Macroeconomic Framework for Quantifying Systemic Risk by ...€¦ · d"t "t = mdRt ferent from this literature in that we build a macroeconomic model to understand how economic variablesrelatetosystemic

Macroeconomic Framework for Quantifying Systemic

Risk by Zhiguo He and Arvind Krishnamurthy

Discussion by Tobias Adrian

Federal Reserve Bank of New York

The New Normal for Monetary Policy, FRBSF, March 27, 2015

The views expressed here are those of the author and do not necessarily reflect those

of the Federal Reserve Bank of New York or the Federal Reserve System

Tobias Adrian FRBNY Macro of Systemic Risk March 2015 1

Overview

Overview

I Contribution of the paper

1. He-Krishnamurthy have been pioneering macro-finance models with

intermediaries, building a coherent framework over the years

2. The current paper is applying this framework to study systemic risk

I Review

1. The model

2. The quantitative results

I My comments

1. Funds and banks

2. Stress testing


Review of the Paper

Households and Production

I Households

E

[∫ +∞

0e−(ρt)

((cyt )1−φ(cht )φ

)1−γ1 − γ

dt

]

I Production

Yt = AKt

dKt/Kt = it − δdt + σdZt

Φ (it ,Kt) = itKt +κ

2(it − δ)2 Kt

I Price of capital qt , price of housing Pt


Review of the Paper

Intermediaries

I Mean-variance preferences, equity capacity constraint Et ≤ εt

E [dRt − rtdt] +m

2V [dRt ] s.t.

dεtεt

= mdRt

ferent from this literature in that we build a macroeconomic model to understand how economic

variables relate to systemic risk. Acharya, Pedersen, Philippon, and Richardson (2010) is closest to

our paper in this regard, although the model used in that paper is a static model that is not suited

to a quantification exercise. It is ultimately important that our model-based approach meets the

data-oriented approaches.

The paper is laid out as follows. Section 2 describes the model. Section 3 goes through the

steps of how we solve the model. Section 4 presents our choice of parameters for the calibration.

Sections 5, 6, and 7 present the results from our model. Figures and an appendix with further

details on the model solution are at the end of the paper.

2 Model

Time is continuous and indexed by t. The economy has two types of capital: productive capital

Kt and housing capital H. We assume that housing is in fixed supply and normalize H ≡ 1.

We denote by Pt the price of a unit of housing, and qt the price of a unit of capital; both will be

endogenously determined in equilibrium. The numeraire is the consumption good. There are

three types of agents: equity households, debt households, and bankers.

Intermediary Sector

Capital qtKt

Housing Pt H

Equity Et

Debt Wt − Et

Constraint: Et ≤ Et

HHHHHHY

No constraint��

Financial Wealth

Wt = qtKt + pt H

(1 − λ)Wt

Household Sector

λWt�

'

&

$

%Loans to Capital

Producers it

6

Et ≡ Aggregate bank capital capacity

Figure 1: Model Schematic

We begin by describing the production technology and the household sector. These elements

of the model are a slight variant on a standard stochastic growth model. We then describe bankers

and intermediaries, which are the non-standard elements of the model. We assume that all of the

housing and capital stock are owned by intermediaries that are run by bankers. Intermediaries

also fund new investments. Households are assumed to not be able to directly own the housing

and capital stock. Instead, the intermediaries raise equity and debt from households and use these

6


Review of the Paper

Intermediaries

I Mean-variance preferences, equity capacity constraint Et ≤ εt

E [dRt − rtdt] +m

2V [dRt ] s.t.

dεtεt

= mdRt

ferent from this literature in that we build a macroeconomic model to understand how economic

variables relate to systemic risk. Acharya, Pedersen, Philippon, and Richardson (2010) is closest to

our paper in this regard, although the model used in that paper is a static model that is not suited

to a quantification exercise. It is ultimately important that our model-based approach meets the

data-oriented approaches.

