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