MARKET INSIGHTS

Running Low:
The 2020 Test for Bonds as Hedging Assets
January 2021

Introduction

U.S. Treasuries’ Reaction to
the Pandemic Shock

Much ink has been spilled on how investors should
adjust their portfolios to take into account the low interest
rate environment observed in recent years. In particular,
many have questioned whether government bonds willcontinue to serve their longstanding role as safe havenassets—that is, assets that provide an effective hedge
against significant downturns in equity prices.

As the COVID-19 pandemic spread, uncertainty about theoutlook for global economic activity drove a steep decline
in equity markets beginning in mid-February, with the
S&P 500® experiencing its most severe sell-off since the2008 financial crisis.

Events in 2020 represented a key test in that regard, as
markets faced an extremely large negative shock from astarting point of low rates. By studying that episode, we
can assess the degree to which the hedging properties of
those bonds were impaired.

In response to these developments, central banks took
extraordinary actions, including the U.S. Federal
Reserve’s aggressive steps to inject short-term liquidity
into the financial system and support the functioning of
critical markets.

We find that U.S. government bonds passed the test,
reacting normally to the risk-off episode that struck
markets in February and March. However, with yields now
even lower than they were entering the crisis and with rate
volatility substantially reduced at shorter maturities,
investors may need to shift toward longer-term bondholdings to achieve similar hedging utility going forward.
Moreover, the hedging performance of government bonds
was much worse in countries that began the year with lessroom for monetary policy intervention, suggesting somerisk regarding future conditions in the United States.

The Fed also deployed its traditional monetary policy
instrument to the extent possible. With the federal funds
target rate at just over 1.5%, the Fed was constrained in
the amount that it could reduce short-term rates, giventhat it had ruled out the use of negative interest rates fornow. However, following the playbook that we discussed
in an earlier paper on the lower bound on interest rates, 1
the Fed cut the federal funds rate quickly to the effective
lower bound and communicated that it expected to keep
the rate at that level for an extended period.

Figure 1: Changes in Treasury Yields (Actual and Predicted) during Equity Drawdown in Early 2020
(February 14, 2020 to March 16, 2020)
0
Yield Change (bps)

-20
-25

-40

-43

-60

-48

-55

-80
-100
-106

-120
-140

-97

-93

-84

-86

-52

-53

-55

-57

-79

-70

-120
1y

2y

3y

5y

7y

10y

20y

30y

U.S. Treasury Tenor
ActualPredicted

The graph above reflects actual and predicted changes (in basis points) in constant maturity U.S. Treasury yields during the period indicated. (Forreference, the decline in the S&P 500® over this period was roughly 30%.) Actual changes were calculated by the D. E. Shaw group based ondaily yield data obtained from Bloomberg. Predicted changes were calculated by the D. E. Shaw group using typical betas from regressions ofdaily changes in U.S. Treasury yields on daily changes in the S&P 500® based on an unweighted sample from the period January 1, 2004 throughDecember 31, 2019.
Sources: Bloomberg (U.S. Treasury yield and S&P 500® data); the D. E. Shaw group. Applicable data are used with permission of Bloomberg.
1

Floor It: Market Pricing of the Lower Bound on Interest Rates, available here.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

1

The decline in the federal funds rate and the shift in its
expected path in coming years prompted a sizable rally in
the U.S. Treasury market. As can be seen in Figure 1,
Treasury yields fell notably across all maturities over thisperiod (blue bars). In fact, those changes in yield exceeded
what one might have predicted based on the response ofTreasury yields to equity prices over a long sample periodleading up to 2020 (orange bars).

provide complete comfort. The pattern realized in early2020 reflected the Fed’s ability to push yields toremarkably low levels, so that what seemed to be an
uncomfortably low starting point ended up being lessproblematic than feared. Of course, with yields now ateven lower levels, such concerns may reasonably persist.
Indeed, cracks have begun to appear in the hedging
behavior of Treasury securities over the period since
March. By measuring the relationship of Treasury yields
to daily changes in equity prices observed over this more
recent period, we can examine how one might now
expect Treasury yields to respond in the face of an
S&P 500® downdraft of the same size considered in
Figure 1. These predicted responses are represented by
the blue bars in Figure 2.

