Value at Risk of Commercial Bank

The Banking industry of Taiwan

張大成東吳大學國貿系副教授

dachen@mail2.scu.edu.twTel : (02)2311-1531 ext 2720

BIS vs WB

• BANK FOR INTERNATIONAL SETTLEMENTS (BIS)

• Founded in 1930, the BIS is an international organization which fosters cooperation among central banks and other agencies in pursuit of monetary and financial stability.

• WORLD BANK (WB)

• Founded in 1944, the World Bank Group is one of the world's largest sources of development assistance.

Basel Capital Accord 1988

–Risk Adjusted Asset = Credit Risk + Market Risk + Operation Risk

%8RatioCapitalAssetAdjustedRisk

)III,II,I(CapitalTotal

Basel Capital Accord

1988 1996 1999 2001信用風險 標準法 YCredi t Ri sk 內部模型 基本法

進階法市場風險 標準法 Y Y YMarket Ri sk 內部模型 Y Y Y

作業風險 YOperati ng Ri sk

CountryTotal

Examined

Disclosed

VAR Data

DisclosedDaily P&Lwith VAR

DisclosedInformation onTrading income

Belgium 3 3 1 2

Cancda 6 6 2 5

France 6 6 2 4

Germany 6 5 2 4

Italy 6 5 2 6

Japan, banks 7 7 6 7

Japan, securities houses 2 1 0 2

Luxemburg 2 2 0 0

Netherlands 3 3 0 2

Sweden 2 2 0 1

Swizerland 3 3 3 3

U.K. 7 7 1 7

U.S., banks 9 9 3 8

U.S., securities houses 9 7 5 3

Total in 1998 71 66 27 54

Memo, 1997 78 63 21 74

Memo, 1996 79 50 18 69

Memo, 1995 79 36 11 64

Memo, 1994 79 18 5 59

Memo, 1993 79 4 0 48

Source: Jorion(2000)

Number of I nstitutions

實 務 界

公司 時間 成本 功能Morgan Stanl ey 1986 $60 Mi l l i on 風險控管交易系統 成功CS Fi rst Bank 1990 $100 Mi l l i on 前後檯整合系統 失敗Sal omon 1990 $100 Mi l l i on 前後檯整合系統 失敗Taurn 1990 $630 Mi l l i on 電子交易系統 失敗Source: Jorion(2000)

Definition of VaR

• Value-at-Risk or VaR is “we are X percent certain that we will not lose more than V dollars in the next N days”, the variable V is the VaR of the portfolio (Hull,2000).

• Throughout the lecture, we will use X=1% and N=10-day unless we specify otherwise.

Tail Probability and VaR

Financial Risk

• Financial risks can be defined as those which relate to possible losses in financial markets, such as losses due to price and interest rate movements or defaults on financial obligations.

• Market risks

• Credit risks

• Liquidity risks

Interest Rate

Weekly U.S. T-Bill Rate, Three-Month Maturity, January 1954 to December 1997

Inte

rest

Rat

e (P

erce

nt)

0

4

8

12

16

20

1954 1958 1962 1966 1970 1974 1978 1982 1986 1990 1994 1998

Oil Price

10

15

20

25

30

35

40

1985 1990 1995

Currency

0.8

1.2

1.6

2.0

2.4

2.8

1975 1980 1985 1990 1995 2000

US dollar/British Pound

Recent Cases of Financial Disasters

• Barings PLC

• Metallgesellschaft

• Orange County

• Daiwa Bank

• Kashima Oil

• Procter & Gamble

Barings PLC

• One of the oldest bank in England

• Conservative

• Went bankrupt in 1995 after a single trader, 28 year old Nicholas Leeson lost $1.3 billion from trading Nikkei 225 futures.

• Had $7 Billion exposure to the Nikkei 225, a portfolio of Japanese Stock. Nikkei 225 fell by more than 15% in the first two months of 1995.

Orange County

• Bob Citron, the Orange County treasurer, was entrusted with a $7.5 billion portfolio belonging to county schools, cities, special districts and the county itself.

