Common shocks in stocks and bonds - Wild Apricot · 2020. 10. 5. · Common shocks in stocks and...

Anna Cieslak and Hao Pang (Duke Fuqua) 1

Q Group Fall Seminar on Zoom

Common shocks in stocks and bonds

Anna Cieslak

Duke University, Fuqua School of Business, NBER, and CEPR

Hao Pang

Duke University, Fuqua School of Business

October 19, 2020

Motivation


� Interest in how the Fed affects financial markets (and the economy)

Motivation



� Estimated effects of the Fed on financial markets are large

� But some open questions remain

– Mechanism: Short-term rate, risk premia, expectations about the economy?– Consistency across asset classes: Stocks vs. bonds?

Motivation






→ Need a methodology to jointly identify the different economic shocks induced by the Fed

Motivation






→ Need a methodology to jointly identify the different economic shocks induced by the Fed

→ Yield curve to help

This paper


� Approach to identify economic shocks from asset prices alone by combining

– Finance view: discount-rate and cash-flow news (Campbell, Shiller, 1988)– Macro view: structural disturbances (Sims, 1980)

This paper




� Decompose daily innovations in stock returns and yield changes into orthogonal sourcesof news

ω =

ωg growth news (cash-flow risk)

ωm monetary news (pure discount-rate risk via short rate)

ωp+ hedging premium news (compensation for cash-flow risk)

ωp− common premium news (compensation for discount-rate risk)

This paper




� Decompose daily innovations in stock returns and yield changes into orthogonal sourcesof news

ω =

ωg growth news (cash-flow risk)

ωm monetary news (pure discount-rate risk via short rate)

ωp+ hedging premium news (compensation for cash-flow risk)

ωp− common premium news (compensation for discount-rate risk)

� Importance of two sources of risk-premium shocks

Applications


� Assess overall impact of different economic shocks on stocks and yields (on all days)6= event studies; e.g., monetary news comes out on a continuous basis, not just in event windows ...

Applications



� Dissect news content of Fed and macro announcements... and even on “event” days news is not one-dimensional

Applications



� Dissect news content of Fed and macro announcements... and even on “event” days news is not one-dimensional

� Interpret shocks to asset prices day-by-day during the Covid-19 crisis

Structural VAR interpretation of asset pricing models


� Models commonly express transformed asset prices Yt (bond yields, log pd ratio) as≈affinefunctions of state variables Ft

Yt = a+ AFt rank(A) = dim(Ft)

Ft = µF + ΦFt−1 + ΣFωt Var(ωt) = I and ΣF diagonal

Ft: beliefs about growth, monetary policy, uncertainty, time-varying risk aversion, ...




Yt = a+ AFt

Ft = µF + ΦFt−1 + ΣFωt ←structural form


� We usually do not observe Ft directly, but we observe Yt

Yt = µY +ΨYt−1 + ut ←reduced form




Yt = a+ A Ft





... and we have theory-based predictions about structural loadings A




Yt = a+ A Ft






→ Back out structural shocks ωt from ut and restrictions on A

ωt︸︷︷︸

structural

= A−1

ut︸︷︷︸

reduced

with A = AΣF . (1)




Yt = a+ A Ft






→ Back out structural shocks ωt from ut and restrictions on A

ωt︸︷︷︸

structural

= A−1

ut︸︷︷︸

reduced

with A = AΣF . (1)

Caveats: orthogonality, micro-foundations, stochastic volatility

Literature


Term-structure models. Cochrane, Piazzesi (2005); Bansal, Shaliastovich (2013); Green-wood, Vayanos (2013); Cieslak, Povala (2015, 2016); Duffee (2018)

Stock-bond comovement. Connolly, Stivers, Sun (2005); Andersen, Bollerslev, Diebold,Vega (2007); Bekaert, Engstrom, Xing (2008); Baele, Bekaert, Inghelbrech (2010); Lettau,Wachter (2011); David, Veronesi (2013); Campbell, Sunderam, Viceira (2017); Campbell,Pflueger, Viceira (2019); Koijen, Lustig, Van Nieuwerburgh (2017); Song (2017); Pfluegerand Rinaldi (2020)

Identification of monetary surprises. Rigobon, Sack (2004); Gurkaynak, Sack, Swanson(2005); Bernanke, Kuttner (2005); Campbell, Evans, Fisher, Justiniano (2012); Hanson, Stein(2015); Nakamura, Steinsson (2018); Swanson (2017); Cieslak, Schrimpf (2019); Jarocinski,Karadi (2019); Miranda-Agrippino, Ricco (2019)

