MARKET INSIGHTS

Floor It:
Market Pricing of the Lower Bound on
Interest Rates
May 2019

Introduction
In the early 2000s, Japan was an anomaly. The
Bank of Japan had lowered short-term interest rates tonear zero percent, a policy stance that had not been
implemented by any other major central bank for morethan half a century. But even with that seemingly extreme
policy response, the country’s inflation stayed at
uncomfortably low levels, and its economic growth
remained stuck at an anemic pace. The rest of the world
watched with concern, but most observers assumed thatthese challenges were specific to Japan. 1
Since that time, the limitations faced by the Bank of Japan
have become the dominant policy issue confronting major
central banks throughout the world. Many of those central
banks have spent the past decade probing the lower limits
of nominal policy rates, given the difficulties they have
faced in generating sufficiently strong economic growthand boosting inflation rates to targeted levels.

Financial markets have failed to account fully for thesefundamental changes in the policy environment. Adjusting
to this environment is no simple task, since the lowerbound constraint introduces complexities into thedetermination of interest rates that result in considerably
different distributions of rate outcomes than those
produced by conventional models. Our analysis reveals
that market pricing of interest rate outcomes still has along way to go. Moreover, the potential implications
extend well beyond interest rates, affecting a wider set ofassets and the properties of investors’ portfolios.

To be sure, the past decade was far from ordinary. The
global economy suffered a tremendous blow from thefinancial crisis, and the resulting economic damage
propelled central banks around the world into unusuallyaccommodative policy settings. However, there were also
important structural changes taking place at the same timethat have continued to exert downward pressure on theneutral level of policy rates. Given those structuralchanges, confronting the lower bound on interest rates
likely will be a recurring feature of the monetary policy
landscape for many years to come.

1

Ben Bernanke, then a governor at the Federal Reserve Board, offered a useful account of the situation and its potential lessons in a well-known
2003 speech titled “Deflation: Making Sure ‘It’ Doesn’t Happen Here.”

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

1

Policy Challenges at theLower Bound

As noted above, the increasing relevance of the ELB
constraint in part reflects important structural changes in
the global economy. As shown in Figure 2, the neutrallevels of inflation-adjusted (i.e., real) policy rates appear tohave moved substantially lower—a trend that has been
taking place for some time but accelerated after thefinancial crisis. 2 The causes of the decline in the neutral realinterest rate are not entirely understood, but slowing
population growth and high savings rates in certain
regions have likely contributed to this pattern. The current
level of the neutral real policy rate for the United States, atjust below 1%, corresponds to a neutral nominal rate ofCollectively, the policy rates of the Federal Reserve,
European Central Bank, Bank of England, and Bank ofJapan have spent 85% of the past decade at the effective
lower bound (“ELB”), or the lowest policy rate that thosebanks perceived to be possible at a given time. As shownin Figure 1, this recent pattern contrasts with the history
before that period, when only the Bank of Japan waspressed against that boundary for meaningful periods of
time.

16%

Figure 1: Policy Rates of Major Central Banks
Federal Funds Rate
ECB Main Refinancing Rate
BOE Official Bank RateBOJ Overnight Call Rate

14%
12%
Policy Rate

10%
8%
6%
4%
2%
0%
-2%
1987

1991

1995

1999

2003

2007

2011

2015

2019

ECB rate information is shown since the ECB began conducting monetary policy operations in 1999.
Sources: U.S. Federal Reserve, Bank of England, European Central Bank, and Association of Call & DiscountCompanies/Nikkei.

Figure 2: Neutral Real Policy Rates of Major Central Banks
5%
USEuro Area
UK
Japan

Neutral Real Policy Rate

4%
3%
2%
1%
0%
-1%
1965

1969

1973

1977

1981

1985

1989

1993

1997

2001

2005

2009

2013

2017

U.S. rates based on the Laubach-Williams measure; Euro Area and U.K. rates based on the Holston-Laubach-Williams measure;Japan rates based on the Imakubo-Kojima-Nakajima measure for 2-year neutral rate of interest. Japan rates presented with respect
to periods of available data only.
Sources: Federal Reserve Bank of New York; Bank of Japan.
2

The neutral policy rate is defined as the interest rate consistent with an economy at full employment and inflation at its targeted level over the
medium term, in the absence of additional shocks to the economy.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

2just below 3% if we take into account the Federal
Reserve’s inflation target of 2%.
The implications of the ELB for financial markets will
depend critically on the policies that central banks
implement in response to these circumstances. One
immediate question is obvious: why do central banks not
simply push policy rates lower? The answer to thisquestion is not simple, but it stems in part from thepublic’s ability to hold physical currency that earns 0%
interest, as well as from the reluctance of the official
community to allow retail bank deposit rates to turnnegative. Thus, even in the face of economic shocks thatmight otherwise warrant a deeply negative policy rate,
central banks generally have not viewed such a response
as feasible. 3
Central banks therefore have been left looking for otherapproaches to promote more accommodative financial
conditions. The most widely discussed option has been
quantitative easing (“QE”), which over the past decade
has become an active policy instrument for many central
banks. The extent to which QE can substitute for the
traditional rate policy instrument is a matter of extensive
debate. In any case, it is likely not a perfect substitute, andhence central banks bound by the ELB still face anenvironment in which they are unable to ease rates
sufficiently.
When faced with that scenario, central banks typicallycompensate for their inability to lower the policy ratefurther by keeping it at the ELB for a longer period of timeand by subsequently maintaining a lower policy rate thanthey otherwise would. That is, they substitute “longer” for“lower.” This substitution turns out to be an effective policy
approach in many economic models.

Modeling Alternative Policy
Paths at the Lower BoundTo further explore the low-for-longer approach, we
introduce an economic model. Our goal is to capture theinteractions between economic developments andmonetary policy in the United States in a relatively simple
structure. Specifically, we consider a model with thefollowing three components:
1) an equation that determines the unemployment gap—

the level of the unemployment rate relative to its
sustainable level—as a function of the real short-term
interest rate, to capture the effects of monetary policy on
the business cycle (an investment/savings or “IS” curve,
written in terms of the unemployment gap);
2) an equation that determines the rate of inflation as afunction of the unemployment gap (a Phillips curve); and3) an equation that determines the setting of the policy rate

in light of the unemployment gap and the inflation rate
(a monetary policy reaction function for the Fed).
In specifying these equations, we assume that the U.S.
neutral nominal policy rate is just below 3%, consistent
with the most recent reading shown in Figure 2. We allow
the equations to be subject to shocks that produce thetype of fluctuations observed historically for the U.S.
economy, including a set of shocks calibrated to match the
dynamics observed when the economy entered a recession.
The constraints that arise from the ELB can be seen in thismodel by looking at how the Federal Reserve tends to
respond to the arrival of these “recession shocks.” Weassume that the economy begins in its steady state—with
the unemployment gap at zero, inflation at target, and thepolicy rate at its neutral level—and is then subject torecession shocks.
Left unconstrained, the standard response of the Fed
would be to cut the federal funds rate to -2%, as shownby the orange line in Figure 3. Of course, the central bankcannot follow that path because of the ELB constraint. But
an alternative policy path that lowers the policy rate to 0%
and keeps it there for longer, as shown by the red line,
appears to return the economy to full employment nearlyas quickly. This alternative path does not begin to tighten
policy until more than a year later than the unconstrained
path, and it also maintains a lower rate profile thereafter.
One way to interpret these results is to consider that the
integral of the deviation between the policy rate and its

3

Some central banks have pushed short-term nominal rates into negative territory, but none have solved the ELB problem and reached the deeply
negative rates that could prove beneficial in some circumstances. The lowest policy rate setting has been -0.75%, which was implemented by the
Swiss National Bank in 2015. A number of proposals have been made to allow interest rates to become deeply negative even in the presence ofphysical currency (see, for example, Miles Kimball, “Breaking Through the Zero Lower Bound,” IMF Working Paper, 2015), but none has been
implemented to date.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

3

Figure 3: Modeled Policy Paths for the Fed in Recession Scenarios
4%

Modeled Policy Rate

3%
2%
1%
0%
-1%

No recession
Recession without ELB-2%

Recession with ELB

-3%
0

4

8

12

16

20

24

Quarters Ahead
The graph above shows hypothetical median policy responses from 100,000 simulations of the economic model described in thissection, using the three types of recession assumptions shown. The neutral level shown here is slightly higher than that from
Figure 2 because it is conditioned on the realization of shocks that occur during expansions.
Source: The D. E. Shaw group.

neutral level (that is, the area enclosed between theorange or red line and the blue line) is what restores
economic activity after a negative shock. Our model
indicates that, when confronted with the inability to ease
rates to the extent desired in the presence of the ELB, acentral bank will instead maintain a lower rate setting for alonger period in order to deliver the same aggregate
amount of stimulus to the economy. 4 The results of thesesimulations suggest that the policy rate will remain at thelower bound for more than two years after recession
shocks occur, and possibly longer if additional negative
shocks are realized.