• Borrowed $12.5 billion and essentially place a bet on the interest rate movement.

• Lost $1.8 billion and the Orange County declared bankruptcy.

Metallgesellschaft

• The 14th largest industrial group in Germany

• Offer a long term contracts for oil products and hedge its exposure by rolling short term futures.

• Exposed to the basis risk, which is the risk that short term oil prices temporarily deviate from long term prices.

• Loss of $1.3 billion and the company nearly went bankrupt.

The Lesson

• All three disasters involves losses in excess of $1 billion

• Common elements are:

– Poor management of financial risk

– Absence of enforced risk management policy

Why Risk Management?

• Reduce the probability of bankruptcy and financial distress.

• Increase the firm’s debt capacity and allow it to make better use of the tax shield of debt.

• Profit enhancement

What is the appropriate measure of risk?

• Beta? – systematic risk

• Volatility? – total risk

– downside risk

– upside risk

• Downside risk

– VaR

Advantages of VaR

• It captures an important aspect of risk in a single number

• It is easy to understand

• It asks the question: “How bad can thing get?”

• Asset Allocation

VaR

VaR with Normal Distribution

• If portfolio returns are normally distributed with standard deviation of , the 1% VaR of the portfolio is then:

VaR = ( 2.33 ) Current Portfolio Value

( V )

Computing VaR

• VaR = ( 2.33 ) V

• V is typically known. Need to figure out .

• If you need daily VaR, you should use daily standard deviation, .

Computing VaR (1)

• Example1: You have IBM stock of $10 million. Suppose the annualized standard deviation is 32%. What is your 10 day VaR?

• Daily = 32% / 2500.5 = 2%

• 10-day VaR =100.5 ( 2.33 2% ) $10 mil = $ 1,473,621

• There is a 1% chance that you will lose $1,473,621 or more during the next 10 day.

Computing VaR (2)

• Example2: You have AT&T stock of $5 million. Suppose the annualized standard deviation is 16%. What is your 10-day VaR?

• Daily = 16% / 2500.5 = 1%

• 10-day VaR =100.5 ( 2.33 1% ) $5 mil

= $ 368,405

• There is a 1% chance that you will lose $368,405 or more during the next 10 day.

Portfolio VaR

• Example3: You have IBM stock of $10 million, the annualized is 32%, and AT&T stock of $5 million, the annualized is 16%. In addition, the correlation between IBM and AT&T is 0.7 What is your 10-day VaR of your portfolio??

• Daily volatility of portfolio p =

• 10-day VaR =1,751,379

• There is a 1% chance that you will lose $1,751,379 or more during the next 10 day.

The Benefits of Diversification

• Example 1: IBM,10M, 10day VaR= $1,473,621

• Example 2: AT&T,5M, 10day VaR= $368,405

• Example 3: IBM,10M+AT&T,5M, 10day VaR=$1,751,379

• The Benefits of Diversification =$(1,473,621+ 368,405)- 1,751,379 =$90,647

The Methods of VaR

• Local valuation Simple Moving AverageSimple Moving Average Exponentially Weighted Moving AverageExponentially Weighted Moving Average

•Full Valuation Historical SimulationHistorical Simulation Monte Carlo Simulation

Extreme Value Theory

Model Verification

•Basel rule of back testing

•LR test of Kupiec (1995)

This Paper

•Taiwan Listed 27 Banks

•Period 1996-2000

•VaR for per NT$100

•Backtesting

•Correlation test

Table1 : The average of VaR85(T=284) 86(T=286) 87(T=270) 88(T=265) 89(T=270)

