1. Value at Risk of Commercial Bank The Banking industry of Taiwan
張大成
東吳大學國貿系副教授
Tel : (02) ext 2720

2. 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.

3. Basel Capital Accord 1988
Risk Adjusted Asset = Credit Risk + Market Risk + Operation Risk

4. Basel Capital Accord
VaR

6. 實 務 界

7. 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.

8. Tail Probability and VaR

9. 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

10. Interest Rate

11. Oil Price

12. Currency

13. Recent Cases of Financial Disasters
Barings PLC
Metallgesellschaft
Orange County
Daiwa Bank
Kashima Oil
Procter & Gamble

14. 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.

15. 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.

16. 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.

17. 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

18. 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

19. What is the appropriate measure of risk?
Beta? – systematic risk
Volatility? – total risk
downside risk
upside risk
Downside risk
VaR

20. 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

21. VaR

22. 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 )

23. 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, .

24. 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% / = 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.

25. 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% / = 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.

26. 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.

27. 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, ,405)- 1,751,379
=$90,647

28. The Methods of VaR Full Valuation Local valuation
Simple Moving Average
Exponentially Weighted Moving Average
Full Valuation
Historical Simulation
Monte Carlo Simulation
Extreme Value Theory

29. Model Verification
Basel rule of back testing
LR test of Kupiec (1995)

30. This Paper
Taiwan Listed 27 Banks
Period
VaR for per NT$100
Backtesting
Correlation test

31. VaR of Banks

32. Backtesting of VaR

33. Mean of VaRs

34. Correlation Regression

35. Panel Regression

36. Robustness