RDP 1999-09: Australian Banking Risk: The Stock Market's Assessment and the Relationship Between Capital and Asset Volatility Appendix C: Capital and Risk Relationship

Marianne Gizycki and Brenton Goldsworthy

November 1999

Impact of the 1988 Capital Accord

Table C1: Impact of Risk-based Capital Adequacy Standards
Regression: Inline Equation
where δ = 1 if t ≤ December 1988 and 0 otherwise
Monthly; March 1983 – April 1998 (excluding October – December 1987)
Bank Constant Lags of change in capital Lags of asset volatility
(pre-Accord) 		Lags of asset volatility
(post-Accord) 		Significance of testing
Inline Equation
No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients
A 0.001
(0.143)		 1
 		 0.136
(0.243)		 6
 		 −0.136
(0.000)***		 1
 		 0.009
(0.831)		 0.049**
 
D 0.004
(0.001)***		 1
 		 0.134
(0.071)*		 12
 		 −0.543
(0.080)*		 11
 		 −0.179
(0.004)***		 0.012**
 
E 0.002
(0.281)		 1
 		 0.025
(0.835)		 5
 		 0.175
(0.000)***		 1
 		 −0.089
(0.238)		 0.000***
 
G 0.001
(0.169)		 1
 		 0.157
(0.062)*		 5
 		 −0.081
(0.000)***		 4
 		 −0.033
(0.000)***		 0.645
 
J 0.001
(0.267)		 1
 		 0.071
(0.377)		 3
 		 −0.073
(0.146)		 1
 		 −0.043
(0.249)		 0.502
 
M 0.001
(0.014)**		 1
 		 0.439
(0.000)***		 1
 		 −0.269
(0.002)***		 10
 		 −0.063
(0.005)***		 0.000***
 
N 0.005
(0.092)*		 4
 		 0.159
(0.024)**		 5
 		 0.198
(0.000)**		 9
 		 −0.256
(0.010)***		 0.422
 

Notes: The numbers in parentheses show the significance level from testing whether all lagged variables can be excluded from the regression.
***, **, * denote significance at the 1, 5 and 10 per cent levels respectively.
Δkt is the month-to-month change in the capital-asset ratio.
k t and σAt are obtained from the Case III paramaterisation of the model using historical estimates of σE.

Table C2: Impact of Risk-based Capital Adequacy Standards
Regression: Inline Equation
where δ = 1 if t ≤ December 1988 and 0 otherwise
Monthly; March 1983 – April 1998 (excluding October – December 1987)
Bank Constant Trend 1 Trend 2 Lags of change in capital
(pre-Accord) 		Lags of change in capital
(post-Accord) 		Lags of volatility Significance of testing
Inline Equation
No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients
A −0.001
(0.248)		 0.00008
(0.003)***		 0.00005
(0.001)***		 1
 		 0.358
(0.046)**		 10
 		 0.733
(0.020)**		 1
 		 0.647
(0.000)***		 0.445
 
D 0.001
(0.471)		 0.00005
(0.144)		 0.00004
(0.003)***		 1
 		 0.369
(0.004)***		 2
 		 0.218
(0.016)**		 1
 		 0.675
(0.000)***		 0.320
 