This pattern, in which yields fall and produce positive
realized returns on Treasury securities, is typical during
periods of weakening economic outlook and rising risk
aversion. It is the foundation for why government debt
securities have been considered an effective hedging
instrument and thus often play a key role in portfolio
diversification. 2 What is notable, however, is that the lowlevel of rates at the start of 2020 did not appear to curtailthe rally in Treasury securities.

The results provide a cautionary message. From April
through December, when the yield curve was at lower
levels than at the start of the year, the response of yields
to equity prices was much more muted. If that more recent
relationship were to continue to hold going forward,
Treasury securities would provide meaningfully lessprotection against a substantial decline in equity prices.

Cracks Starting to Show
The observed behavior of U.S. Treasury securities throughthe equity market sell-off is encouraging, but fails to

Figure 2: Predicted Changes in Treasury Yields during Large Equity Drawdown0-3

Yield Change (bps)

-10

-5
-11

-20
-30

-15

-25

-26
-35

-40

-41

-41

-43

-50

-48

-60

-55

-57

-55

-53

-52

-70
1y

2y

3y

5y

7y

10y

20y

30y

U.S. Treasury Tenor
January 2004 to December 2019 sample

April 2020 to December 2020 sample

The graph above reflects predicted changes (in basis points) in constant maturity U.S. Treasury yields during an equity market drawdown of thesame magnitude as that considered in Figure 1. Predicted changes were calculated by the D. E. Shaw group using typical betas from regressionsof daily changes in U.S. Treasury yields on daily changes in the S&P 500® based on an unweighted sample from each of the periods (i) January 1,
2004 through December 31, 2019 and (ii) April 1, 2020 through December 31, 2020.
Sources: Bloomberg (U.S. Treasury yield and S&P 500® data); the D. E. Shaw group. Applicable data are used with permission of Bloomberg.
2

In our earlier paper Positively Negative: Stock-Bond Correlation and Its Implications for Investors (available here), we argued that the correlation
between Treasury security prices and equity prices depends on the underlying shocks in the economy, and that the greater importance of changes
in the growth outlook and risk aversion (relative to inflation) had pushed the correlation negative. Based on that perspective, we would expect thefavorable correlation properties of Treasury securities to remain in place in the absence of a significant inflationary shock.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

2

A Closer Look across the
Yield Curve

Table 1: Variation in Yield Betas over Time
PeriodDeterioration in the hedging properties of Treasury
securities since March has been more acute at short andintermediate maturities. That conclusion is apparent in thesensitivities shown in Figure 2 (blue bars), and it isintuitive, as those yields are in closest proximity to theconstraint of the zero lower bound.

2-year10-year30-yearJan 2004 to Dec 2019

1.41

1.69

1.52

Apr 2020 to Dec 2020

0.41

1.00

1.10

The table above presents the D. E. Shaw group’s determinationsof average betas of 2-, 10-, and 30-year U.S. Treasury yields to
the S&P 500® during each of the periods shown. Betas werecomputed using the formula correlation*vol(rate)/vol(equity),
where each correlation was determined as outlined in the note to
Figure 3 below, and implied volatilities of U.S. interest rates werebased on the applicable Barclays aggregate index.
Sources: Bloomberg; Barclays Research Services; the D. E. Shawgroup. Applicable data are used with permission of Bloomberg.

To dive in further, Table 1 takes a closer look at the betasof 2-, 10-, and 30-year Treasury yields to the S&P 500®
over the two periods shown in Figure 2. 3 As one can see,the beta of the 2-year yield to equities fell substantially inthe recent period, while the betas for the 10- and 30-yearyields have held up much better. 4

correlation coefficient between the Treasury yield and the
S&P 500® and the ratio of their respective volatilities. We
consider these two components in turn.

