estimating optimal capital requirements for banks
TRANSCRIPT
Peterson Institute for International Economics | 1750 Massachusetts Ave., NW | Washington, DC 200366/17/2016 1
Estimating Optimal Capital
Requirements for Banks
William R. Cline
Senior FellowPeterson Institute for International Economics
Modigliani-Miller Equity Cost as
Function of Debt/Equity Leverage
๐๐ = ๐ + ๐ โ ๐๐ท๐
๐๐
๐๐ = unit cost of equity
๐ = sectoral capitalization rate
๐ = interest rate
๐ท๐ = debt
๐๐ = shareholder equity
M&M Test for 51 Large US Banks 2001-13
Earnings yield: Adj. R2 = 0.088
eyt = 6.63 + 0.0513 Rtโ1 -1.89 D0810; (19.5) (1.62) (โ7.2)
R: debt/equity D: dummy
Net income/ Book equity Adj. R2 =0.268
NIt/Etโ1 = 7.206 + 0.636 Rtโ1 -5.823 D0810; (10.0) (9.4) (โ10.5)
Losses from a Banking CrisisOutput
Timet0t-1 t1 t2
Qt-1
Q*
Qt0
A
B
Deriving the benefits curve
Baseline damage: ๐ท0 = ๐๐๐0๐0
Crisis probability: ๐๐๐๐ = ๐ด๐๐พ, ๐พ < 0
Benefit: ๐ต = โ(๐๐๐๐ โ ๐๐๐0)๐0
= โ๐ด๐0 ๐๐พ โ ๐0๐พ
Marginal benefit: ๐๐ต
๐๐= โ๐ด๐0๐พ๐
๐พโ1
BCBS Schedule of Crisis Probability
For Alternative Capital Ratios
Benefits of higher capital ratios
0.000
0.005
0.010
0.015
0.020
0.0
39
3
0.0
5
0.0
6
0.0
7
0.0
8
0.0
9
0.1
0.1
1
0.1
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3
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1
0.2
2
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3
0.2
4
0.2
5
TCE/TA
Fraction of GDP
Impact on cost of capital
to the economy
Banks: ๐ง = ๐ง0 + (๐ โ ๐0)(๐๐ต โ ๐๐)(1 โ ๐)
Non-banks: ๐๐๐ต,0 + ๐ ร (๐ง โ ๐ง0)
Economy:
๐ค = ๐๐ต ๐ง + ๐๐ + ๐๐๐ต๐๐๐ต + ๐๐๐๐
Proportional change ๐ฃ =๐ค๐
๐ค0โ 1
Cost of higher capital cost to
economy
๐ถ =๐ฃ ร ๐ผ ร ๐
(1 โ ๐ผ)
= output elasticity with respect to capital
= elasticity of substitution, capital & labor
If =0.33, = 0.5, w0= 0.1, w = 0.01, and
v =0.1, then:
๐ถ = 0.025
Marginal cost to economy from
higher k is constant
๐๐ถ
๐๐=๐๐ถ
๐๐ฃร๐๐ฃ
๐๐คร๐๐ค๐๐ง
ร๐๐ง๐๐
=๐ผ๐
1โ๐ผ
1
๐ค0๐๐ต + ๐๐๐๐ต ๐๐ต โ ๐๐ 1 โ ๐
โก ๐
Benefits and costs of additional
bank capital
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.0
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3
0.0
5
0.0
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0.0
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0.0
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0.1
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0.2
0.2
1
0.2
2
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3
0.2
4
0.2
5
CostBenefit
ratio of capital to total assets
fraction of GDP
Simulation parameters
Parameter Concept Low OCR Base High OCR
Loss from crisis 0.3 0.64 1.0
B Equity cost to banks 0.13 0.10 0.07
M&M offset 0.35 0.45 0.60
Nonbank spillover 0.7 0.5 0.2
Capital elasticity 0.43 0.40 0.33
Substitution elast. 0.8 0.5 0.4
Frequency, optimal capital ratio
0
100
200
300
0.0
5
0.0
6
0.0
7
0.0
8
0.0
9
0.1
0.1
1
0.1
2
optimal capital/asset ratio
Optimal Capital Requirements(tce/rwa %)
Great Recession change, net income/assets,
and log asset size, 50 large US banks
-0.03
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0 1 2 3 4 5 6 7 8