E 0.008
(0.001)***		     3
 		 −0.872
(0.000)***		 1
 		 0.151
(0.041)**		 1
 		 0.583
(0.000)***		 0.032
 
G 0.005
(0.015)**		     1
 		 0.628
(0.657)		 1
 		 0.121
(0.579)		 1
 		 0.682
(0.000)***		 0.728
 
J 0.018
(0.000)***		     1
 		 0.148
(0.131)		 1
 		 0.165
(0.330)		 4
 		 0.425
(0.058)*		 0.930
 
M 0.001
(0.231)		     1
 		 0.392
(0.000)***		 5
 		 1.197
(0.001)***		 6
 		 0.943
(0.006)***		 0.001
 
N 0.002
(0.348)		     1
 		 −0.242
(0.062)*		 1
 		 0.138
(0.342)		 6
 		 0.927
(0.001)***		 0.072
 

Notes: The numbers in parentheses show the significance level from testing whether all lagged variables can be excluded from the regression.
***, **, * denote significance at the 1, 5 and 10 per cent levels respectively.
Δkt is the month-to-month change in the capital-asset ratio.
k t and σAt are obtained from the Case III paramaterisation of the model using historical estimates of σE.
‘Trend 1’ runs from March 1983 to December 1988 and ‘Trend 2’ runs from January 1989 to April 1998.
Table C3: Impulse Response
Bank Pre-Accord Post-Accord
Change in capital (percentage points) Asset volatility (percentage points) Change in capital (percentage points) Asset volatility (percentage points)
A −0.144 0.012 0.001 0.117
D −0.021 −0.003 0.103 0.022
E −0.286 −0.524 −0.003 0.005
G 0.025 −0.032 −0.113 0.013
J −0.018 −0.019 0.010 −0.018
M −0.047 0.030 −0.007 0.237
N 0.132 −0.074 −0.089 0.010

Note: Each column shows the change in the variable (after six months) as a result of a one standard deviation, one period, shock to the other variable.
Table C4: Test for Asymmetry
Regression: Inline Equation
where θ = 1 if Δkt < 0 and 0 otherwise
Monthly; March 1983 – April 1998 (excluding October – December 1987)
Bank Constant Lags of change in capital Asset volatility
(capital increasing) 		Asset volatility
(capital decreasing) 		Significance of testing:
Inline Equation
No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients
A 0.000 (0.397) 1 0.365 (0.024)** 1
 		 −0.041 (0.507) 1
 		 0.102 (0.087)* 0.093*
 
