David Bowman

Senior Advisor to the Board

This information is provided for illustrative and educational purposes only. The views expressed in this presentation are solely those of the author and do not necessarily represent those of the Federal Reserve, the

Alternative Reference Rates Committee or its members or ex officio members.

How to Use SOFR

-2

-1

0

1

2

3

4

5

6

7

2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

Overnight RFRs

SOFR/Historical Repo Rate TONA EONIA SONIA SARON

Percent

-2

-1

0

1

2

3

4

5

6

7

2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

3-Month Averages of Overnight RFRs

SOFR/Historical Repo Rate TONA EONIA SONIA SARON

Percent

AveragingThe financial contracts using overnight RFRs have referenced an average (1-month or 3-month) of the overnight RFR for floating rate payments, not one-day’s value. Those averages tend to be very smooth and appropriate for use in financial contracts (a 3-month average of SOFR is less volatile than 3-month LIBOR, even over year ends).

Source: Bloomberg Source: Bloomberg

Compound versus Simple AveragingCompounding interest reflects the time value of money – for example, a money market account pays compound interest – and is used in OIS swaps and some futures. However, other contracts use simple averaging, largely because of historical precedent. There is some basis between the two types of averaging, but it is generally small and any difference can be adjusted for so that borrowers do not pay more or less under either convention.

Table 2: Basis between Compound and Simple Interest (bp)

Loan Rate: 1 percent 5 percent 10 percent

Loan Maturity:

1-month 0.0 0.9 3.8

3-month 0.1 3.0 12.2

6-month 0.2 6.2 25.0

0

2

4

6

8

10

12

2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

Historical Basis Between Compound and Simple SOFR (bp)

Monthly Quarterly Semiannual

Source: Federal Reserve Bank of New York, staff estimates

Models for Using RFRsThe FSB and National Working Groups are looking at several models for using overnight risk-free rates in cash products

• In Arrearso Plain: Used averaged rate over current interest period, paid on last day of the period (day T)o Payment Delay: Use averaged rate over current interest period, paid k days after day T (Note: ISDA’s

conventions for SOFR swaps use a 1-day payment delay)o Lookback: Use averaged rate over current interest period lagged k days (a 3-5 day lookback has been used

in SONIA FRNs)o Lockout: Use averaged rate over current period with last k rates set at the rate for day T-k (a 3-5 day

lockout has been used in most SOFR FRNs).

• In Advanceo Last Reset: Use averaged RFR from the last interest reset period as rate for current reset periodo Last Recent: Use averaged RFR from a shorter recent period as rate for current reset period

• Hybrid Modelso Principal Accrual: Payments set In Advance, principal and interest accrue In Arrearso Interest Rollover: Payments set In Advance, any missed interest relative to In Arrears is rolled over into

the next payment period.

Plain

ArrearsUse RFR for

Day 1

Use RFR for

Day 2…

Use RFR for

Day T-3

Use RFR for

Day T-2

Use RFR for

Day T-1

Use RFR for

Day T

Payment

Due

(Note:

Technically,

Plain

Arrears is

not Possible

if the RFR is

Published

with a 1-

Day Lag)

Use RFR for

Day 1

Use RFR for

Day 2…

Use RFR for

Day T-3

Use RFR for

Day T-2

Use RFR for

Day T-1

Use RFR for

Day T

Payment

Due

Use RFR for

Day 1

Use RFR for

Day 2…

Use RFR for

Day T-3

Use RFR for

Day T-2

Use RFR for

Day T-2

Use RFR for

Day T-2

Payment

Due

Use RFR for

Day -1

Use RFR for

Day 0…

Use RFR for

Day T-5

Use RFR for

Day T-4

Use RFR for

Day T-3

Use RFR for

Day T-2

Payment

Due

Day 0

(Last Day of

Previous

Period)

Day 1

(First Day

of Interest

Period)

Day 2 … Day T-3 Day T-2 Day T-1 Day T

(Last Day of

Interest

Period)

Day T+1

(First Day

of Next

Period)

Day T+2

RFR for Day

1 Published

RFR for Day

T-4

Published

RFR for Day

T-3

Published

RFR for Day

T-2

Published

RFR for Day

T-1

Published

RFR for

Date T

Published

Table 3: Models for Using RFRs in Arrears

Arrears

with 2-Day

Payment

Lag

(Generally

Used in OIS)

Arrears

with 2-Day

Lockout

Arrears

with 2-Day

Lookback

Pros and ConsPayment Delays or Lookbacks are consistent with ISDA compounding definitions and more easily hedged and do not skip any interest days. A lockout does skip some days and has some basis to the In Arrears model used in OIS swaps (below), On the other hand, for most of the interest period, the daily interest rate will correspond to the most recent published value of the RFR, which may be important to certain investors who do not have hedging needs.

