Collateral Requirements and Asset Prices J. Brumm, M. Grill, F. - - PowerPoint PPT Presentation

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Collateral Requirements and Asset Prices J. Brumm, M. Grill, F. - - PowerPoint PPT Presentation

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Collateral Requirements and Asset Prices J. Brumm, M. Grill, F. Kubler and K. Schmedders June 10th, 2011 Motivation Two old ideas: Borrowing on collateral might enhance volatility of prices (e.g. Geanakoplos (1997) or Aiyagari and

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SLIDE 1

Collateral Requirements and Asset Prices

  • J. Brumm, M. Grill, F. Kubler and K. Schmedders

June 10th, 2011

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SLIDE 2

Motivation

  • Two old ideas:
  • Borrowing on collateral might enhance volatility of prices

(e.g. Geanakoplos (1997) or Aiyagari and Gertler (1999)).

  • Prices of assets that can be used as collateral are above

their ʼfundamental valueʼ

  • Three issues:
  • Quantitative importance of effect is unclear
  • Collateral requirements play a crucial role. What

determines them?

  • Some assets can easily be used as collateral, others not.

What are the general equilibrium effects?

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SLIDE 3

This Paper

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SLIDE 4

This Paper

  • Take Lucas asset pricing model with heterogeneous

agents and incomplete markets, add collateral constraints and model default and collateral requirements as in Geanakoplos and Zame (2002)

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SLIDE 5

This Paper

  • Take Lucas asset pricing model with heterogeneous

agents and incomplete markets, add collateral constraints and model default and collateral requirements as in Geanakoplos and Zame (2002)

  • Pick (reasonable) parameters so that effects of

collateral on asset prices are potentially large (Barroʼs (2011) consumption disaster calibration)

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SLIDE 6

This Paper

  • Take Lucas asset pricing model with heterogeneous

agents and incomplete markets, add collateral constraints and model default and collateral requirements as in Geanakoplos and Zame (2002)

  • Pick (reasonable) parameters so that effects of

collateral on asset prices are potentially large (Barroʼs (2011) consumption disaster calibration)

  • Explore general equilibrium effects of different ways to

ʻsetʼ margin requirements:

  • Two trees with identical cash-flows but different

margin requirements. One treeʼs margin requirements are exogenously regulated

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SLIDE 7

The Economy

  • Discrete time t=0,..., one perishable commodity,

exogenous shocks follow Markov-process with finite support.

  • 2 agents, h=1,2, and 2 trees, a=1,2.
  • Aggregate endowments are
  • Preferences are Epstein-Zin with

(σ) = (σ) + (σ). e ˉ ∑

h∈H

eh ∑

a∈A

da (c) = Uh

st

+ β ⎧ ⎩ ⎨ ⎪ ⎪ ⎪ ⎪ [ ( )] ch st

ρh

π( | ) ⎡ ⎣∑

st+1

st+1 st ( (c)) Uh

st+1 αh⎤

⎦

ρh αh ⎫

⎭ ⎬ ⎪ ⎪ ⎪ ⎪

1 ρh

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SLIDE 8

Financial Markets

  • In addition to the trees there are J bonds that

distinguish themselves by their collateral requirements.

  • Assume that trees have to be held as collateral in
  • rder to establish a short position in the bonds
  • What determines the collateral requirement?

Tree holding, , and bond holdings, , must satisfy θh

a

ϕh

j

( ) + ( )[ ( ) ≥ 0, a = 1, … , A. θh

a st

∑

j∈J

kj

a st ϕh j st ]−

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SLIDE 9
  • Make the strong

assumption that all loans are non-recourse and that there are no penalties for defaulting

  • Borrower hands over

collateral whenever promise exceeds value of collateral

( ) = min 1, ( )( ( ) + ( )) . fj st ⎧ ⎩ ⎨ ∑

a∈A

kj

a st−1

qa st da st ⎫ ⎭ ⎬

Collateral and Default

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SLIDE 10
  • Campbell et al. (2010) find

an average ‘foreclosure discount’ of 27 percent

  • We assume that part of the

payment of the borrower is lost and that the loss is proportional to the difference between the face value of the debt and the value of collateral.

Default is Costly

The loss is given by: λ(1 − ( )( ( ) + ( ))) kj

a st−1

qa st da st

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SLIDE 11

Margin-Requirements

  • We consider two determinants for k:
  • As in Geanakoplos and Zame (2002) all

contracts are available for trade. With moderate default costs only one is traded in equilibrium. More...

