GLOBAL FINANCIAL VOLATILITY

ROBERT ENGLENYU STERN

2007

RISK

Advance knowledge of risks allows us to avoid them. But what would we have to do to avoid them altogether??? Imagine!

Some risks are worth taking because the possible benefit exceeds the possible costs.

Both the costs and the benefits are in the future so this is a probabilistic calculation

FINANCE

This is the fundamental idea of finance phrased in three ways:

--- “What risk must we take to achieve a satisfactory return?”---- “What is the tradeoff between risk and return”----- “Which risks are not worth taking”

NOBEL ANSWERS

Markowitz (1952) and Tobin (1958) received Nobel awards in 1990 and 1981 for associating risk with the variance of financial returns.Sharpe(1964) showed that if investors behaved this way, then expected returns should follow the Capital Asset Pricing Model or CAPM. Only variances that could not be diversified would be rewarded. Prize also in 1990

BLACK-SCHOLES AND MERTON

Options can be used as insurance policies. For a fee we can eliminate financial risk for a period. What is the right fee?Black and Scholes(1972) and Merton(1973) developed an option pricing formula from a dynamic hedging argument. Their answer also satisfies the CAPM.They received the Nobel prize in 1997

IMPLEMENTING THESE MODELS

PRACTITIONERS REQUIRED ESTIMATES OF VARIANCES AND COVARIANCESEQUIVALENTLY WE SAY

VOLATILITIES (Standard deviation which is the square root of the variance)

AND CORRELATIONS(which is the covariance divided by the product of the standard deviations)

ESTIMATES DIFFER FOR DIFFERENT TIME PERIODS

Volatility is apparently varying over time

What is the volatility NOW!What is it likely to be in the future?

How can we forecast something we never observe?

ARCH, BUT WHAT IS ARCH?

Autoregressive Conditional Heteroskedasticity

Predictive (conditional)Uncertainty (heteroskedasticity)That fluctuates over time (autoregressive)

THE ARCH ANSWER

Use a weighted average of the volatility over a long period with higher weights on the recent past and small but non-zero weights on the distant past.

Choose these weights by looking at the past data; what forecasting model would have been best historically? This is a statistical estimation problem.

FROM THE SIMPLE ARCH GREW:

GENERALIZED ARCH (Bollerslev) a most important extensionTomorrow’s variance is predicted to be a weighted average of the

Long run average varianceToday’s variance forecastThe news (today’s squared return)

AND

EGARCH (Nelson) very important as it introduced asymmetry

Weights are different for positive and negative returns

OTHERS allowed non-linearities, long memory and more complex dynamics. Many developments at UCSD by students and colleagues.

NEW ARCH MODELS

GJR-GARCHTARCHSTARCHAARCHNARCHMARCHSWARCHSNPARCHAPARCHTAYLOR-SCHWERT

FIGARCHFIEGARCHComponent Asymmetric ComponentSQGARCHCESGARCHStudent tGEDSPARCHSPLINE GARCH

SURPRISING SUCCESS

Although the original application was macroeconomic, the big success was for financial data.ARCH was ideally suited to modeling some key features of financial dataThe simple GARCH(1,1) model has proven a good starting point for almost every type of financial return series. WHY?

VOLATILITY HISTORY

U.S. BROAD MARKET INDEX S&P500

RETURNS FROMJan 1963 TO Nov. 2003

0

400

800

1200

1600

-.3

-.2

-.1

.0

.1

55 60 65 70 75 80 85 90 95 00 05

SPCLOSE SP

50

100

150

200

250

300

-.06

-.04

-.02

.00

.02

.04

.06

66 68 70 72 74 76 78 80 82 84 86

SPCLOSE SP

0

400

800

1200

1600

-.08

-.04

.00

.04

.08

89 90 91 92 93 94 95 96 97 98 99 00

SPCLOSE SP

600

800

1000

1200

1400

1600

-.08

-.04

.00

.04

.08

2000 2001 2002 2003 2004 2005 2006

SPCLOSE SP

ROLLING WINDOW VOLATILITIESNUMBER OF DAYS=5,260,1300

.0

.2

.4

.6

64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02

V5 V260 V1300

ARCH/GARCH VOLATILITIES

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

65 70 75 80 85 90 95 00

GARCHVOL

CONFIDENCE INTERVALS

-.10

-.05

.00

.05

.10

1990 1992 1994 1996 1998 2000 2002

3*GARCHSTD SPRETURNS -3*GARCHSTD

IS RISK PRICED OVER TIME?

WHEN RISK IS PREDICTED TO CHANGE, DO PRICES CHANGE?

When one asset is riskier than another, we will only buy it if it is less expensive (per dollar of expected payout).When an asset is predicted to be riskier in the future than it was in the past, its price should fall.Volatility news predicting higher future risks should be accompanied by falling prices.