-15

-10

-5

0

5

10

15

20

25

2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

Basis between Quarterly Compounded 3-day Lockout vs Pure Arrears (bp)

Source: Federal Reserve Bank of New York, staff estimates

In Advance versus In ArrearsThe tension between In Arrears and In Advance is that borrowers will reasonably prefer to know their payments ahead of time – well ahead of time for a consumer product – and so prefer In Advance, while investors will reasonably prefer returns based on rates over the interest period (In Arrears) and view rates set In Advance as “out of date”.

But this isn’t an entirely new problem: One-Year LIBOR (which is used in most adjustable rate mortgages currently) can often quickly become out of date, by about the same magnitude that a compound overnight rate (here EFFR) has become out of date, so while these issues will rightly be an area of focus, this is already an issue in the current market although it does not receive much focus.

0

2

4

6

8

10

12

1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 2015 2018

Historical Gaps Between LIBOR and LIBOR ARM Resets

1-Year USD LIBOR

Monthly Rate on a 1-Year LIBOR ARM with resets at thestart of each year

Percent

-6

-4

-2

0

2

4

6

1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018

Comparing Changes in 1-Year LIBOR to the Difference between Compound EFFR in Advance and In Arrears

Annual Change in 1-Year LIBOR

Difference between 1-Year Compound EFFR In Arrears and In Advance

Percent

Source: Federal Reserve Bank of New York, staff estimates Source: Federal Reserve Bank of New York, staff estimates

In Arrears/In Advance (continued)The amount of basis between In Advance and In Arrears also depends on the frequency of interest periods. With a one-month reset, the basis is comparable to the amount of basis between simple and compound averaging. Even at 3- or 6-month resets the basis is limited and averages out to zero over longer periods of time. The below graph shows what would have been the historical basis on a hypothetical 5-year loan based on EFFR in Advance relative to a loan based on EFFR in arrears for 1-month, 3-month, and 6-month interest periods.

-60

-50

-40

-30

-20

-10

0

10

20

30

40

1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012

Basis Spread between in Advance and In Arrears 5-Year Loan with Monthly Payments (bp)

1MonthSpread 3MonthSpread 6MonthSpread

Source: Federal Reserve Bank of New York, staff estimates

Models of In AdvanceUsing “Last Reset” with a shorter reset period and/or Using “Last Recent” can substantially cut the basis to relative to In Arrears. Below we show what the historical basis would have been on a hypothetical 5/1 ARM based on EFFR in Advance relative to EFFR in Arrears using different reset periods and different variations of “Last Recent”/”Last Reset”

-60

-40

-20

0

20

40

60

1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Comparing Bases to In Arrears for Different Models of In Advance Mortgages

One Year Reset, Last Three Months Advance One Year Reset, Last Year Advance

One Month Reset, Last Month Advance Three Month Reset, Last Three Months Advance

Six Month Reset, Last Six Months Advance Six Month Reset, Last Three Months Advance

Six Month Reset, Last Month Advance

Basis Points

Source: Federal Reserve Bank of New York, staff estimates

Sizing the Amount of Basis RiskBy way of a comparison, the amount of basis risk in a Last Reset 6-month SOFR In Advance Mortgage would historically have been clearly smaller than the amount of risk involved in a mortgage being prepaid one year earlier or later than expected. And the basis risk involved should be easier to hedge and is only ever relevant for hybrid ARMs that move in to the variable rate – more than half close out before a variable rate applies.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

-50

-45

-40

-35

-30

-25

-20

-15

-10 -5

-2.5 0

2.5 5

10

15

20

25

30

35

40

45

50

55

Mor

e

Comparing Basis Risks

Basis Risk of Last Reset 6 Month SOFR in Advance

Basis Risk of 1 Year Earlier/Later Prepayment

Source: Federal Reserve Bank of New York, staff estimates

Hybrid ModelsHybrid models would be new but eliminate almost all basis relative to in Arrears and in a loan or mortgage while allowing the borrower to know their payments in Advance. If used in a consumer ARM, they would not materially alter the cumulated mortgage payments that a consumer would make or the principal they would pay down, for example, relative to a basic Last Reset 6 Month In Advance Mortgage. However, they would be a new form of product and would need to be explained in a way that consumers felt comfortable with, and servicers would need to be able to support these models.

40%

50%

60%

70%

80%

90%

100%

110%

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010

Cumulated Mortgage Payments

Last Reset 6M Principal Accrual Interest Rollover

Percent of Loan Amount

2%

4%

6%

8%

10%

12%

14%

16%

18%

1983 1986 1989 1992 1995 1998 2001 2004 2007 2010

Principal Paid Down

Last Reset 6M Principal Accrual Interest Rollover

Percent of Loan Amount

Source: Federal Reserve Bank of New York, staff estimates Source: Federal Reserve Bank of New York, staff estimates