Why have the hedging properties of longer-term Treasury
yields held up better? To understand this divergence, it isinstructive to look at the components of the beta.
Empirical beta can be expressed as the product of theFirst, as can be seen in Figure 3, the correlations of the 10and 30-year yields to equity prices have been relatively
high in recent years. Those correlations appear even higher
than they were in the early 2000s, despite short-term rates

Figure 3: Correlation of Treasury Yields to S&P 500®
0.5

0.4

0.3

0.2

0.1

0.0
2004

2006

2008

2010
2-year2012

2014
10-year

2016

2018

2020

30-year

The graph above reflects the D. E. Shaw group’s determinations of rolling correlations over the period shown between (i) daily changes in
U.S. Treasury yields (2-, 10-, and 30-year) and (ii) daily S&P 500® returns. Such correlations were calculated after exponentially weighting eachseries with a half-life of four years and rolling window of eight years.
Sources: Bloomberg (U.S. Treasury yield and S&P 500® data); the D. E. Shaw group. Applicable data are used with permission of Bloomberg.
3

An estimated beta of 1.41, for example, means that a 10% move in the S&P 500® would produce a yield response of 14.1 basis points in thesame direction.

4
The 2004–2019 sample used for comparison includes a substantial period when the policy rate was at the lower bound, which likely reduces thebeta on the 2-year Treasury yield. Indeed, over the period from January 2004 through November 2008, before the lower bound was reached, thebeta for the 2-year yield was significantly higher, at 1.67. Nevertheless, even with some dampening effect from the lower bound, there wasenough variation in the 2-year yield over the full 2004–2019 sample to produce a much higher beta than observed in the more recent subsample.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

3having frequently been constrained by the lower bound in
the more recent period. It may be that constraints onlowering short-term interest rates have forced the Fed tooperate further out the yield curve, through both policy
guidance and asset purchases, helping to keep these
correlations elevated. In fact, the correlations of the 10and 30-year yields with the S&P 500® have been higher
than that of the 2-year yield since 2012.
Volatility, the second component of the beta, has also held
up better for longer-term yields, as shown in Figure 4. The
sharp decline in implied volatility of the 2-year yieldfollowing the initial pandemic shock is hardly detectible inthe volatilities of the 10- and 30-year yields, as the primaryeffect on rate volatility has been to steepen its term
structure. This pattern suggests that markets still see
longer-term yields as having considerable room to vary—aview that, when combined with high correlation to equity
prices, has sustained the hedging benefits of longer-term
Treasury securities.

A Hedging Approach for
U.S. Markets?
One approach to preserving the role of U.S. Treasury
securities as a portfolio hedge seems straightforward,
then—move out the curve. The higher betas of the yields
on longer-term Treasury securities suggest that those
instruments will continue to serve as an effective hedge
against equity prices going forward. 5
Alternatively, to the extent that deterioration in thehedging properties of shorter-term Treasury securities is
associated with lower rate volatility, another approach
would be to apply leverage to those holdings; many
investors, however, are constrained in their ability to
deploy leverage. Moreover, as shown in Figure 3, thecorrelations of longer-term yields to equities are now
actually higher than that of the 2-year yield, making
longer-term securities a more apt hedge against equity
prices than their shorter-term counterparts.

Figure 4: Implied Volatility of Interest Rates
200
175
150

Volatility (bps)

125
100
75
50
25
0
2004

2006

2008

2010
2-year2012

2014
10-year

2016

2018

2020

30-year

The graph above presents the implied volatility of interest rates (in basis points) of each of the 2-, 10-, and 30-year U.S. Treasury yields during
the period shown, in each case with a one-year horizon. Implied volatilities were based on the applicable Barclays aggregate index.
Sources: Barclays Research Services; the D. E. Shaw group.
5
Of course, a complete assessment of the potential advantages of longer-maturity Treasury securities in a diversified portfolio would have to take
into account their estimated risk premium, as well as other factors. This paper has a narrower scope, focused on those assets’ capacity to provide
useful hedging properties and on drawing lessons from what we can observe from 2020.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets4

