# How to Calculate an Overnight Index Swap (OIS) and Its Benefits

![Overnight Index Swap (OIS): A hedging arrangement in which a cash flow based on an overnight lending rate is exchanged for another predetermined cash flow.](https://www.investopedia.com/thmb/0yu3fpPvpgDVw0fVlz1h5CLXc2M=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/overnightindexswap.asp-final-216af61ba0f84575815b62a83457d7b9.jpg)

*— Investopedia / Jake Shi*

> **Definition**
>
> An overnight index swap is a financial contract used to manage interest rate risk. In this hedging agreement, one party pays a fixed interest rate while the other pays a floating rate based on an overnight index.

## What Is an Overnight Index Swap (OIS)?

An index swap is a hedging contract in which one party exchanges a predetermined cash flow with a counterparty on a specified date. An overnight index swap applies an overnight rate index, such as the federal funds rate, to the contracts. Index swaps are specialized groups of conventional fixed-rate swaps, with terms that can be set from three months to more than a year.

Overnight Index Swaps play an important role because they are used as a benchmark for risk-free interest rates and provide banks and investors with insights into the interbank credit market and its liquidity.

### Key Takeaways

*   An Overnight Index Swap (OIS) is primarily used by financial institutions to hedge against fluctuations in short-term interest rates, providing stability in their interest cost obligations.
*   The swap involves exchanging a fixed interest rate for a floating rate, typically based on an overnight rate index such as the federal funds rate.
*   Calculation of an OIS involves compounding the overnight rate and understanding terms structured according to financial industry practices, such as using a 360-day year for calculations.
*   OIS contracts are favored by traders and speculators for their ability to serve as indicators of the interbank credit markets and are often viewed as less risky than traditional interest rate spreads.
*   The process is significant for financial professionals, as it offers a strategic tool for managing interest rate risk, appealing to a range of market participants from hedge fund managers to large enterprises.

## Functionality of Overnight Index Swaps

In an overnight index swap, the overnight rate is exchanged for a [fixed interest rate](https://www.investopedia.com/terms/f/fixedinterestrate.asp). An overnight index swap uses an overnight rate index such as the federal funds rate as the underlying rate for the floating leg, while the fixed leg would be set at a rate agreed upon by both parties.

The interest of the overnight rate portion of the swap is compounded and paid at reset dates, with the fixed leg being accounted for in the swap's value to each party.

The floating leg's present value (PV) is determined by either compounding the overnight rate or by taking the geometric average of the rate over a given period.

Financial institutions prefer overnight index swaps because the overnight index reliably reflects interbank credit markets and is less risky than traditional spreads.

## Calculating an Overnight Index Swap: A Step-by-Step Guide

There are eight steps to calculate a bank's dollar benefits from an overnight index swap:

1.  **Determine the Swap Period**: Multiply the overnight rate by the number of days the swap encompasses. For a swap starting on a Friday, the period is three days; otherwise, it's one day.  
    
2.  **Effective Rate Calculation**: Divide the effective overnight rate by 360, following industry practice. For instance, using an overnight rate of 0.005%, calculate as follows: 0.005% / 360 = 1.3889 x 10.
3.  **Add One to the Result**: Add 1 to the result from step two to create a new rate: 1.3889 x10 + 1 = 1.000013889.
4.  **Multiply by the Principal**: Apply this new rate to the principal amount. For a $1 million loan, the calculation would be: 1.000013889 x $1,000,000 = $1,000,013.89.
5.  **Adjust Daily for Multi-Day Loans**: Repeat the above calculations daily if the loan spans multiple days with varying rates.
6.  **Recalculate With Fixed Rate**: Similar to step two, divide the rate by 360 and add 1. For example, with a rate of 0.0053%, compute: ( 0.0053% / 360 ) + 1 = 1.00001472.
7.  **Exponentiate and Finalize Calculation**: Raise this rate to the power of the loan days and multiply by the principal: 1.00001472^ x $1,000,000 = $1,000,014.72.
8.  **Calculate Profit**: Subtract the two calculated sums to find the bank's profit: $1,000,014.72 - $1,000,013.89 = $0.83.

## What Is an Overnight Index Swap?

An overnight index swap is a bet on the direction of short-term interest rates. One party agrees to pay a fixed interest rate, while the other party agrees to pay a floating rate based on the overnight index. When the overnight index rate is calculated for the relevant time period, one party pays the other party the difference between the fixed and floating rates for that period.

## Why Does Anyone Undertake an Overnight Index Swap?

Financial institutions and other large enterprises use the overnight index swap as a hedge against sudden adverse swings in short-term interest rates. They are effectively protecting their interest rate costs by locking in the short-term rate they will pay. Traders and speculators also use this strategy when they expect a swing in short-term interest rates.

## Is an Overnight Index Swap a Derivative?

Yes. The overnight index swap is a type of derivative contract. That is, it is based on short-term interest rates but does not represent an actual investment in any asset.

## The Bottom Line

The overnight index swap is a hedging contract used to exchange predetermined cash flows and cash flows based on an overnight lending rate. It is a tool also used by hedge fund managers, financial institutions, and market speculators to place bets on short-term interest rate movements.

OISs involve exchanging a floating rate based on an overnight index for a fixed interest rate and are considered less risky than traditionally used interest rate spreads due to the use of overnight indexes.

> **Article Sources**
>
> 1.  Cbonds. "[Overnight Index Swap](https://cbonds.com/glossary/overnight-index-swap-ois/)."
>     
> 2.  Cbonds. "[Overnight Index Swap](https://cbonds.com/glossary/overnight-index-swap-ois/#:~:text=Unlike%20other%20yield%20curves%20that,for%20risk%2Dfree%20interest%20rates.)."