaction.