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ESSAYS ON ISSUES
	

	 THE FEDERAL RESERVE BANK	
OF CHICAGO

AUGUST 2014
	 NUMBER 325

Chicag­ Fed Letter
o
Is there a trade-off between low bond risk premiums and
financial stability?
by Ben Chabot, financial economist

It has been suggested that financial instability may be more likely following periods of
low bond market risk premiums. The timing of past episodes of instability casts doubt
upon the hypothesis that low levels of risk premiums sow the seeds of future instability.
There is considerable evidence that nontraditional policies adopted in the wake
of the 2008 financial crisis by the Federal
Open Market Committee (FOMC) have
lowered long-term bond yields, term
premiums, and credit spreads.1 With
inflation still below target and unemployment unacceptably high, the FOMC has
stated that continued accommodation
is still appropriate.2

Sixty years of data suggest
that large increases in bond
risk premiums are independent
of the recent level or change
in risk premiums or federal
funds rate.

There is a concern, however, that a
continuation of highly accommodative
monetary policy may increase the risk
of financial instability. Forward guidance
and large-scale asset purchases (LSAPs)
reduce long-term interest rates by lowering the path of expected future shortterm rates and by removing duration risk
from private portfolios, thereby reducing the term premium required by private investors. The concern is that
yield-seeking investors will respond to
depressed bond yields by increasing
leverage or crowding into riskier investments. This shift into riskier bonds
could further depress credit risk premiums (the increased return investors
demand to hold higher-risk bonds)
and encourage even more reach for
yield. If enough investors crowd into
bonds with high credit or duration risk,
a sudden change in risk appetite could
result in a sharp spike in bond risk premiums if investors sell bonds en masse.
A sharp increase in bond risk premiums

may make it more difficult for the
FOMC to achieve its dual-mandate objectives of maximum employment and
price stability. If monetary policy does
in fact affect the probability of a sharp
increase in bond risk premiums, then
there may be a role for financial stability considerations in the setting of optimal monetary policy. But degrading
monetary accommodation when the
economy is still recovering is costly. An
FOMC that gives weight to financial stability, said former Fed Governor Jeremy
C. Stein, will determine that “all else being equal, monetary policy should be less
accommodative—by which I mean that it
should be willing to tolerate a larger forecast shortfall of the path of the unemployment rate from its full-employment
level—when estimates of risk premiums in
the bond market are abnormally low.”3
Before we conclude that this might be
an appropriate monetary policy response,
we should be certain that low levels
risk premiums do in fact increase the
likelihood of future spikes in risk premiums. In this Chicago Fed Letter, I evaluate the usefulness of policy rates and
bond risk premiums as predictors of
large increases in risk premiums.
Measures of bond risk premiums

I consider three measures of bond risk
premiums: Moody’s Baa–Aaa spread, the
Kim–Wright ten-year term premium, and

1. Large increases in risk premium series
A. Baa–Aaa spread

B. Kim–Wright ten-year term premium

percentage points

percentage points

4

6
5

3

4
3

2

2
1

1

0
−1

0
1952’57 ’62 ’67 ’72 ’77 ’82 ’87 ’92 ’972002 ’07 ’12

−2
1952’57 ’62 ’67 ’72 ’77 ’82 ’87 ’92 ’972002 ’07 ’12

C. Expected bond premium (EBP)
percentage points
3
2
1
0
−1
−2
1973

’78

’83

’88

’93

’98 2003 ’08

’13

Notes: The three measures are the Moody’s Baa–Aaa spread, the Kim–Wright ten-year term premium, and the Gilchrist
and Zakrajšek corporate expected bond premium (EBP). Periods of large increase are denoted by shaded regions.
Sources: Baa data from http://research.stlouisfed.org/fred2/series/BAA; Aaa data from http://research.stlouisfed.org/
fred2/series/AAA; Kim–Wright ten-year term premium data based on calculations by staff economists at the Board of
Governors of the Federal Reserve System; and EBP data from http://people.bu.edu/sgilchri/Data/data.htm.

the Gilchrist and Zakrajšek corporate
expected bond premium (EBP). The
first two are traditional measures of
the credit and term premiums investors demand for holding credit default
risk and duration risk, respectively.
The third measure is an estimate of
the expected premium on corporate
bonds subject to default risk, introduced in recent work by Gilchrist and
Zakrajšek (2012).4 The Baa–Aaa spread
and Kim–Wright ten-year term premium are available for the 1954–2013
period of our study, and the EBP is
available for 1973–2012.
Are large increases in bond risk premiums more likely to occur following
a period of low risk premiums? To
answer this question, I need to identify
“large” increases in a time series of
risk premiums. I use a dating algorithm
to select the largest trough-to-peak
increases in the quarterly time series

