### Summary

#### Focus

This note looks at different ways of constructing term rates from overnight rates. When LIBOR goes out of use, as planned for the end of 2021, financial contracts will need to use LIBOR's alternative rates. For the US market, this is the Secured Overnight Financing Rate (SOFR), a measure of the cost of borrowing cash overnight collateralised by Treasury securities. However, unlike LIBOR, which is a term rate, SOFR and the other alternative rates are all overnight rates.

Ideally, financial contracts would use a term rate based on compounded overnight rates over the interest rate period (a method known as "in arrears"). Doing that, the interest rate payment is known at the end of the period. This is already standard in the derivatives market. But, in the cash market, the standard so far is based on quarterly payments, where the interest rate payment is known at the beginning of an interest rate period. Hence, the need to change the standard in the cash market is hampering the shift from LIBOR to alternative rates.

#### Contribution

We show how to optimally determine a term rate known at the beginning of an interest rate period by only using overnight rates (a method typically referred to as "in advance"). While the resulting term rates are known at the beginning - a desirable feature they share with LIBOR - a common objection is that this method introduces a lagged behaviour (or "basis"), which can be especially severe in periods when policy rates change rapidly. In this note, we analyse how the basis can be reduced.

To avoid using reference rates based on unreliable data, thus recreating the fallibility of LIBOR, only robust reference rates should be used, such as the alternatives to LIBOR. Using past overnight rates to determine the payment of the next interest period is robust.

#### Findings

In this note, we compare several approaches to reduce the basis by using term rates known at the beginning of the interest period. One approach includes an adjustment factor, which can be seen as the convenience premium to have the term rate pre-determined. We conclude that the ideal option is to use a shortened observation period when compounding overnight rates to derive a pre-determined term rate.

#### Abstract

This note evaluates ways of how new loans can be based on risk-free overnight (O/N) rates, the chosen successors to LIBOR (e.g. SOFR in the US). So far, O/N rates have not been widely adopted in the loan market, as this market is used to know the term rate at the beginning of an interest period. The loan market would prefer to replace LIBOR with another forward-looking term rate, i.e. a term rate that is known at the beginning and reflects expectation. However, these term rates currently do not exist and have several disadvantages. Instead of a forward-looking term rate one can also use past realizations of O/N rates to define a term rate at the beginning of an interest rate period. A common objection by using past realizations of O/N rates is that this introduces a lagged behavior (or 'basis'), which can be especially severe in periods when policy rates change rapidly. In this note, we evaluate the basis and show ways how to minimize it. We conclude that the ideal option to reduce the basis is to use a shortened observation period when computing term rates based on past O/N rate realizations.

JEL Classification: D47, E43, G21, G23

Keywords: LIBOR, interest rate benchmarks, SOFR, loan market, financial reform