  • The margin requirement is exogenously fixed

( ) = hj

a st

( ) − ( ) kj

aqa st

pj st ( ) kj

aqa st

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SLIDE 12

Calibration I

  • Aggregate endowments grow at a stochastic rate
  • We assume there are 6 possible shocks

= g( ) ( ) e ˉ st+1 ( ) e ˉ st st+1

1 2 3 4 5 6 Prob g

0.005 0.005 0.024 0.065 0.836 0.065 0.566 0.717 0.867 0.966 1.025 1.089

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SLIDE 13

Calibration I

  • Aggregate endowments grow at a stochastic rate
  • We assume there are 6 possible shocks

= g( ) ( ) e ˉ st+1 ( ) e ˉ st st+1

1 2 3 4 5 6 Prob g

0.005 0.005 0.024 0.065 0.836 0.065 0.566 0.717 0.867 0.966 1.025 1.089

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SLIDE 14

Disasters

  • Consumption disaster calibration is from Barro

and Jin (2011)

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SLIDE 15

Calibration II

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SLIDE 16

Calibration II

  • Agent 1 is small, receives 9.2 percent of

aggregate endowments as income, and has low risk aversion of 0.5

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SLIDE 17

Calibration II

  • Agent 1 is small, receives 9.2 percent of

aggregate endowments as income, and has low risk aversion of 0.5

  • Agent 2 is big, receives 82.8 percent of aggregate

endowments as income, and has high risk aversion of 6

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SLIDE 18

Calibration II

  • Agent 1 is small, receives 9.2 percent of

aggregate endowments as income, and has low risk aversion of 0.5

  • Agent 2 is big, receives 82.8 percent of aggregate

endowments as income, and has high risk aversion of 6

  • Both agents have IES of 1.5 and discount with

0.95

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SLIDE 19

Calibration II

  • Agent 1 is small, receives 9.2 percent of

aggregate endowments as income, and has low risk aversion of 0.5

  • Agent 2 is big, receives 82.8 percent of aggregate

endowments as income, and has high risk aversion of 6

  • Both agents have IES of 1.5 and discount with

0.95

  • The two trees each pay 4 percent of aggregate

endowments as dividends

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SLIDE 20

Results A

  • Suppose first tree 1 can be held as collateral with

endogenous collateral requirement while tree 2 cannot be used to secure short positions in bonds

20 40 60 80 100 120 140 160 180 200 0.8 1 1.2 1.4 1.6 1.8 2

Normalized Prices

Tree 1 Tree 2

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SLIDE 21

Results A

0.2 0.4 0.6 0.8 1 1.4 1.6 1.8 2 2.2 2.4 2.6

Price of Tree 1

0.2 0.4 0.6 0.8 1 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Price of Tree 2

0.2 0.4 0.6 0.8 1 0.98 0.985 0.99 0.995 1 1.005 1.01 1.015

Price of NoDefault Bond

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 1 Holding of Agent 1

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 2 Holding of Agent 1

0.2 0.4 0.6 0.8 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

NoDefault Bond Holding of Agent 1

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SLIDE 22

Results A

0.2 0.4 0.6 0.8 1 1.4 1.6 1.8 2 2.2 2.4 2.6

Price of Tree 1

0.2 0.4 0.6 0.8 1 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Price of Tree 2

0.2 0.4 0.6 0.8 1 0.98 0.985 0.99 0.995 1 1.005 1.01 1.015

Price of NoDefault Bond

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 1 Holding of Agent 1

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 2 Holding of Agent 1

0.2 0.4 0.6 0.8 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

NoDefault Bond Holding of Agent 1

Normal times

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SLIDE 23

Results A

0.2 0.4 0.6 0.8 1 1.4 1.6 1.8 2 2.2 2.4 2.6

Price of Tree 1

0.2 0.4 0.6 0.8 1 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Price of Tree 2

0.2 0.4 0.6 0.8 1 0.98 0.985 0.99 0.995 1 1.005 1.01 1.015

Price of NoDefault Bond

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 1 Holding of Agent 1

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 2 Holding of Agent 1

0.2 0.4 0.6 0.8 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

NoDefault Bond Holding of Agent 1

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SLIDE 24

Results A

0.2 0.4 0.6 0.8 1 1.4 1.6 1.8 2 2.2 2.4 2.6

Price of Tree 1

0.2 0.4 0.6 0.8 1 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

Price of Tree 2

0.2 0.4 0.6 0.8 1 0.98 0.985 0.99 0.995 1 1.005 1.01 1.015

Price of NoDefault Bond

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 1 Holding of Agent 1

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Tree 2 Holding of Agent 1

0.2 0.4 0.6 0.8 1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

NoDefault Bond Holding of Agent 1

Bad shock

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SLIDE 25

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

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SLIDE 26

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 27

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 28

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 29

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 30

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 31

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 32

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 33

Results A: Moments

  • In order to quantify the results consider first and

second moments of tree returns. Two benchmarks: An economy with no borrowing (B1) and an economy with natural debt constraints (B2)