Bank SMA EWMA HS SMA EWMA HS SMA EWMA HS SMA EWMA HS SMA EWMA HS2801彰銀 1.471 1.440 1.804 0.753 0.755 0.797 0.742 0.742 0.827 1.410 1.166 1.578 1.611 1.556 1.7332802一銀 1.879 1.884 2.199 1.090 1.046 1.274 1.315 1.345 1.695 4.256 3.560 4.664 2.120 2.034 2.4082803華銀 3.742 3.584 4.330 2.557 2.539 2.814 2.563 2.615 2.869 4.213 3.552 4.545 3.511 3.353 3.8672806中銀 0.520 0.573 0.585 0.585 0.451 0.777 1.320 0.920 1.658 1.957 1.233 1.724 1.399 1.689 1.4502807竹商銀 3.843 3.803 5.217 2.722 2.552 3.712 2.424 2.376 2.775 3.622 3.255 3.780 3.188 2.943 3.3102808北商銀 0.405 0.433 0.527 0.173 0.202 0.185 0.243 0.194 0.255 0.372 0.317 0.442 0.277 0.266 0.2532811東企 4.003 3.927 5.092 3.404 3.020 4.452 3.331 3.251 4.181 4.152 3.887 4.513 3.687 3.234 4.4062812台中銀 4.733 4.533 5.994 1.748 1.695 1.942 2.066 2.097 2.423 2.101 1.909 2.239 1.852 1.683 2.1472815中信銀 1.336 1.356 1.759 0.483 0.482 0.777 0.573 0.540 0.714 0.821 0.722 0.863 1.092 1.020 1.1382824交銀 3.197 3.388 3.875 4.899 3.545 5.469 3.682 3.630 4.378 4.113 4.081 4.331 3.397 2.979 3.9982826世華 4.201 4.228 5.369 3.353 3.103 4.506 3.181 3.088 3.490 4.311 3.916 4.546 3.634 3.310 3.7622828萬通 2.771 2.622 3.240 1.964 1.932 2.828 2.039 2.060 2.321 2.739 2.400 2.898 2.669 2.524 2.8612829大安 3.311 3.214 4.112 0.161 0.182 0.456 1.935 1.779 1.947 2.735 2.374 2.748 2.350 2.303 2.4772830北銀 0.544 0.581 0.835 0.565 0.573 1.058 0.606 0.557 0.842 0.703 0.620 0.763 0.651 0.609 0.7782831中華銀行 1.980 1.918 2.684 4.021 3.456 4.662 3.304 3.315 3.910 4.782 4.145 5.720 3.769 3.507 4.3092834台企 1.045 1.030 1.260 1.089 1.062 1.480 2.900 2.950 3.352 3.697 3.239 3.754 3.408 3.194 3.5282836高雄銀行 0.698 0.698 0.777 3.049 2.988 4.324 0.993 1.005 1.118 0.409 0.359 0.404 4.324 4.124 4.5552837萬泰 2.862 2.806 3.539 2.912 2.816 4.069 2.721 2.734 3.078 4.066 3.594 4.196 3.591 3.380 3.7342838聯邦銀 3.763 3.659 4.522 2.019 1.972 2.774 2.011 1.995 2.223 2.837 2.522 2.883 2.842 2.676 2.9402839華信銀 4.985 4.748 6.420 0.241 0.259 0.228 1.858 1.490 2.300 1.208 0.911 1.027 1.255 1.337 1.5582840玉山銀 5.014 4.782 6.208 1.601 1.577 2.298 1.454 0.850 0.919 1.992 2.611 1.620 1.621 1.532 1.7792842富邦銀 0.876 0.880 0.998 1.182 1.119 1.593 0.243 0.195 0.443 2.286 2.064 2.449 2.553 2.341 2.6632843亞太銀 0.611 0.619 0.717 0.501 0.511 0.493 1.104 1.118 1.184 1.979 1.730 2.220 2.307 2.187 2.5842844台新銀 3.870 3.972 4.331 4.151 4.106 4.785 3.322 3.237 3.951 4.604 4.104 5.144 3.861 3.614 4.2862845遠東銀 1.079 1.053 1.360 0.237 0.263 0.240 1.191 1.174 1.378 2.570 2.235 2.635 2.401 2.324 2.9172847大眾銀 5.008 4.756 6.364 3.016 3.076 4.103 3.132 3.077 3.474 4.159 3.710 4.228 3.569 3.288 3.6402849安泰銀 4.281 4.150 5.124 2.895 2.846 3.169 2.707 2.726 3.190 4.067 3.339 4.476 3.847 3.738 4.105

