Value at Risk of Commercial Bank The Banking industry of Taiwan

1. Value at Risk of Commercial BankThe Banking industry of Taiwan 張大成 東吳大學國貿系副教授 dachen@mail2.scu.edu.tw Tel : (02)2311-1531 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% / 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.

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% / 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.

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

28. The Methods of VaR • 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 1996-2000 • 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