The paper is laid out as follows. Section 2 describes the model. Section 3 goes through the

steps of how we solve the model. Section 4 presents our choice of parameters for the calibration.

Sections 5, 6, and 7 present the results from our model. Figures and an appendix with further

details on the model solution are at the end of the paper.

2 Model

Time is continuous and indexed by t. The economy has two types of capital: productive capital

Kt and housing capital H. We assume that housing is in fixed supply and normalize H ≡ 1.

We denote by Pt the price of a unit of housing, and qt the price of a unit of capital; both will be

endogenously determined in equilibrium. The numeraire is the consumption good. There are

three types of agents: equity households, debt households, and bankers.

Intermediary Sector

Capital qtKt

Housing Pt H

Equity Et

Debt Wt − Et

Constraint: Et ≤ Et

HHHHHHY

No constraint��

Financial Wealth

Wt = qtKt + pt H

(1 − λ)Wt

Household Sector

λWt�

'

&

$

%Loans to Capital

Producers it

6

Et ≡ Aggregate bank capital capacity

Figure 1: Model Schematic

We begin by describing the production technology and the household sector. These elements

of the model are a slight variant on a standard stochastic growth model. We then describe bankers

and intermediaries, which are the non-standard elements of the model. We assume that all of the

housing and capital stock are owned by intermediaries that are run by bankers. Intermediaries

also fund new investments. Households are assumed to not be able to directly own the housing

and capital stock. Instead, the intermediaries raise equity and debt from households and use these

6


Review of the Paper

Amplification: Model and Data

(a) Model

Matching Data: Data(L) and Model(R)

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Note: The model does poorly on many standard macro calibration targets (e.g.,no labor)

Model does well in capturing non-linearity in a select set of economic measures

... We will have to argue that our metric is a good one

He and Krishnamurthy (Chicago, Stanford) Systemic Risk Central Bank of Chile, December 2014 3 / 42

(b) Data

Matching Data: Data(L) and Model(R)

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Note: The model does poorly on many standard macro calibration targets (e.g.,no labor)

Model does well in capturing non-linearity in a select set of economic measures

... We will have to argue that our metric is a good one


I Strong amplification effects when the capital constraint binds

I Captures joint dynamics of intermediary equity, land prices, spreads


Review of the Paper

Intermediary Wealth Share e = E/K as Key State Variable

Results(1): State variable is et = Et/Kt

0 5 10 15 200

2

4

6

8Sharpe ratio

0 5 10 15 20−0.1

−0.05

0

0.05

0.1interest rate

0 5 10 15 200.085

0.09

0.095

0.1

0.105

investment I/K

scaled intermediary reputation e0 5 10 15 20

0.95

1

1.05q(e), capital price

scaled intermediary reputation e

Capital constraint binds for e < 0.435


I Leverage inversely related e

I Systemic risk when capital constraint binds and leverage shoots up


Review of the Paper

Key Assumption: Capital Constraint is Mutual Fund

Flow-Performance Chevalier-Ellison 1997risk taking by mutal funds 1179

Fig. 2.—Flow-performance relationship f̂ for old funds (age . 10) with 90 percentconfidence bands.

We report estimates of the other parameters of the model ob-tained from the subsamples of young and old funds in columns 1and 2, respectively, of table 2. To interpret the age category–specificscale and shift parameters, keep in mind that the omitted categoriesare 2-year-old and 11-year-old and older funds in the two subsam-ples. Hence, for example, to obtain a graph of the expected growthrate of a 4-year-old fund (having otherwise the standard characteris-tics), one would multiply the curve in figure 1 by a factor of .66 (51 2 .34) and then shift it down by .02. A 4-year-old fund that matchesthe market return would thus be expected to grow by about 8 per-cent, with the expected growth increasing to about 36 percent if itsreturn is 10 points above the market. In column 1 we see that theestimates of the multiplicative terms γ3, γ4, and γ5 for funds of ages3–5 are negative and monotonically decreasing. This indicates thatthe older funds’ flows are increasingly less sensitive to their mostrecent performance. While these parameters are not very preciselyestimated, the sensitivity of the 4-year-old and 5-year-old funds toyear t returns is significantly smaller than that for 2-year-old fundsat the 5 percent level in a one-tailed test. In the subsample of olderfunds, our point estimates are that flows into the 6–7 and 8–10-year-old funds are more sensitive to year t returns than flows into fundsthat are 11 years of age or more, although the differences fail to besignificant. The additive effects are all small and insignificant.

