WHY IS VOLATILITY SO HIGH?

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WHY IS VOLATILITY SO HIGH?

• Robert Engle
• Stern School of Business
• 2th Annual Risk Management Conference, RMI, NUS

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MODELING VOLATILITY

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

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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?

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SP500 1990 to JAN 2008
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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

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Plus and Minus three Sigma
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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

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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?

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Plus and Minus 3 sigma using 2004 model
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AGAINST THE VIX
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EXTENSIONS - ASYMMETRY

• TARCH
• Or EGARCH
• Or NARCH or PARCH
• Negative returns predict higher future volatility
  than positive returns!

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NON-STATIONARITY

• Does the volatilty process change over time?
• Do macroeconomic conditions influence volatility?

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

• Robert Engle and Jose Gonzalo RangelReview of
  Financial Studies 2008

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EXAMPLES FOR US SP500

• DAILY DATA FROM 1963 THROUGH 2004
• ESTIMATE WITH 1 TO 15 KNOTS
• OPTIMAL NUMBER IS 7

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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

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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

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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?

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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?

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SP 500 Asymmetric GARCH
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One year
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Wilshire Small Cap 250
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10 year SWAP rate
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Lehman US Agg Government
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ML HYCASH Pay C All
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IShares MSCI Japan
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IShares MSCI SINGAPORE
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IShares MSCI HONG KONG
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Japanese Yen in Dollars
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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.

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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 90s
  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?

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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?

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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.

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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.

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THE FINANCIAL MARKET
BORROWERS- Homeowners Commercial
Business Corporate
BROKERS
INVESTORS Stocks Bonds Direct investments
BANKS
CDO2
BANKS
CDOs
HEDGE FUNDS
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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.

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HOW LONG WILL IT TAKE TO UNWIND THESE POSITIONS?
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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.

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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.

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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.

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ANTICIPATING CORRELATIONSmy 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.