B 0.006 (0.011)** 1
 		 −0.115 (0.445) 1
 		 −0.294 (0.047)** 1
 		 −0.480 (0.022)** 0.165
 
C 0.009 (0.000)*** 5
 		 −0.379 (0.000)*** 6
 		 −0.184 (0.008)*** 3
 		 −0.570 (0.007)*** 0.099*
 
D 0.001 (0.020)* 1
 		 0.234 (0.031)** 1
 		 −0.070 (0.255) 1
 		 −0.030 (0.378) 0.542
 
E 0.002 (0.256) 1
 		 −0.022 (0.869) 5
 		 −0.136 (0.118) 1
 		 −0.077 (0.378) 0.321
 
G 0.000 (0.663) 1
 		 0.036 (0.786) 1
 		 0.112 (0.091)* 1
 		 0.005 (0.949) 0.209
 
H 0.001 (0.364) 1
 		 0.326 (0.017)** 1
 		 −0.065 (0.385) 1
 		 0.023 (0.647) 0.145
 
I −0.002 (0.464) 3
 		 −0.090 (0.000)*** 3
 		 0.115 (0.000)*** 1
 		 0.066 (0.564) 0.760
 
J 0.000 (0.767) 1
 		 −0.044 (0.726) 1
 		 0.020 (0.650) 1
 		 −0.080 (0.034)** 0.038**
 
K 0.003 (0.038)** 3
 		 0.380 (0.007)*** 1
 		 −0.119 (0.157) 1
 		 −0.139 (0.100) 0.781
 
L −0.002 (0.571) 1
 		 0.149 (0.540) 2
 		 0.098 (0.055)* 2
 		 0.075 (0.077)* 0.807
 
M 0.001 (0.033)** 1
 		 0.252 (0.034)** 1
 		 −0.044 (0.513) 1
 		 −0.092 (0.021)** 0.526
 
N 0.006 (0.006)*** 10
 		 0.347 (0.047)* 10
 		 −0.433 (0.048)* 1
 		 −0.164 (0.280) 0.162
 
O −0.001 (0.724) 1
 		 0.218 (0.258) 1
 		 0.008 (0.912) 2
 		 0.045 (0.582) 0.618
 

Notes: The numbers in parentheses show the significance level from testing whether all lagged variables can be excluded from the regression.
***, **, * denote significance at the 1, 5 and 10 per cent levels respectively.
Δkt is the month-to-month change in the capital-asset ratio.
k t and σAt are obtained from the Case III paramaterisation of the model using historical estimates of σE.
Table C5: Test for Asymmetry
Regression: Inline Equation
where θ = 1 if Δkt < 0 and 0 otherwise
Monthly; March 1983 – April 1998 (excluding October – December 1987)
Bank Constant Trend Trend 1 Trend 2 Lags of change in capital
(capital increasing) 		Lags of change in capital
(capital decreasing) 		Lags of asset volatility Significance of testing
Inline Equation
No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients No. of
lags		 Sum of coefficients
A 0.000
(0.698)		   0.00003
(0.036)**		 0.00004
(0.002)***		 1
 		 0.461
(0.002)***		 1
 		 −0.227
(0.304)		 1
 		 0.621
(0.000)***		 0.034**
 
B 0.005
(0.008)***		       1
 		 −0.120
(0.552)		 1
 		 0.249
(0.012)**		 1
 		 0.754
(0.000)***		 0.133
 
C 0.031
(0.00)***		 −0.00025
(0.000)***		     1
 		 0.377
(0.052)*		 1
 		 0.104
(0.148)		 2
 		 0.458
(0.000)***		 0.195
 
D 0.001
(0.421)		 0.00004
(0.004)***		     1
 		 0.367
(0.011)**		 1
 		 −0.122
(0.314)		 1
 		 0.684
(0.000)***		 0.033**
 
E 0.009
(0.000)***		       1
 		 0.210
(0.277)		 1
 		 −0.032
(0.648)		 2
 		 0.462
(0.000)***		 0.267
 
G 0.004
(0.001)***		       3
 		 0.285
(0.000)***		 1
 		 −0.971
(0.037)**		 2
 		 0.642
(0.000)***		 0.052*
 
H −0.014
(0.000)***		 0.00014
(0.000)***		     7
 		 2.125
(0.000)***		 10
 		 −1.129
(0.003)***		 2
 		 0.261
(0.000)***		 0.002***
 
I −0.032
(0.000)***		 0.00031
(0.000)***		     1
 		 0.225
(0.199)		 4
 		 0.610
(0.012)**		 1
 		 0.155
(0.389)		 0.451
 
J 0.026
(0.000)***		 −0.00006
(0.004)***		     1
 		 0.367
(0.129)		 1
 		 0.113
(0.402)		 2
 		 0.364
(0.000)***		 0.436
 
K 0.020
(0.001)***		   0.00010
(0.039)**		 0.00002
(0.614)		 3
 		 0.605
(0.002)***		 1
 		 −0.463
(0.122)		 9
 		 0.050
(0.000)***		 0.046**
 
L 0.033
(0.000)***		       4
 		 −2.297
(0.000)***		 6
 		 1.746
(0.000)***		 4
 		 −0.386
(0.000)***		 0.000***
 
M 0.001
(0.211)**		       1
 		 0.222
(0.048)**		 12
 		 0.475
(0.103)		 5
 		 0.958
(0.000)***		 0.435
 
N 0.002
(0.243)		       1
 		 0.575
(0.012)***		 12
 		 0.114
(0.000)***		 6
 		 0.845
(0.000)***		 0.291
 
O 0.001
(0.705)		       3
 		 1.885
(0.072)*		 3
 		 −0.835
(0.057)*		 1
 		 0.700
(0.000)***		 0.010***
 

Notes: The numbers in parentheses show the significance level from testing whether all lagged variables can be excluded from the regression.
***, **, * denote significance at the 1, 5 and 10 per cent levels respectively.
Δkt is the month-to-month change in the capital-asset ratio.
k t and σAt are obtained from the Case III paramaterisation of the model using historical estimates of σE.
‘Trend’ is a full sample trend while ‘Trend 1’ runs from March 1983 to December 1991 and ‘Trend 2’ runs from January 1992 to April 1998.