VaR of Banks

Table2 : The number of exceptions and LR test85(T=284) 86(T=286) 87(T=270) 88(T=265) 89(T=270)

Banks SMA EWMA HS SMA EWMA HS SMA EWMA HS SMA EWMA HS SMA EWMA HS2801彰銀 3(0.0089) 4(0.42) 1(1.60) 9(8.49)c 19(40.61)b 7(4.31)b 3(0.03) 3(0.03) 3(0.03) 4(0.60) 10(12.07)c 3(0.04) 8(6.88)c 11(14.56)c 5(1.58)

2802一銀 2(0.28) 3(0.0089) 1(1.60) 9(8.49)c 23(57.08)c 6(2.65) 3(0.03) 6(3.02)a 4(0.55) 4(0.60) 7(4.97)b 3(0.04) 7(4.81)b 11(14.56)c 5(1.58)

2803華銀 3(0.0089) 5(1.35) 2(0.28) 9(8.49)c 19(40.62)c 6(2.65) 3(0.03) 3(0.03) 3(0.03) 3(0.04) 8(7.09)c 3(0.04) 9(9.22)c 11(14.56)c 5(1.58)

2806中銀 1(1.60) 1(1.60) 1(1.60) 17(33.04)c 33(104.46)c 11(13.59)c 6(3.02)a 11(14.56)c 3(0.03) 3(0.04) 8(7.09)c 4(0.60) 1(1.42) 4(0.55) 1(1.42)

2807竹商銀 2(0.28) 5(1.35) 1(1.60) 12(16.44)c 17(33.04)c 5(1.32) 5(1.58) 6(3.02)a 3(0.03) 3(0.04) 6(3.15)a 3(0.04) 6(3.02)a 15(27.42)c 6(3.02)a

2808北商銀 2(0.28) 4(0.42) 0(na) 6(2.65) 11(13.59)c 5(1.32) 4(0.55) 7(4.81)b 5(1.58) 4(0.60) 9(9.46)c 4(0.60) 2(0.20) 7(4.81)b 7(4.81)b

2811東企 4(0.42) 7(4.37)b 2(0.28) 10(10.94)c 21(48.64)c 7(4.31)b 5(1.58) 6(3.02)a 2(0.20) 5(1.67) 7(4.97)b 3(0.04) 9(9.22)c 19(42.56)c 5(1.58)

2812台中銀 3(0.0089) 6(2.69) 3(0.0089) 10(10.94)c 18(36.77)c 7(4.31)b 3(0.03) 5(1.58) 3(0.03) 3(0.04) 7(4.97)b 3(0.04) 7(4.81)b 16(31.01)c 4(0.55)

2815中信銀 3(0.0089) 4(0.42) 2(0.28) 9(8.49)c 15(25.96)c 3(0.0068) 5(1.58) 5(1.58) 2(0.20) 4(0.60) 8(7.09)c 4(0.60) 10(11.79)c 13(20.67)c 7(4.81)b

2824交銀 2(0.28) 3(0.0089) 1(1.60) 18(36.77)c 36(120.11)c 13(19.45)c 3(0.03) 4(0.55) 1(1.42) 5(1.67) 5(1.67) 4(0.60) 10(11.79)c 20(46.64)c 6(3.02)a

2826世華 3(0.0089) 5(1.35) 2(0.28) 13(19.45)c 17(33.04)c 6(2.65) 4(0.55) 5(1.58) 3(0.03) 3(0.04) 7(4.97)b 3(0.04) 7(4.81)b 19(42.56)c 7(4.81)b

2828萬通 3(0.0089) 5(1.35) 2(0.28) 7(4.31)b 16(29.44)c 3(0.0068) 3(0.03) 4(0.55) 1(1.42) 4(0.60) 8(7.09)c 4(0.60) 7(4.81)b 12(17.53)c 7(4.81)b

2829大安 3(0.0089) 5(1.35) 3(0.0089) 13(19.46)c 17(33.04)c 1(1.63) 3(0.03) 6(3.02)a 3(0.03) 4(0.60) 8(7.09)c 4(0.60) 7(4.81)b 11(14.56)c 7(4.81)b