Turning to the control variables in the lower part of the table, wesee that year t 2 1 and t 2 2 excess returns also have substantial andstatistically significant effects on flows in year t 1 1. For example,the 1.86 and 0.73 coefficients on rit 21 2 rm t 21 and rit 22 2 rm t 22 in the

This content downloaded from 4.79.228.100 on Mon, 16 Mar 2015 09:55:36 AMAll use subject to JSTOR Terms and Conditions

I Skin in the game constraint is key amplification mechanism

I Generates strongly countercyclical leverage


Comments

Comments

1. Funds and banks

2. Stress testing


Comment 1: Funds and Banks

Countercyclial Net Equity Issuance of Banks

-100

0

100

200

300

Bill

ions

US

D

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

I Huge issuance in the depth of the crisis

I Same is true for dealers



Countercyclical e = E/K for Banks

.012

.014

.016

.018

.02

.012

.014

.016

.018

.02

Ban

k E

quity

/Non

finan

cial

Equ

ity

1980q1 1990q1 2000q1 2010q1

Detrended Commerical Bank Equity Ratio

I Ratio of commercial bank equity to nonfinanical equity declines

during expansions and rises sharply during downturns



Procyclical Book Leverage of Banks

8

10

12

14

Det

rend

ed B

ook

Leve

rage

1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

I Countercyclical equity results in procyclical leverage




16.4

16.6

16.8

17

Det

rend

ed L

og A

sset

s

8

10

12

14

Det

rend

ed B

ook

Leve

rage

1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

Leverage

Log Assets

I Adrian-Shin 2008, 2010, 2014




16.6

16.7

16.8

16.9

17

Det

rend

ed L

og A

sset

s

10

11

12

13

14D

etre

nded

Boo

k Le

vera

ge

2005q1 2006q1 2007q1 2008q1 2009q1 2010q1

Detrended Leverage

Detrended Log Assets



Procyclical Book Leverage of Broker-Dealers

15.8

16

16.2

16.4

16.6

Det

rend

ed L

og A

sset

s

12

14

16

18

20D

etre

nded

Boo

k Le

vera

ge

1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

Detrended Book Leverage

Detrended Log Assets



Procyclical Equity of He-Krishnamurthy

I Countercyclical leverage is due to procyclical equity flows

I Data strongly supports this for mutual funds

-30

-20

-10

0

10

20

Dow

Jon

es In

dust

rial A

vera

ge R

etur

n (Y

/Y)

-60

-40

-20

0

20

40

US

Equ

ity F

unds

: Net

Cas

h In

flow

(B

il.$)

2000m1 2005m1 2010m1 2015m1

US Equity Funds

DJIA



Reconciling Cyclicality of Leverage

Adrian-Boyarchenko 2013

HouseholdsInvest in risk-free debt,non-bank financial sec-tor and bank financialsector

BanksCreate new capital; fi-nanced by debt issuanceto the households

FundsHold existing capi-tal; financed by profitsharing contracts withhouseholds

ProducersA-K production tech-nology; financed byfinancial sector

πbtwhtπftwht

CbtbhtπftwhtdR

ft

Atkt Atkht

Φ (it) kt

T. Adrian, N. Boyarchenko Intermediary Balance Sheets 6Tobias Adrian FRBNY Macro of Systemic Risk March 2015 16


Leverage Growth and Financial Sector Asset Growth

(c) Model

-.4

-.3

-.2

-.1

0.1

.2.3

.4.5

.6.7

Cro

ss-c

orre

latio

n

-10 -5 0 5 10Lag (quarters)