Structural VARs. Faust (1998); Faust, Swanson, Wright (2004); Uhlig (2005); Rubio-Ramirez, Waggoner, Zha (2010); Arias, Caldara, Rubio-Ramirez (2019); Ludvigson, Ma, Ng(2019)

Identification idea


� Use the entire yield curve and stocks jointly to identify the loadings matrix A

Identification idea



� Impose two sets of restrictions [SDF modely]

Identification idea




i. Monotonicity restrictions across yield maturities

Identification idea





ii. Sign restrictions between stocks and yields

Identification idea





ii. Sign restrictions between stocks and yields

� Note: We focus on the comovement between stock returns and yield changes(+) stock-yield comovement ←→ (−) stock-bond return comovement

Identification: Monotonicity restrictions across yield maturities


[SDF model: Yieldsy]

� Impact of short-rate expectations shocks decays with maturityBlanchard-Quah-type long-run restriction in the cross-section of yields (here: not a zero restriction)





� Impact of risk-premium shocks increases with maturityBansal and Shaliastovich (2013) (two factors: real and nominal uncertainty); Greenwood and Vayanos (2013)

(bond supply); Hanson and Stein (2015) (demand of reaching-for-yield investors)

� Empirical magnitudes: Impact of 1σ risk-premium shock ∼2x larger on 10y than 2y yieldCieslak and Povala (2015, 2016) y





� Impact of risk-premium shocks increases with maturityBansal and Shaliastovich (2013) (two factors: real and nominal uncertainty); Greenwood and Vayanos (2013)

(bond supply); Hanson and Stein (2015) (demand of reaching-for-yield investors)

� Empirical magnitudes: Impact of 1σ risk-premium shock ∼2x larger on 10y than 2y yieldCieslak and Povala (2015, 2016) y

Identification: Sign restriction between stocks and yields


ShocksShort-rate expectations Risk premium

growth monetary hedging commonωg ↑ ωm ↑ ωp+ ↑ ωp− ↑

Yield changes (+) (+) (−) (+)Stock returns (+) (−) (−) (−)Stock-yield comovement (+) (−) (+) (−)

[SDF model: Comovementy]







� Growth news ωg ↑ raises yields and stock pricesLRR-type model: IES > 1; Taylor rule: Fed tightens less than 1-for-1 with growth news y








� Monetary news ωm ↑ lowers stock prices, raises yieldsNK channel: real rate gap ↑; discount-rate effect via risk-free rate









� Suppose ωg and ωm shocks are priced and earn time-varying risk premia

– Hedging premium ωp+: bonds hedge growth/cash-flow risk in stocksFlight-to-safety; real/cash-flow uncertainty









� Suppose ωg and ωm shocks are priced and earn time-varying risk premia

– Hedging premium ωp+: bonds hedge growth/cash-flow risk in stocksFlight-to-safety; real/cash-flow uncertainty

– Common premium ωp−: both stocks and bonds exposed to discount-rate riskMonetary/discount-rate uncertainty

Implementation


� Estimate VAR(1) in yield changes ∆y(n)t and log stock returns ∆st to obtain reduced-form

shocks ut

zt = ∆Yt = (∆y(2)t ,∆y

(5)t ,∆y

(10)t ,∆st)

′ (2)

– Daily sample 1983–2017 (extended through Covid-19 crisis)

� Recover structural shocks ω =(ωg, ωm, ωp+, ωp−

)′by sign and monotonicity restrictions

on the structural matrix A = AΣF

– Set identification as opposed to point identification

Implementation


� Start from Cholesky decomposition of the reduced-form covariance matrix

Σu = PP′ and ut = Pω

∗t

– P lower triangular, ω∗t uncorrelated shocks, V ar(w∗

t ) = I

� Simulate rotation matrices Q such that QQ′ = Q′Q = I

ut = PQ′

︸︷︷︸

A(Q)

Qw∗t

︸︷︷︸

ωt(Q)

– Qw∗t is another set of uncorrelated shocks

� Store 1000 Q’s for which A(Q) = PQ′ satisfies restrictions

� Select the median-target (MT) solution with θi = vec(A(Qi))

θMT = min

i

[θi − median(θi)

std(θi)

]′[θi − median(θi)

std(θi)

]

– i.e., pick solution for which on-impact responses to ω are closest to the median of on-impact

responses across solutions

Paths of cumulative shocks


Validity of identified shocks


� Growth shocks ωg comove strongly with real GDP growth forecast updates (Blue Chipsurvey) y




−4

−2

0

2

12

−m

on

th c

um

ula

tiv

e, z

−sc

ore

s

1985 1990 1995 2000 2005 2010 2015

Growth shocks

Survey real GDP forecast updates (1−qtr ahead)




� Monetary shocks ωm have significantly higher volatility on scheduled FOMC announce-ment days y