2830北銀 2(0.28) 4(0.42) 1(1.60) 4(0.41) 8(6.27)b 1(1.63) 5(1.58) 6(3.02)a 1(1.42) 3(0.04) 10(12.07)c 3(0.04) 10(11.79)c 16(31.01)c 4(0.55)

2831中華銀行 3(0.0089) 5(1.35) 1(1.60) 7(4.31)b 19(40.62)c 7(4.31)b 4(0.55) 5(1.58) 3(0.03) 5(1.67) 10(12.07)c 3(0.04) 7(4.81)b 15(27.42)c 5(1.58)

2834台企 3(0.0089) 6(2.69) 2(0.28) 8(6.27)b 15(25.96)c 3(0.0068) 3(0.03) 6(3.02)a 3(0.03) 4(0.60) 7(4.97)b 4(0.60) 6(3.02)a 13(20.67)c 7(4.81)b

2836高雄銀行 3(0.0089) 4(0.42) 4(0.42) 9(8.49)c 15(25.96)c 3(0.0068) 4(0.55) 3(0.03) 1(1.42) 4(0.60) 9(9.46)c 3(0.04) 8(6.88)c 12(17.53)c 8(6.88)c

2837萬泰 3(0.0089) 6(2.69) 2(0.28) 10(10.94)c 17(33.04)c 2(0.29) 3(0.03) 5(1.58) 3(0.03) 4(0.60) 8(7.09)c 4(0.60) 6(3.02)a 12(17.53)c 7(4.81)b

2838聯邦銀 3(0.0089) 5(1.35) 3(0.0089) 9(8.49)c 20(44.58)c 3(0.0068) 3(0.03) 5(1.58) 3(0.03) 4(0.60) 7(4.97)b 4(0.60) 6(3.02)a 12(17.53)c 7(4.81)b

2839華信銀 4(0.42) 5(1.35) 3(0.0089) 6(2.65) 14(22.63)c 7(4.31)b 5(1.58) 7(4.81)b 1(1.42) 3(0.04) 6(3.15)a 4(0.60) 5(1.58) 9(9.22)c 3(0.03)

2840玉山銀 3(0.0089) 5(1.35) 3(0.0089) 7(4.31)b 16(29.44)c 3(0.0068) 2(0.20) 3(0.03) 3(0.03) 2(0.18) 3(0.04) 4(0.60) 8(6.88)c 13(20.67)c 8(6.88)c

2842富邦銀 3(0.0089) 3(0.0089) 3(0.0089) 13(19.45)c 21(48.64)c 5(1.32) 4(0.55) 6(3.02)a 1(1.42) 4(0.60) 6(3.15)a 4(0.60) 6(3.02)a11(14.56)b 6(3.02)a

2843亞太銀 2(0.28) 3(0.0089) 1(1.60) 6(2.65) 13(19.45)c 8(6.27)b 3(0.03) 3(0.03) 3(0.03) 4(0.60) 9(9.46)c 3(0.04) 8(6.88)c 12(17.53)c 5(1.58)

2844台新銀 2(0.28) 2(0.28) 1(1.60) 2(0.29) 2(0.29) 2(0.29) 3(0.03) 5(1.58) 3(0.03) 4(0.60) 8(7.09)c 3(0.04) 5(1.58) 13(20.67)c 5(1.58)

2845遠東銀 3(0.0089) 4(0.42) 1(1.60) 7(4.31)b 12(16.44)c 7(4.31)b 4(0.55) 4(0.55) 4(0.55) 4(0.60) 7(4.97)b 3(0.04) 8(6.88)c 11(14.56)c 4(0.55)

2847大眾銀 2(0.28) 4(0.42) 2(0.28) 9(8.49)c 14(22.63)c 2(0.29) 3(0.03) 5(1.58) 3(0.03) 3(0.04) 7(4.97)b 3(0.04) 8(6.88)c 16(31.01)c 6(3.02)a