B1 B2 Tree 1 Tree 2 Std Returns Avg Exc Returns

5.33 5.38 6.56 7.98 NA 0.55 3.69 6.71

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SLIDE 34

Results A

20 40 60 80 100 120 140 160 180 200 1.5 2

Normalized Price of Tree 1

20 40 60 80 100 120 140 160 180 200 1 2

Tree 1 Holding of Agent 1

20 40 60 80 100 120 140 160 180 200 0.7 0.8 0.9

Normalized Price of Tree 2

20 40 60 80 100 120 140 160 180 200 1 2

Tree 2 Holding of Agent 1

20 40 60 80 100 120 140 160 180 200 −1 −0.5 0.5

No−Default Bond Holding of Agent 1

20 40 60 80 100 120 140 160 180 200 −1 −0.5 0.5

1−Default Bond Holding of Agent 1

20 40 60 80 100 120 140 160 180 200 −1 −0.5 0.5

2−,3− and 4−Default Bond Holding of Agent 1

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SLIDE 35

Endogenous Margins

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SLIDE 36

Endogenous Margins

  • Even if default costs are zero only risk-free bond

is traded at normal times

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SLIDE 37

Endogenous Margins

  • Even if default costs are zero only risk-free bond

is traded at normal times

  • Default bonds are only traded in (or after) disaster

shocks

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SLIDE 38

Endogenous Margins

  • Even if default costs are zero only risk-free bond

is traded at normal times

  • Default bonds are only traded in (or after) disaster

shocks

  • Default costs of 10 percent suffice to uniquely

determine margin-requirements: Only the risk-free bond is traded

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SLIDE 39

Endogenous Margins

  • Even if default costs are zero only risk-free bond

is traded at normal times

  • Default bonds are only traded in (or after) disaster

shocks

  • Default costs of 10 percent suffice to uniquely

determine margin-requirements: Only the risk-free bond is traded

  • Obviously not a good theory of why people default

since we have no idiosyncratic risk

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SLIDE 40

Results B

  • Now suppose tree 2 can also be held as collateral

but that margin requirement is exogenously set. Price-dynamics of the tree will obviously depend

  • n the margin requirement...

20 40 60 80 100 120 140 160 180 200 0.7 0.75 0.8 0.85 0.9 0.95 1

Normalized Price of Tree 2

20 40 60 80 100 120 140 160 180 200 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65

Normalized Price of Tree 2

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SLIDE 41

First and Second Moments

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.04 0.045 0.05 0.055 0.06 0.065

Haircut on Tree 2 Excess Return Excess Return Tree 1 Excess Return Tree 2 Excess Return Aggregate

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0.065 0.07 0.075 0.08 0.085 0.09

Haircut on Tree 2 STD Returns STD Tree 1 STD Tree 2 STD Aggregate

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SLIDE 42

Sensitivity Analysis

  • Results are relative robust with respect to IES and

size of trees

  • Disaster shocks are obviously a dubious

assumption and might seem to drive results...

  • Halve the size of disaster shocks
  • But increase second agentʼs risk aversion to 10

s=1 s=2 s=3

  • ld g

new g

0.566 0.717 0.867 0.783 0.8585 0.9335

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SLIDE 43

Sensitivity analysis 2

  • As before, take as benchmark an economy with

no borrowing (B1)

  • Consider the case where tree 2 cannot be used as

collateral:

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SLIDE 44

Sensitivity analysis 2

  • As before, take as benchmark an economy with

no borrowing (B1)

  • Consider the case where tree 2 cannot be used as

collateral:

B1 aggr. Tree 1 Tree 2 Std Returns Avg Exc Returns

3.42 5.05 4.41 6.68 NA 1.02 0.77 1.65

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SLIDE 45

Conclusion

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SLIDE 46

Conclusion

  • Collateral requirements have large effects of first

and second moments of asset prices

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SLIDE 47

Conclusion

  • Collateral requirements have large effects of first

and second moments of asset prices

  • These effects occur because of changes in the

wealth distribution due to uninsurable shocks

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SLIDE 48

Conclusion

  • Collateral requirements have large effects of first

and second moments of asset prices

  • These effects occur because of changes in the

wealth distribution due to uninsurable shocks

  • We assume that only tree can be used as

collateral, what happens if bonds can be used to secure short-positions in the tree?

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SLIDE 49

Endogenous Margins

  • Instead of having infinitely many bonds, it

suffices to focus on S basic ones. Bond 1 Bond 2 Bond 3

( )( ( , 1) + ( , 1)) k1

a st

qa st da st ( )( ( , 2) + ( , 2)) k1

a st

qa st da st ( )( ( , 1) + ( , 1)) k2

a st

qa st da st

1 1 1 1 1 1

st

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