If we accept that investor appetite for longer-term
Treasury securities as a portfolio hedge should be
increasing, it is reasonable to consider whether that kind ofasset migration on a large scale might create a meaningfulsupply/demand imbalance in the market. For example,
such a shift might further depress term premia at longer
horizons—already negative, according to several widelyused models—making those Treasuries less attractive on a
go-forward basis. 6

Treasury debt outstanding has increased rapidly in recent
years as a result of large budget deficits. 7 In notional terms(upper-left panel), much of this supply has been in shortand intermediate-term securities, which at first might seem
problematic for the approach discussed here. But by
expressing these amounts in terms of duration (upper-rightpanel), we show that it is the issuance of securities at thelonger end that creates the majority of duration available
to the market.

On that question, we would simply note that there is
ample supply of duration in the U.S. Treasury market. As
can be seen in Figure 5, the notional amount of U.S.

Even if we account for the reduction in implied volatility toderive a measure of the total risk available to the market(bottom panel), we see that Treasury issuance has been

Figure 5: Supply of Hedging Capacity
8

9

7

8
6
5
4
3
2

6

Market Value ($trn)

7

5
4
3
2
1

1

0

0
2007

2009

2011

2013

2015

2017

Interest Rate Sensitivity ($bn/bp)

10

2007

2019

2009

2011

2013

2015

2017

2019

40
35
30

20
15
10
5

Risk ($bn/day)25

20-30y10-20y
7-10y
5-7y
3-5y
1-3y

0
2007

2009

2011

2013

2015

2017

2019

The graphs above present outstanding nominal, coupon-bearing U.S. Treasury securities held by market participants other than the U.S. Federal
Reserve (grouped by time to maturity) in terms of market value, duration, and risk, respectively, in each case over the period indicated. The
risk measure for each maturity group was computed based on the implied volatilities of swaptions with one-year expiries on the underlying
swap with a corresponding time to maturity.
Sources: Bloomberg (outstanding U.S. Treasury market data); Barclays Research Services (swaption implied volatility data); the D. E. Shawgroup. Applicable data are used with permission of Bloomberg.

6
Measuring term premia is challenging, and the estimates that are available depend on the assumed structure of the model used to constructthem. Two of the most widely used models are published by the Federal Reserve Board (available here) and by the Federal Reserve Bank of New
York (available here).
7
This figure is based on the Barclays aggregate index and excludes holdings of the Federal Reserve. Thus, it is a measure of the supply of Treasury
securities available in aggregate to private investors.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

5sufficient to offset that effect. The front end is providing
less duration risk because of the fall in volatility, but
longer-term securities have made up for that decline. The
market remains well supplied with Treasury interest raterisk at longer maturities, suggesting that extending out the
curve is indeed a viable option for those in search ofhedging assets.

In Germany, the 10-year bund yield was -40 basis points(bps) in mid-February, compared to the central bankdeposit rate of -50 bps; in Japan, the 10-year JGB yield
was -5 bps, compared to the central bank deposit rate of-10 bps. Moreover, the Bank of Japan had implemented ayield curve control regime in which it explicitly targets alevel for the 10-year yield, thereby limiting movement inthat rate (absent a decision to change that target).

Perspectives from Germany
and Japan

Given those circumstances, it is not surprising that in the
February–March market crisis period, the 10-year yields inGermany and Japan moved to a much more limited degree
than U.S. yields, as shown in Figure 6. 8

Although this approach for the U.S. yield curve seems
appealing, observations from other countries raise more
substantial concerns. Based on the 2020 test, Germany
and Japan—two countries that entered the pandemic withyield curves at notably lower levels—have already reacheda point at which their government bonds are meaningfully
impaired as hedging assets.

