WHY IS VOLATILITY SO HIGH?WHY IS VOLATILITY SO HIGH?

Robert Engle

Stern School of Business

2th Annual Risk Management Conference, RMI, NUS

MODELING VOLATILITY

• Can we measure and forecast volatility when it is changing?

• Why does it change?

• How well does this work in turbulent times?

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?

S&P500 1990 to JAN 2008

0

400

800

1,200

1,600

-.08

-.04

.00

.04

.08

90 92 94 96 98 00 02 04 06

SPRET SPCLOSE

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

Plus and Minus three Sigma

-.100

-.075

-.050

-.025

.000

.025

.050

.075

.100

90 92 94 96 98 00 02 04 06

3*SPVOL SPRET -3*SPVOL

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

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?

Plus and Minus 3 sigma using 2004 model

-.06

-.04

-.02

.00

.02

.04

.06

2004 2005 2006 2007

3*SPVOL04 SPRET -3*SPVOL04

AGAINST THE VIX

5

10

15

20

25

30

35

05M01 05M07 06M01 06M07 07M01 07M07 08M01

SPVOL04*100*SQR(252) VIXCLOSE

EXTENSIONS - ASYMMETRY

• – TARCH– Or EGARCH– Or NARCH or PARCH

• Negative returns predict higher future volatility than positive returns!

NON-STATIONARITY

• Does the volatilty process change over time?

• Do macroeconomic conditions influence volatility?

THE SPLINE GARCH MODEL OF LOW FREQUENCY VOLATILITY AND ITS MACROECONOMIC CAUSES

Robert Engle and Jose Gonzalo RangelReview of Financial Studies 2008

EXAMPLES FOR US SP500

• DAILY DATA FROM 1963 THROUGH 2004

• ESTIMATE WITH 1 TO 15 KNOTS

• OPTIMAL NUMBER IS 7

0.0

0.2

0.4

0.6

0.8

1.0

1.2

60 65 70 75 80 85 90 95 00

CVOL UVOL

S&P500

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

90 92 94 96 98 00 02

CVOL UVOL ANNUAL RV

India,5

0

1

2

3

4

90 92 94 96 98 00 02

CVOL UVOL ANNUAL RV

Argentina, 3

0.0

0.2

0.4

0.6

0.8

1.0

90 92 94 96 98 00 02

CVOL UVOL ANNUAL RV

Japan,4

0.0

0.5

1.0

1.5

2.0

2.5

3.0

90 92 94 96 98 00 02

CVOL UVOL ANNUAL RV

Brazil,6

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

90 92 94 96 98 00 02

CVOL UVOL ANNUAL RV

South Africa,3

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

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

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?

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?

S&P 500 Asymmetric GARCH

One year

Wilshire Small Cap 250

10 year SWAP rate

Lehman US Agg Government

ML HYCASH Pay C All

IShares MSCI Japan

IShares MSCI SINGAPORE

IShares MSCI HONG KONG

Japanese Yen in Dollars

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.

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?

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?

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.

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.

THE FINANCIAL MARKET

BORROWERS-

Homeowners

Commercial

Business

Corporate BANKS

BROKERS

CDO’s

CDO2BANKS

HEDGE FUNDS

INVESTORS

Stocks

Bonds

Direct investments

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.

HOW LONG WILL IT TAKE TO UNWIND THESE POSITIONS?

HOW LONG WILL IT TAKE TO UNWIND THESE POSITIONS?

• 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.

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.

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.

“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.