Financial Market Pricing of
the Lower Bound
This policy approach at the ELB suggests that theprobability of short-term interest rates being pinned at thelower bound is sizable—much higher, it turns out, than iscurrently priced into financial markets.

The dynamics that lead to this outcome are straightforward.
When recession shocks are realized, they drive the policy
rate to the lower bound and, because of central banks’inability to ease further, the policy rate remains there forseveral years. As a result, the probability of being at thelower bound at any point in the future is determined by
the cumulative probability that recession shocks occurredin any quarter over the preceding several years.
This “accumulation effect” is notable. In order to calibrate
it, we need to assume an arrival rate for recession shocks.
We think a reasonable starting point is the observed
average frequency at which a set of major economies hasentered into a recession in a given quarter, conditional on
being in an expansion, which has run at a 10% annualized
rate since the mid-1980s.
With that arrival rate, the steady-state distribution ofpolicy rate outcomes ends up having significant mass at
the lower bound, as shown by the leftmost bar in theupper panel of Figure 4. In fact, under this model, there isa one-in-five chance that the policy rate will be pinned
against the lower bound in any given quarter in the future.

4
The argument for “longer” is even stronger if one takes into account the forward-looking behavior of economic agents. In that case, if a central
bank communicates its intentions to keep rates low for a longer period, it can achieve immediate effects on longer-term rates and financial
conditions that will deliver stimulus to the economy. This argument is the primary rationale for the use of forward guidance by central banks.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

4

The distribution of outcomes has a strongly bimodal shape,
as policy will tend to be near its neutral level (or slightly
above it) during non-recession periods and will be stuck at
the ELB during recessions and in their wake. 5
The modeled distribution over the next few years should
also incorporate the currently heightened probability ofrecession perceived by financial market participants. The

lower panel of Figure 4 shows policy rate distributions athorizons of one to three years when we calibrate thearrival rate of recession outcomes to match a recent
survey. 6 The lower tail at a one-year horizon is relatively
small because the accumulation of recession odds does nothave long to build, but it quickly grows at horizons of two
and three years.

Figure 4: Modeled Distributions of the Policy Rate
30%

Policy Rate Distribution: Steady State

25%

Probability

20%
15%
10%
5%
0%

Policy Rate

30%

Policy Rate Distribution: Next 3 Years

25%
1 year ahead

Probability

20%

2 years ahead
3 years ahead

15%
10%
5%
0%

Policy Rate
The graphs above show hypothetical future policy rate distributions based on 100,000 simulations of the model referenced inthis section, incorporating the survey-based arrival rate of recession outcomes described above.
Source: The D. E. Shaw group.

5This shape is not specific to the model used here. A similar result is obtained in a paper by Michael Kiley and John Roberts, using two moresophisticated models: the Fed’s large-scale economic model (FRB/US) and a dynamic stochastic general equilibrium model. Those two models
show that the policy rate under a typical monetary policy rule would spend 32% and 17% of the time at the ELB, respectively, when the neutral
real policy rate is 1%. (See Table 2 from “Monetary Policy in a Low Interest Rate World,” Brookings Papers on Economic Activity, 2017.)

6

Specifically, we use the median response for recession probabilities through 2020 from a survey conducted by the National Association ofBusiness Economists (NABE) in March 2019. The perceived probabilities of a recession beginning in 2019 and 2020 were 20% and 15%,
respectively. Thereafter, we assume that the arrival rate for recessions steps down to the 10% rate that we assumed in the steady state.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

5

Market pricing does not imply anything close to thisbimodal pattern for short-term interest rates. Figure 5
shows the distribution for the policy rate in December
2020 that is implied by swaptions expiring at that time
(adjusting for the basis between the swap rate and thepolicy rate). 7 As shown below, the market appears to bepricing a distribution of outcomes for the short-term ratewith a shape much closer to what one might expect whenrates are not near the ELB, rather than the bimodal shapethat arises in the presence of the ELB constraint, as
indicated by our economic model. According to our model,

the market is substantially understating the probability ofrates ending up at the lower bound.
This difference in the probability of low-rate outcomes isapparent across a range of horizons, as shown in Figure 6.
The probability of low-rate outcomes in our model (theblue line) rises rapidly as a result of the accumulation effectfor recession odds discussed above. This modeled
probability reaches relatively high levels over the next
several years given the elevated recession probabilities
perceived by market participants, before settling to a

Figure 5: Comparison of Model- and Market-Implied Policy Distributions (as of March 29, 2019)
Policy Rate Distributions: December 202020%

Probability

15%

Model-implied distribution
Market-implied distribution

10%

5%

0%

Policy Rate

Low-Rate Probability (Policy Rate < 50 bps)

Sources: The D. E. Shaw group; Barclays Capital Inc.; portions used with permission of Bloomberg.