2849安泰銀 3(0.0089) 5(1.35) 2(0.28) 10(10.94)c 18(36.77)c 8(6.27)b 4(0.55) 3(0.03) 3(0.03) 3(0.04) 9(9.46)c 3(0.04) 9(9.22)c 11(14.56)c 5(1.58)

Backtesting of VaR

Value at Risk ( Five Years Average, %)

0

1

2

3

4

5

彰化

第一

華南

中銀

竹商

北商

東企

台中

中信

交銀

世華

萬通

大安

台北

中華

台企

高雄

萬泰

聯邦

華信

玉山

富邦

亞太

台新

遠東

大眾

安泰

Mean of VaRs

Correlation Regression

t,i4t,i3t,i2t,i10t,i TA_COSTTA_LOANRA_CAPNPLVaR

t,it,i6t,i5 BRANCHshare_LOAN

Panel RegressionTable 4: The results of Basic Regression

OLS Fixed Effect Random EffectConstant -3.3524 -2.4780

(-1.3292) (-0.8854)NPL 0.2655 0.0254 0.1146

(4.8232)*** (0.2889) (1.7407)*Cap_RA 0.0147 0.0899 0.0863

(0.3638) (1.6578)* (2.0390)**LOAN_A 10.2336 5.9623 7.7958

(4.1661)*** 1.6164 (2.6883)***Cost_Ass -0.3324 -0.2907 -0.2672

(-1.1350) (-0.9547) (-1.0133)L_share 0.6347 0.0377 0.3896

(3.3765)*** (0.0605) (1.3357)NUM -0.0316 -0.0141 -0.0190

(-3.79551*** (-0.6520) (-1.5163)

R2 0.2634 0.6617 0.6481Rbar2 0.2288 0.5555 0.6316note:H0: No individual effect( the OLS is correct)

F(26,102)=4.61809 with Significance Level 0.00000001

H0: No correelation between the individual effect and explanatory variables

(the random effect model is correct)

Chi-Squared(6)= 4.412521 with Significance Level 0.62103546

t value in parenthesis,

*, ** and *** denote the significance at the 10%, 5% and 1% level, respectively

RobustnessTable5: The Robustness test of Basic Regression Model

1 2 3 4 5 6Constant -2.4780 -2.4673 -2.5487 -2.7053 -3.0392 -2.4722

(-0.8854) (-0.8828) (-0.9193) (-0.9544) (-1.0523) (-0.8826)NPL 0.1146 0.1159 0.1179 0.1212 0.1252 0.1137

(1.7407)* (1.7633)* (1.7302)* (1.8156)* (1.8638)* (1.6668)*Cap_RA 0.0863 0.0939 0.0842 0.0898 0.0937 0.0868

(2.0390)** (2.1855)** (1.9278)* (2.0688)** (2.1601)** (2.0171)**LOAN_A 7.7958 7.7565 7.9140 7.6406 7.9057 7.7861

(2.6883)*** (2.6778)*** (2.7573)*** (2.6049)*** (2.72398)*** (2.67649)***Cost_Ass -0.2672 -0.3010 -0.2686 -0.2606 -0.2660 -0.2671

(-1.0133) (-1.1333) (-1.0169) (-0.9882) (-1.0092) (-1.0138)L_share 0.3896 0.5686 0.3940 0.4295 0.4293 0.3935

(1.3357) (1.6734)* (1.3164) (1.4117) (1.4512) (1.3430)NUM -0.0190 -0.0194 -0.0197 -0.0185 -0.0179 -0.0191

(-1.5163) (-1.5522) (-1.5420) (-1.4709) (-1.4209) (-1.5258)Gov -0.7984

(-1.0117)AGE 0.0013

(0.0672)NEW 0.2556

(0.3839)GROUP 0.4362

(0.7800)NI_Ass -0.0122

(-0.0803)

R2 0.6481 0.6474 0.6463 0.6472 0.6475 0.6480Rbar2 0.6316 0.6280 0.6268 0.6278 0.6281 0.6286

F test 4.6181 4.2613 4.5402 4.5247 4.2947 4.5268Chi-Squared test 4.4125 4.5816 4.9530 4.5481 4.8708 4.6128