1. WHY IS VOLATILITY SO HIGH? Robert Engle Stern School of Business 2 th Annual Risk Management Conference, RMI, NUS

2. MODELING VOLATILITY Can we measure and forecast volatility when it is changing? Why does it change? How well does this work in turbulent times?

3. MODELING VOLATILITY Can we measure and forecast volatility when it is changing? Why does it change? How well does this work in turbulent times? Can we extend this to forecasting correlations?

4. S&P500 1990 to JAN 2008

5. GARCH MODEL The GARCH model predicts the variance of returns on the next day. It relies on two features of returns –Volatility Clustering –Mean Reversion of Volatility Econometric Methods fit this model to data

6. Plus and Minus three Sigma

7. OBSERVATIONS CONFIDENCE INTERVAL IS CHANGING GREEN CURVE IS APPROXIMATELY VAR.6% RETURNS EXCEED INTERVAL LARGEST IS -6.8 SIGMA! (oct 27 1997) MORE EXTREMES THAN EXPECTED FOR A NORMAL BUT NOT FOR A STUDENT-T

8. DOES THIS WORK IN TURBULENT TIMES? ESTIMATE THROUGH 2004 KEEPING SAME PARAMETERS, FORECAST TO END OF SAMPLE ONE DAY AT A TIME. DO WE SEE MULTI-SIGMA MOVES?

9. Plus and Minus 3 sigma using 2004 model

10. AGAINST THE VIX

11. EXTENSIONS - ASYMMETRY – TARCH –Or EGARCH –Or NARCH or PARCH Negative returns predict higher future volatility than positive returns!

12. NON-STATIONARITY Does the volatilty process change over time? Do macroeconomic conditions influence volatility?

13. THE SPLINE GARCH MODEL OF LOW FREQUENCY VOLATILITY AND ITS MACROECONOMIC CAUSES Robert Engle and Jose Gonzalo Rangel Review of Financial Studies 2008

14. EXAMPLES FOR US SP500 DAILY DATA FROM 1963 THROUGH 2004 ESTIMATE WITH 1 TO 15 KNOTS OPTIMAL NUMBER IS 7

21. MODEL LOW FREQUENCY VOLATILITY Low frequency Volatility is regressed against explanatory variables with observations for countries and years. Within a country residuals are auto-correlated due to spline smoothing. Hence use SUR. Volatility responds to global news so there is a time dummy for each year. Unbalanced panel

22. WHAT MAKES FINANCIAL MARKET VOLATILITY HIGH? High Inflation Slow output growth and recession High volatility of short term interest rates High volatility of output growth High volatility of inflation Small or undeveloped financial markets Large countries

23. WHY IS VOLATILITY SO HIGH? It is high but not as high, for most indices, as it was in 2002 Because of macroeconomic uncertainty- are we in a recession or not? Because of the credit crunch. Will the banking sector collapse?

24. MACRO ECONOMY Housing is doing very badly bringing other sectors down. Export sector is doing well due to weak dollar. Which will win? Fed has reduced rates six times in six months. Government has passed a tax rebate and other stimulus measures. Will these be enough?

25. S&P 500 Asymmetric GARCH

26. One year

27. Wilshire Small Cap 250

28. 10 year SWAP rate

29. Lehman US Agg Government

30. ML HYCASH Pay C All

31. IShares MSCI Japan

32. IShares MSCI SINGAPORE

33. IShares MSCI HONG KONG

34. Japanese Yen in Dollars

35. CREDIT CRISIS Banks, hedge funds, brokerages invested in securities that have lost much of their value. Many are near insolvency. Sub-prime mortgages are most dramatic but other assets have also fallen substantially in value.

36. SUB-PRIME MORTGAGES Subprime mortgage holders generally expect some defaults. They are now predicted to be greater than historically observed. Why is this surprising? –Our last housing crisis was in the early 90’s before subprime lending was important so there is no useful data –Some inappropriate or fraudulent lending occurred. Securitization of these contracts has made it difficult to know the risks. These securities were originally rated AAA and are now very substantially downgraded. Why?

37. WHAT IS A CDO? Collateralized Debt Obligation – a portfolio of bonds, residential mortgages, subprime mortgages, loans, and other types of credit. Investors can buy tranches of this portfolio that have more risk or less risk. How does this work?

38. SAND OR OIL? An analogy – mix sand, water and oil Tranches –Senior and Super Senior Tranche –Mezzanine Tranche –Equity Tranche Under what circumstances are the senior tranches risky? Rising volatility and correlation.

39. THE CREDIT CRUNCH Banks, investors, Hedge Funds, …bought tranches as investments Often investors bought AAA senior tranches with a few basis points of extra interest above much safer investments. These have lost value and are not marketable because the value is so uncertain. These are the heart of the Bear Stearns collapse.

40. THE FINANCIAL MARKET BORROWERS - Homeowners Commercial Business Corporate BANKS BROKERS CDO’s CDO 2 BANKS HEDGE FUNDS INVESTORS Stocks Bonds Direct investments

41. WHAT HAPPENED? Housing prices fell and these losses needed to be transferred to investors Risk increased and investors required higher returns to justify the risks. Investors lose. Borrowers must pay more for future loans.

42. HOW LONG WILL IT TAKE TO UNWIND THESE POSITIONS?

43. It has already taken a very long time The liquidity has disappeared from the subprime mortgage market Other mortgage and credit markets are now frozen. Margin calls are forcing some funds to liquidate. Yield spreads between treasuries and other debt are still at high levels.

44. A STORY Clearly, the value of CDO tranches is difficult to estimate. The bid-ask spread is very wide Banks and funds believe their assets are worth more than the bid price. Consequently, large portions of the portfolio are frozen and are not even useful as collateral. Need for new capital and no appetite for other relatively riskless investments.

45. WHAT IS NEXT? Investors with minimal losses will prepare for the bottom. This will include European and Asian investors. Bargains will be available when firms are forced to sell by margin calls or other losses. Capital will then come back onto balance sheets and business can continue. Federal Reserve has agreed to hold mortgages as collateral. This should help.

46. “ANTICIPATING CORRELATIONS” my new book, forthcoming August MARKET VOLATILITY IS A BIG COMPONENT OF CORRELATIONS. MACROECONOMIC UNCERTAINTY IS AN IMPORTANT COMPONENT OF HIGH CORRELATIONS THE CURRENT RISE IN MARKET VOLATILITY HAS LEAD TO THE EXPECTED RISE IN CORRELATIONS. THESE MODELS GIVE IMPROVED RISK EVALUATION FOR LARGE DYNAMIC PORTFOLIOS.