Figure 6: Term Structure of Low-Rate Outcome Probability (as of March 29, 2019)
35%
30%
25%
20%
15%
10%

Model-implied probability
Market-implied probability

5%
0%
0

4

8

12

16

20

24

28

32

36

40

Quarters Ahead
Sources: The D. E. Shaw group; Barclays Capital Inc.; portions used with permission of Bloomberg.

7

The calculation is based on swaptions tied to a 1-year LIBOR-based swap rate beginning in December 2020 and assumes risk-neutral pricing.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

6

steady-state level of approximately 20%. In contrast, themarket prices a much flatter term structure of low-rate
probabilities (the orange line) over the next five years. 8

Tracing the extent of these broader effects is beyond thescope of this paper, but consider the following possibilities:

Overall, this simple economic model suggests that the
distribution of probable policy rate outcomes in the UnitedStates looks very different from what would be obtained
based on historical norms, given the close proximity ofneutral rates to the ELB. That contrast is likely to be evenmore dramatic for the Euro Area and Japan, as theireconomies face even lower levels of neutral policy rates
and have policy settings that are already pressed against
the lower bound.

economy remaining weak and inflation remaining low
for long periods after significant downturns in asset
prices or economic conditions. That could push theaverage level of yields lower, by even more thanobserved to date, if the market sees larger and more
persistent effects from those shocks.

Broad Implications for
Financial Markets
Monetary policy has become a more complicated process,as central banks contend with a significant constraint on
their ability to adjust policy. This constraint is a focal pointof policy discussions among central banks around theworld, and it deserves just as much attention in our
analysis of financial markets. The effects on asset prices
can be substantial, and a new framework is needed tocalibrate them properly.
In our view, markets have not fully adjusted to this new
reality. In terms of first-order effects, traditional models thathave been used to assess the front end of the yield curveshould be discarded, including those that assume that shortterm interest rates will have a normal-shaped distribution ofoutcomes. Instead, market participants should adapt theirmodels in ways that allow for extended periods at the lower
bound and the considerable probability of low-rate
outcomes at any point in the future.
But the implications of this argument extend well beyond
the front end of the yield curve. The path of short-term
interest rates determined by a central bank, along with thebank’s ability to influence the course of the broader
economy, is deeply intertwined with the determination ofprices across a broad set of assets.

• Markets may need to price in greater risk of the• We previously argued that the term premium, especiallyat shorter maturities, tends to be negative as a result offavorable correlation properties of rates with risky
assets. 9 That correlation arises primarily from the policy
responses of central banks to shocks to aggregate
demand or investor risk preferences. If those responses
now extend farther into the future—because the central
banks substitute “longer” for “lower”—they could pushthat negative term premium out to longer maturities.
• The downside risk to equities and other risky assets

might be greater than historically observed. The ability
to lower policy rates in response to shocks that pressure
risky assets provides an important buffer that limits such
assets’ ultimate movement. To the extent that thecapacity to ease is constrained, this buffer is impaired,allowing for sharper declines in those asset prices.
• Currencies could more frequently move in ways thatseem counterintuitive. Without the ELB constraint, ashock that weakens an economy and lowers inflation
prospects would typically weaken a currency, as thecentral bank would ease policy in response. However, if
the central bank cannot fully respond, real interest rates
might actually rise after a negative shock, which could
lead the currency to strengthen.
Until we return to an environment in which policy rates
can move up and down freely, financial markets will haveto adapt to this important constraint. The macroeconomic
research community has engaged this topic with vigor,
and financial market participants are also paying close
attention. Nevertheless, we feel that financial markets arestill some distance from pricing in the full extent of the
ELB constraint.

8

This contrast remains stark even though the market’s pricing-in of low rates has increased meaningfully over the past several quarters. A similar
chart from the middle of 2018 would show an even larger gap between probabilities implied by model results and market pricing.