– Note: We do not use any information about the timing of FOMC meetings– Significant relation to monetary surprises in event studies (GSS (2005); Swanson (2017)) y






� Risk-premium shocks ωp+ and ωp− relate with innovations to standard measures of bondand equity risk premium with expected signs

Equity risk premium Bond risk premium

Lettau Kelly Martin Cochane CieslakLudvigson Pruitt Piazzesi Povala

hedging premium, ωp+ ↑ (+) (+) (+) (−) (−)common premium, ωp− ↑ (+) (+) (+) (+) (+)






� Risk-premium shocks ωp+ and ωp− relate with innovations to standard measures of bondand equity risk premium with expected signs

Equity risk premium Bond risk premium

Lettau Kelly Martin Cochane CieslakLudvigson Pruitt Piazzesi Povala

hedging premium, ωp+ ↑ (+) (+) (+) (−) (−)common premium, ωp− ↑ (+) (+) (+) (+) (+)

� Results for expected inflation y and breakeven inflation rates y

Impulse responses


0 200 400 600-10

-5

0

5

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15

0 200 400 600-10

-5

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15

0 200 400 600-10

-5

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0 200 400 600-10

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0 200 400 600-10

-5

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0 200 400 600-10

-5

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0 200 400 600-10

-5

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0 200 400 600-10

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0 200 400 600-200

-100

0

100

0 200 400 600-200

-100

0

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0 200 400 600-200

-100

0

100

0 200 400 600-200

-100

0

100

IRFs obtained with Jorda’s (2005) local projections; response to 1σ shock

Variance decompositions: How important are different shocks?


2y yld 5y yld 10y yld stocks0

0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6

� growth news, ωg� hedging premium news, ωp+

� monetary news, ωm� common premium news, ωp−

� Over 1983–2017 sample, monetary and growth news accounts for 80% of daily variation in 2yyield changes, 40% in stock returns

� Risk-premium news generates 80% of variation in 10y yield changes, 60% in stock returns

Variance decompositions: Pre/post-1998



0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6

� growth news, ωg� monetary news, ωm

� Post-1998, monetary and common premium news ↓, growth and hedging premium news ↑

→ Switch in stock-yield comovement from (−) to (+)→ Consistent with Campbell, Pflueger, Viceira (2020)

Variance decompositions: Pre/post-1998



0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6


0.1

0.2

0.3

0.4

0.5

0.6

� hedging premium news, ωp+� common premium news, ωp−

� Post-1998, monetary and common premium news ↓, growth and hedging premium news ↑

→ Switch in stock-yield comovement from (−) to (+)→ Consistent with Campbell, Pflueger, Viceira (2020)

Dissecting news content on Fed announcement days


� Fed events are a multidimensional information bundle→ Interpretation has been challenging




� Stocks but not bonds earn high returns on days of scheduled FOMC meetings and atregular intervals over the FOMC cycle

Lucca and Moench (2015); Cieslak, Morse, Vissing-Jorgensen (2019)






� Channels of Fed transmission:

– Conventional monetary channel : Fed exogenously changes (expected) short rate

– Information channel : Fed reveals information about growth that investors did not haveCampbell, Evans, Fisher, Justiniano (2012); Nakamura and Steinsson (2018)

– Risk-premium channel : Fed influences amount or price of risk perceived by investorsHanson and Stein (2015)






� Channels of Fed transmission:

– Conventional monetary channel : → ωm

– Information channel : → ωg

Campbell, Evans, Fisher, Justiniano (2012); Nakamura and Steinsson (2018)

– Risk-premium channel : → ωp+, ωp−

Hanson and Stein (2015)

FOMC announcement-day returns


returnt or return component(ωit) = γ0 + γ11t,FOMC + εt (1994–2017)

−10

0

10

20

30

40

−1.5

−1

−.5

0

.5

−1.5

−1

−.5

0

.5

1

∆y(10) (bps)∆y(2) (bps)∆s (bps)

overalloveralloverall ωgωgωg ωmωm

ωm ωp+ωp+ωp+ ωp−ωp−

ωp− rprprp

ωg : growth news; ωm: monetary news; ωp+: hedging premium news; ωp−: common premium news




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

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1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp


� FOMC-day effect on stock returns is 28bps




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

.5

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.5

1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp


� FOMC-day effect on stock returns is 28bps; insignificant for yield changes at −0.5bps




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

.5

0

.5

1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp



� High stock returns driven by risk-premium news and monetary news




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

.5

0

.5

1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp



� High stock returns driven by risk-premium news and monetary news

� Nearly 70% of high stock returns on FOMC days due to news that reduces risk premium

yAll solutions yCMVJ cycle




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

.5

0

.5

1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp


� Monetary and common premium ωp− news reduces yields...