of EBP, the Baa–Aaa spread, and the
Kim–Wright ten-year term premium.5
I consider thresholds that generate 12
“large” increases in the 60-year Baa–Aaa
and Kim–Wright term premium samples
and eight “large” increases in the 40-year
EBP sample. These thresholds correspond to an unconditional hazard of
one large increase every five years.
Figure 1 plots the risk premium series
and periods of large increase.6
The timing of large increases in risk
premiums suggests that policymakers
should be suspicious of the hypothesis
that low levels of risk premiums sow the
seeds of future instability. While nine
of the 12 largest trough-to-peak increases
in the Baa–Aaa spread were preceded
by troughs below the median level of
this spread, five of these nine were within
10 basis points of the median. The link
between the level of risk premiums and
subsequent large increase is even more

tenuous in the other series. Only three
of the eight largest up cycles in EBP
were preceded by troughs below the
median level of EBP, and one of these
three was only 1 basis point below the
median. Finally, only five of the 12 largest
increases in the Kim–Wright term premium were preceded by a trough below
the median level of that series.
Figure 2 plots the proportion of large
increases in each risk premium series
that began with a trough level below a
certain percentile. If low levels of risk
premiums do in fact increase the likelihood of future sharp increases in risk
premiums, we would expect the plots in
figure 2 to lie well above the 45-degree
line. In fact, the plots are close to or
below the 45-degree line.
Figures 1 and 2 suggest that a policymaker who hopes to enhance financial
stability by removing monetary accommodation when risk premiums fall below a pre-set level would be plagued by
false positives, as the risk premium series
often decline to low levels without subsequent spikes. This policy would lead
to monetary policy that was more contractionary than necessary.
Determining the probability of a rare
but costly outcome

Policymakers often have to make difficult decisions based upon a noisy signal
about the probability of a rare but, if
realized, costly outcome. The decision
to evacuate a city in the path of a hurricane, ground a class of airliners after a
malfunction, or scramble fighters in
response to blips on a radar screen all
require policymakers to weigh the cost
of a false positive (ordering costly precautionary action to avoid an event that
will not actually occur) against the cost
of a false negative (taking no precautionary action when the dangerous event
does in fact transpire). In the monetary
policy context, a policymaker who is
concerned that low risk premiums signals
a future episode of financial instability
could set a certain level of risk premiums
as a discrimination threshold and adopt
a policy of removing monetary stimulus
whenever one of the risk premium series
declines below this threshold. If the risk
premium series does in fact transition to

2. Distribution of troughs preceding large increases

3. ROC curves

Proportion of large increases preceded by trough level less than risk
premium percentile

True positive rate

1.0

1.0
0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0.0

0.0
0

10

20

30

40

50

60

70

80

90

100

Risk premium percentile

0.0 0.1

0.2

0.3

0.4 0.5 0.6 0.7
False positive rate

0.8

0.9

1.0

EPB

Baa−Aaa spread

45-degree line

Baa−Aaa spread

45-degree line

EPB

Kim−Wright ten-year term premium

Kim−Wright ten-year term premium

Note: The three measures are the Moody’s Baa–Aaa spread, the Kim–Wright
ten-year term premium, and the Gilchrist and Zakrajšek corporate expected bond
premium (EBP).

Note: The three measures are the Moody’s Baa–Aaa spread, the Kim–Wright
ten-year term premium, and the Gilchrist and Zakrajšek corporate expected bond
premium (EBP).
Source: Author’s calculations based on the data series in figure 1.

Source: Author’s calculations based on the data series in figure 1.

a large increase when the level is
below the selected threshold, the
discrimination threshold accurately
predicts the transition and we observe
a true positive. On the other hand,
the risk premium series may continue
with no spike in levels. In this case,
the discrimination threshold has
generated a false positive.
Can risk premium levels accurately
predict future financial instability?
One way to measure the accuracy of
a model of rare events is the receiveroperating-characteristic (ROC) curve,
a tool commonly used in signal theory, engineering, and medicine to
help policymakers visualize the information content of a model based
on noisy signals.7 The ROC curve
plots the trade-off between the true
positive and the false positive rate
as the policymaker varies the discrimination threshold below which
he will deviate from otherwise optimal monetary policy. The area under
the ROC curve (AUC) is a summary
statistic of the model’s goodness of
fit. A model based on a perfectly informative signal can successfully predict every large increase with no false
positives and will have an AUC of 1,
while a model based on uninformative

random guesses will have an AUC of 0.5.
Figure 3 plots the AUC curves for the
three risk premium series.
Figure 3 illustrates the difficulty a policymaker would face trying to use the current level of risk premiums to predict
large future increases in risk premiums.
A policymaker who wished to choose a
threshold in the Baa–Aaa spread that
successfully predicts 90% of the large
increases in this spread would have to
set a threshold that generates a false
positive rate of 91%! If the policymaker
lowered the discrimination threshold
to generate a more palatable false positive rate of 20%, the true positive rate
would fall to a mere 16.66% and the
threshold would fail to predict five out
of every six spikes in the Baa–Aaa spread.
The policymaker would fare even
worse using the EBP or Kim–Wright
term premium.
The ROC curves suggest that simple rules
such as “reduce accommodation whenever risk premiums decline below a
certain threshold” will be ineffective.
Perhaps more complex models based
on multiple inputs could generate a more
accurate predictor of financial instability?
To investigate this further, I use multiple predictors to model the hazard of a
large increase in bond risk premiums.8