9

For a discussion of the negative term premium based on the correlation of rates to equity prices, please see our February 2019 paper, “Positively
Negative: Stock-Bond Correlation and Its Implications for Investors.”

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

7

THIS DOCUMENT IS PROVIDED TO YOU FOR INFORMATIONAL PURPOSES ONLY AND DOES NOT CONSTITUTEINVESTMENT ADVICE OR AN OFFER TO SELL (OR THE SOLICITATION OF AN OFFER TO BUY) ANY SECURITY, INVESTMENTPRODUCT, OR SERVICE.
THE VIEWS EXPRESSED IN THIS DOCUMENT ARE SOLELY THOSE OF THE D. E. SHAW GROUP AS OF THE DATE OF THISDOCUMENT, ARE SUBJECT TO CHANGE WITHOUT NOTICE, AND MAY NOT REFLECT THE CRITERIA EMPLOYED BY ANYPERSON OR ENTITY IN THE D. E. SHAW GROUP TO EVALUATE INVESTMENTS OR INVESTMENT STRATEGIES. SIMILARLY,
THE INFORMATION CONTAINED IN THIS DOCUMENT IS PRESENTED SOLELY WITH RESPECT TO THE DATE OF THISDOCUMENT (UNLESS OTHERWISE INDICATED) AND MAY BE CHANGED OR UPDATED AT ANY TIME WITHOUT NOTICE TOANY OF THE RECIPIENTS OF THIS DOCUMENT. THE INFORMATION CONTAINED IN THIS DOCUMENT HAS BEEN
DEVELOPED BY THE D. E. SHAW GROUP AND/OR OBTAINED FROM SOURCES BELIEVED TO BE RELIABLE; HOWEVER, THE
D. E. SHAW GROUP DOES NOT GUARANTEE THE ACCURACY, ADEQUACY, OR COMPLETENESS OF SUCH INFORMATION.
FURTHER, THIS DOCUMENT CONTAINS PROJECTIONS AND OTHER FORWARD-LOOKING STATEMENTS REGARDING
FUTURE EVENTS, TARGETS, OR EXPECTATIONS. SUCH STATEMENTS ARE BASED IN PART ON CURRENT MARKETCONDITIONS, WHICH WILL FLUCTUATE AND MAY BE SUPERSEDED BY SUBSEQUENT MARKET EVENTS OR OTHER
FACTORS. HISTORICAL MARKET TRENDS ARE NOT RELIABLE INDICATORS OF FUTURE MARKET BEHAVIOR OR THE FUTUREPERFORMANCE OF ANY PARTICULAR INVESTMENT AND SHOULD NOT BE RELIED UPON AS SUCH.
MORE GENERALLY, NO ASSURANCES CAN BE GIVEN THAT ANY AIMS, ASSUMPTIONS, EXPECTATIONS, AND/OROBJECTIVES DESCRIBED IN THIS DOCUMENT WILL BE REALIZED. NONE OF THE ENTITIES IN THE D. E. SHAW GROUP; NORANY OF THEIR RESPECTIVE AFFILIATES; NOR ANY SHAREHOLDERS, PARTNERS, MEMBERS, MANAGERS, DIRECTORS,PRINCIPALS, PERSONNEL, TRUSTEES, OR AGENTS OF ANY OF THE FOREGOING SHALL BE LIABLE FOR ANY ERRORS (AS A
RESULT OF NEGLIGENCE OR OTHERWISE, TO THE FULLEST EXTENT PERMITTED BY LAW IN THE ABSENCE OF FRAUD) IN
THE PRODUCTION OR CONTENTS OF THIS DOCUMENT, OR FOR THE CONSEQUENCES OF RELYING ON SUCH CONTENTS.
NEITHER THIS DOCUMENT NOR ANY PART OF THIS DOCUMENT MAY BE REPRODUCED OR DISTRIBUTED WITHOUT THE
PRIOR WRITTEN AUTHORIZATION OF THE D. E. SHAW GROUP. BY ACCEPTING THIS DOCUMENT, YOU ACKNOWLEDGE
AND AGREE THAT ALL OF THE INFORMATION CONTAINED IN THIS DOCUMENT SHALL BE KEPT STRICTLY CONFIDENTIALBY YOU.
COPYRIGHT © 2019 D. E. SHAW & CO., L.P. ALL RIGHTS RESERVED.

MARKET INSIGHTS | Floor It: Market Pricing of the Lower Bound on Interest Rates

8