Bank sector

Nonbank financial sector

(d) Data

-.2

-.1

0.1

.2.3

.4.5

Cro

ss-c

orre

latio

n

-10 -5 0 5 10Lag (quarters)

Bank sector

Nonbank financial sector



Funds and Banks

I He-Krishnamurthy matches the fund sector well

I Modeling the bank sector requires different constraints

I This explains procyclicality of financial sector assets0

510

15

1968

Q1

1973

Q1

1978

Q1

1983

Q1

1988

Q1

1993

Q1

1998

Q1

2003

Q1

2008

Q1

2013

Q1


Comment 2: Stress Testing

Stress Testing in He-Krishnamurthy

I Stress test scenario is mapped into underlying shock to capital

I Stress test assumptions similar to CCAR

I 6 quarters of adverse shocks to equity

I Cumulatively -30% return on equity

I Probability of crisis calculated via simulation

I Model captures feedback effects



Probability of Crisis in He-Krishnamurthy

Stress testing

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of capital constraint being binding: hitting ecrisis

=0.4354

starting value einit

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.40.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of being distressed: hitting edistress

=1.27

starting value einit

in next 2 years

in next 5 years

in next 10 years

in next 2 years

in next 5 years

in next 10 years

Map “stress test" into a shock to e.


I What if capital regulation would be based to stress tests?



Stress Test based Capital Regulation

I Consider a forward-looking capital constraint

max{i ,β,k}

Et

[∫ τD

te−ρ(s−t)wt (i , β, k) ds

]s.t.

θ−1t ≥ ϑ

√Et

[∫ T

t

(σ2k,s

)ds

]I “Choose optimal capital plan”

I While VaR constraint is proportional to contemporaneous risk, CCAR

makes capital proportional to forward looking risk

I Equilibrium dynamics change

I Adrian-Boyarchenko 2012 conjecture that this mitigates procyclicality


Conclusion

Conclusion

I He and Krishnamurthy have pioneered models of financial

intermediation within a macro context

I Contribution of this paper is to consider systemic risk

I My comments

1. The theory models fund sector, not banking

I Banks exhibit procyclical leverage (Adrian-Shin)

I Risk based capital constraints can explain procyclicality

(Adrian-Boyarchenko)

2. How do stress tests influence equilibrium outcomes?

I Impact of stress tests on equilibrium outcomes is not modeled

I Conjecture that CCAR mitigates procyclicality


Appendix

Countercyclical Dealer Equity

0

5

10

15

0

5

10

15

1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

Broker-Dealer Equity Ratio


Appendix

Book Leverage is Procyclical

Market Leverage is Countercyclical

-5

0

5

10

15

Qua

rterly

Ass

et G

row

th (%

)

-20 -10 0 10 20Quarterly Book Leverage Growth (%)

β = .448t-stat = 105.703

R2 = .301

JPM, BoA, C

-5

0

5

10

15

20

Qua

rterly

Ent

erpr

ise

Valu

e G

row

th (%

)

-100 -50 0 50 100Quarterly Market Leverage Growth (%)

β = -.064t-stat = -134.906

R2 = .073

JPM, BoA, C


Appendix

Market Leverage moves with Book-to-Market

-40

-20

0

20

40

60

Qua

rterly

Mar

ket L

ever

age

Gro

wth

(%)

-40

-20

0

20

40

60

Qua

rterly

Boo

k/M

arke

t Gro

wth

(%)

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1Date

Quarterly Book/Market Growth (%)Quarterly Market Leverage Growth (%)

Commerical Banks

I The book-to-market ratio is outside of the control of banks

I Banks manage accounting based ROE and book leverage


Documents

Macroeconomic Framework for Quantifying Systemic Risk by ...€¦ · d"t "t = mdRt ferent from this literature in that we build a macroeconomic model to understand how economic variablesrelatetosystemic