� Hedging premium news ωp+ raises yields as bond insurance premium becomes less valuable




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

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1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp


� Monetary and common premium ωp− news reduces yields...

� Hedging premium news ωp+ raises yields as bond insurance premium becomes less valuable

� Combination of these effects leads to insignificant yield changes overall




10

0

10

20

30

40

1.5

1

.5

0

.5

1.5

1

.5

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1

∆y(10) (bps)∆y(2) (bps)∆s (bps)



ωp− rprprp


� Weaker FOMC-day effect before mid-1990s: only common premium ωp− significant yPre-1994

� Consistent with Fed facing growth-inflation tradeoff, thus not being able to reduce hedgingpremium ωp+ (growth uncertainty)

Interpretation of monetary policy surprises


� High-frequency changes in interest rates around FOMC announcements are a standardway of measuring monetary policy surprises

� Target, path, LSAP shocks ...

Interpretation of monetary policy surprises


Gurkaynak-Sack-Swanson shocks (narrow window)

(1) (2) (3) (4) (5)

all meetings scheduled meetings1991:7-2015:10 1994–2015:10 2009–2015:10

Target Path Target Path LSAP

growth ωg 0.052 0.170* 0.100 0.256*** 0.108(0.50) (1.86) (1.01) (2.84) (0.88)

monetary ωm 0.563*** 0.375*** 0.396*** 0.517*** 0.027(4.67) (3.83) (3.83) (6.53) (0.17)

hedging pr ωp+ 0.011 0.010 0.008 -0.064 -0.338**(0.16) (0.16) (0.11) (-0.97) (-2.22)

common pr ωp− -0.044 0.361*** -0.011 0.352*** 0.715***(-0.63) (5.32) (-0.12) (4.53) (3.13)

R2 0.34 0.30 0.18 0.46 0.68N 213 213 175 175 55

Coefficients are standardized

� Target shock significantly associated only with monetary news

� Negative path shock can arise from negative growth news (stocks↓, yields↓) • news about monetaryeasing (stocks↑, yields↓) • news that reduces the risk premium (stocks↑, yields↓)

� LSAP shock is all about risk premium; little evidence of the QE signalling effect

x

Stock returns on non-farm payroll announcements


� Similar to FOMC announcement days, on macro announcements investors updateexpectations not just about the state of the economy

� News of rising unemployment (bad news) is good for stocks during economic expansions

Boyd, Hu, Jagannathan (2005); Law, Song, Yaron (2018)



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BG: Bad NFP news, good times (69) BB: Bad NFP news, bad times (72)

GG: Good NFP news, good times (59) GB: Good NFP news, bad times (58)bp

s

ωgωg ωmωm ωp+ωp+ ωp−ωp− overalloverall

Good/bad times = top/bottom terciles of output gap. MMS/Bloomberg: Good/bad NFP surprises

BG: Bad NFP news in good times is good news for stocks



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BG: Bad NFP news in good times is good news for stocks in expectation of monetary easing



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BB: Bad NFP news in bad times is unambiguous: direct effect on growth expectations



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GG: Good NFP news in good times offset by expectation of monetary tightening



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GG: Good NFP news in good times offset by expectation of monetary tightening



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GB: Good NFP news in bad times induces significant risk-premium reactionωp+ ↓, ωp− ↑: less real uncertainty, more monetary uncertainty

Covid-19 crisis


Cumulative S&P 500 returns and shock contributions since Jan 2, 2020

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cumulative overall returngrowth news ωg

hedging premium news ωp+ (flight-to-safety)monetary news ωm

common premium news ωp−

The plot reports simple cumulative returns; overall return Rt =∏

j(1 + Rt(ωj)) − 1

Covid-19 crisis



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j(1 + Rt(ωj)) − 1

Covid-19 crisis



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j(1 + Rt(ωj)) − 1

Covid-19 crisis



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j(1 + Rt(ωj)) − 1

Covid-19 crisis



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j(1 + Rt(ωj)) − 1

Conclusions


� Recover economically interesting shocks from VAR + intuitive restrictions on stocks andthe yield curve

– Motivated by theory but not married to a specific parametric model

– Trace out shocks on any day and over long sample ( 6=event studies)

– Analyze financial market reaction to macro events and Fed announcements

� Highlight the effect of the Fed on risk premia

� Importance of two risk-premium shocks

– Hedging and common premium

– Ambiguous impact on stocks and bonds

Date post:	29-Mar-2021
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Common shocks in stocks and bonds - Wild Apricot · 2020. 10. 5. · Common shocks in stocks and...

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