I model the hazard of a large increase in
the risk-premium series as a time-varying
function of the risk spreads and monetary policy. The first six model specifications allow the hazard of a large increase
in our series of interest to vary with the
level of EBP or the Baa–Aaa spread, and

Charles L. Evans, President  Daniel G. Sullivan,
;
Executive Vice President and Director of Research;
Spencer Krane, Senior Vice President and Economic
Advisor ; David Marshall, Senior Vice President, financial
markets group  Daniel Aaronson, Vice President,
;
microeconomic policy research; Jonas D. M. Fisher,
Vice President, macroeconomic policy research; Richard
Heckinger,Vice President, markets team; Anna L.
Paulson, Vice President, finance team; William A. Testa,
Vice President, regional programs, and Economics Editor ;
Helen O’D. Koshy and Han Y. Choi, Editors  ;
Rita Molloy and Julia Baker, Production Editors 
;
Sheila A. Mangler, Editorial Assistant.
Chicago Fed Letter is published by the Economic
Research Department of the Federal Reserve Bank
of Chicago. The views expressed are the authors’
and do not necessarily reflect the views of the
Federal Reserve Bank of Chicago or the Federal
Reserve System.
© 2014 Federal Reserve Bank of Chicago
Chicago Fed Letter articles may be reproduced in
whole or in part, provided the articles are not
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Prior written permission must be obtained for
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ISSN 0895-0164

a proxy for monetary policy—the real fed
funds rate measured as the nominal rate
minus the change in the Consumer Price
Index (CPI) over the previous year. It
is often suggested that the detrimental
effects of low risk premiums take a while
to build up in the financial system and
the current level of risk premiums may
not matter as much as the average level
over time. The next six specifications
replace current levels of the predictors
with their average level over the previous
year. Finally, I consider the possibility
that the level of risk premiums does not
matter but changes in risk premiums
encourage destabilizing investor behavior.
The final six specifications replace the
level measures with change over the
previous year.
The hazard model results suggest that
the current levels and past changes in
1	

2

risk premiums are poor predictors of
the risk of future large increases in risk
premiums. The level and change in the
real fed funds rate and risk premiums
are insignificant in most specifications.
In the few cases where the variables do
significantly shift the hazard, the sign is
always the opposite of what one would
expect if low risk premiums or accommodative monetary policy did indeed
sow the seeds of future instability. The
hazard model suggests large increases
in risk premiums are less likely when
risk premiums have been depressed or
have declined over the past year.
Conclusion

Financial instability is costly. It has been
suggested that low bond risk premiums
may predict future financial instability
and that policymakers should take this

Details of these and other programs are
available at www.federalreserve.gov/faqs/
money-rates-policy.htm. For evidence of
the effectiveness of these policies, see
www.federalreserve.gov/newsevents/
speech/bernanke20120831a.htm; www.
federalreserve.gov/newsevents/speech/
stein20121011a.htm#fn3; and www.
newyorkfed.org/research/
epr/11v17n1/1105gagn.pdf.

3	

See www.aeaweb.org/articles.
php?doi=10.1257/aer.102.4.1692.

http://www.federalreserve.gov/newsevents/
press/monetary/20140618a.htm.

6	

others/people/research_resources/chabot_
ben/chabot_cfl_325_appendix.pdf,
describes the large increases in each series.

See www.federalreserve.gov/newsevents/
speech/stein20140321a.htm.

4	

into account and respond to low risk
premiums by adopting less accommodative monetary policy than would
otherwise be justified by economic conditions. But before we conclude that the
economic cost of a potentially sharp
increase in bond risk premiums justifies
less accommodative monetary policy, we
should be certain that financial instability
is in fact more likely to arise when bond
risk premiums are low. This study casts
doubt upon the hypothesis that low levels
of bond risk premiums increase the likelihood of destabilizing sharp increases.
To the contrary, the past 60 years of
data suggest that large increases in bond
risk premiums are independent of the
recent level or change in risk premiums
or the real federal funds rate.

5	

The data sources and algorithm are
available in the online appendix at www.
chicagofed.org/digital_assets/others/
people/research_resources/chabot_ben/
chabot_cfl_325_appendix.pdf.
Table A1, in the online appendix available
at www.chicagofed.org/digital_assets/

7	

See J. A. Swets, 1988, “Measuring the accuracy
of diagnostic systems,” Science, Vol. 240,
No. 4857, June 3, pp. 1285–1293.

8	

A technical description of the hazard
model and table of coefficient estimates
are available in the online appendix at
www.chicagofed.org/digital_assets/others/
people/research_resources/chabot_ben/
chabot_cfl_325_appendix.pdf.


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