U.S. yields simply had more room to decline coming into
the crisis. Even over the ensuing period from April throughDecember, the 10-year U.S. Treasury yield remained at an
average level of about 75 bps, still leaving a substantial
cushion above its lower bound compared to the moreconstrained yields in Germany and Japan.
Nevertheless, it is hard to rule out the possibility that theUnited States could evolve in the direction of those othercountries, eroding the hedging properties of Treasury
securities, even at longer maturities. Although extending
the duration of Treasury holdings appears to provide
investors a hedging approach in U.S. markets undercurrent circumstances, that approach might not remain
viable if the U.S. yield curve declines further.

In the period leading up to the pandemic, each country’s
central bank had pushed the effective lower bound for its
policy rate into negative territory. Nevertheless, at theonset of the pandemic, the yield curve in each country was
already pressed closer to that lower bound than was thecase in the United States.

20

Figure 6: Changes in Government Bond Yields during Equity Drawdown in Early 2020
(February 14, 2020 to March 16, 2020)
3

4

1

4

Yield Change (bps)

0

-40

-8

-18

-23

-24

-2

-4

-8

-20

-3

-6

-8

-24

-28

-60
-80
-100
-120
-140

-93

-97

-106

-84

-86

-79

-70

-120
1y

2y

3y

5y
Germany

7y
Bond Tenor
Japan

10y

20y

30y

United States

Source: Bloomberg (German bund, Japanese Government Bond, and U.S. Treasury yield data); the D. E. Shaw group. Applicable data are usedwith permission of Bloomberg.
8
The German bund yield demonstrated volatility over the first half of March that makes the changes reported in Figure 6 sensitive to the exact
window chosen. However, it is clear that German yields did not demonstrate the substantial decline observed in U.S. yields through the middle ofthe year.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

6

The Path Forward
In hindsight, for those who entered the year concerned
about the hedging properties of U.S. Treasury securities,
the 2020 test offered both comfort and caution. Treasury
yields fell sharply during the market crisis, passing this test
and validating their utility as haven assets. However, theresulting decline in yields may make it all the morechallenging for Treasury securities to provide similar utility
in the future.
Our view is that the hedging capacity of Treasury
securities is still effective at this time, at least with the rightadjustments. In particular, to maintain the hedging
properties of their Treasury holdings, investors may needto push out the duration of those instruments, perhaps to
10-year maturities or longer. We believe that the Treasury
market has the supply of duration risk needed to facilitatesuch a shift, and that this approach has advantages overturning to other types of assets to serve that function. 9
Of course, the situation could change in other ways thatmight alter this conclusion. If Treasury yields grind lower
over time, then the deterioration of Treasury securities’
hedging capacity already observed at shorter maturities
would likely extend further out the curve, resembling what
we have seen in Germany and Japan. 10 Alternatively, ameaningful shift to a less stable inflation environment
could impair those hedging properties by shifting thecorrelation between Treasury yields and equity prices.
For now, however, we believe that this approach—moving out the curve to ensure that Treasury holdings
have sufficient capacity to rally during a downturn—is aviable one.

9
In our view, there are no obvious substitutes for high-quality government securities as canonical haven assets. Various market participants haveproposed a range of alternatives—from corporate credit, to emerging market bonds, to active strategies of various stripes—but we believe thatsuch proposed alternatives have meaningful drawbacks in this regard.
10

In the other direction, yields could move higher over time, which would help to maintain the hedging function of Treasury securities andpossibly restore it at shorter maturities. Moreover, although the Fed has largely ruled out negative interest rates for now, the market has notdispelled that possibility, and any further loosening of that policy constraint perceived by investors would benefit the hedging properties ofTreasury securities. By our estimates, the market’s perception that negative rates are possible accounted for at least 25 basis points of the roughly
100 basis point decline in the 3y1y swap rate observed through the middle of 2020.

MARKET INSIGHTS | Running Low: The 2020 Test for Bonds as Hedging Assets

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