ASYMMETRIC VOLATILITY

Volatility clustering means that large absolute returns today predict higher risk in the future.Rising volatility should mean lower prices. We call this asymmetric volatility.Bad news today will predict higher volatility and hence especially negative returns.Good news will have offsetting effects.

ASYMMETRIC VOLATILITY

Price declines today are associated with higher volatility in the future than are price increases.Nelson and Zakoian

Volatility responds asymmetrically to price movesTARCH and EGARCH are popular specifications

ASYMMETRIC VOLATILITY

Positive and negative returns might have different weights. For example:

We typically find for equities that

1 1

2 21 1 0 2 1 0 1t tt t r t r th r I r I hω α α β

− −− > − < −= + + +

2 1 or equivalently >0α α γ>

1

2 21 1 0 1α γω β

−− − < −= + + +tt t t r th r r I h

NEWS IMPACT CURVE

TODAY’S NEWS = RETURNS

TOMORROWS VARIANCE

Other Asymmetric Models

EGARCH: NELSON(1989)

1

1

1

11)log()log(

−

−

−

−− +++=

t

t

t

ttt h

rhrhh γαβω

NGARCH: ENGLE(1990)1

21 )( −− +−+= ttt hrh βγαω

PARTIALLY NON-PARAMETRICENGLE AND NG(1993)

NEWS

VOLATILITY

ESTIMATE TARCH MODEL

VARIABLE COEF STERR T-STAT

C 1.68E-06 2.58E-07 6.519983

RESID(-1)^2 0.005405 0.008963 0.60306

RESID(-1)^2*(RESID(-1)<0) 0.123800 0.010668 11.6048

GARCH(-1) 0.918895 0.008211 111.9126

TARCH STANDARD DEVIATIONS

.000

.005

.010

.015

.020

.025

.030

.035

95 96 97 98 99 00 01 02 03 04

DJSDGARCH DJSDTARCH

TARCH STANDARD DEVIATIONS

.000

.005

.010

.015

.020

.025

.030

.035

.000 .005 .010 .015 .020 .025 .030

DJSDGARCH

DJS

DTA

RC

H

FINANCIAL RISK TODAY

Most people believe that financial markets today are very risky

Massive budget deficitsBalance of payments deficitExpensive War going badlyChinese ownership of vast US debtHigh energy pricesToo many hedge funds

WHAT WE OBSERVE

RECORD LOW VOLATILITY OF AGGREGATE EQUITY PRICES

S&P 500EUROPEAN EQUITY MARKETSASIAN EQUITY MARKETSGARCH PREDICTIONSVIX

0

10

20

30

40

50

600

800

1000

1200

1400

1600

2000 2001 2002 2003 2004 2005 2006

S P C L O S E S P VO L VIXC L O S E

MAY 10,2007

SINCE JAN 2007

4

8

12

16

20

24

1360

1400

1440

1480

1520

2007M01 2007M02 2007M03 2007M04

S P C L O S E S P V O L V IX C L O S E

EUROPE

-.12

-.08

-.04

.00

.04

.08

1990 1992 1994 1996 1998 2000 2002 2004 2006

DAX

-.12

-.08

-.04

.00

.04

.08

1990 1992 1994 1996 1998 2000 2002 2004 2006

SMI

EURONEXT

-.08

-.04

.00

.04

.08

1990 1992 1994 1996 1998 2000 2002 2004 2006

CAC

-.08

-.04

.00

.04

.08

1990 1992 1994 1996 1998 2000 2002 2004 2006

AEX

ASIA

100

200

300

400

500

-.15

-.10

-.05

.00

.05

.10

1999 2000 2001 2002 2003 2004 2005

KOREA KOREARET

10

20

304050

-.10

-.05

.00

.05

.10

.15

1999 2000 2001 2002 2003 2004 2005

CHINA CHINARET

AUSTRALIA

1000

2000

3000

4000

5000

6000

7000

-.08

-.04

.00

.04

.08

1990 1992 1994 1996 1998 2000 2002 2004 2006

AO R D C L O S E R AO R D

2000

3000

4000

5000

6000

7000

-.04

-.02

.00

.02

.04

2002 2003 2004 2005 2006

AORDCLOSE RAORD

SHANGHAI A SHARES

500100015002000250030003500

-.10

-.05

.00

.05

.10

.15

2000 2001 2002 2003 2004 2005 2006

SHANG HAI RSHANG HAI

A SOLUTION

RISK IS LOW IN THE SHORT RUN BUT HIGH IN THE LONG RUN

THERE IS A TERM STRUCTURE OF RISK

.12

.16

.20

.24

.28

.32

.36

.40

.44

1999 2000 2001 2002

IMP30 IMP547

SPX AT-THE-MONEY IMPLIEDS FOR 1M AND 2Y

.08

.10

.12

.14

.16

.18

.20

.22

04M04 04M07 04M10 05M01 05M04

IMP30 IMP547

SPX AT-THE-MONEY IMPLIED VOLS 1M AND 2Y

WHAT ARE THE IMPLICATIONS?

SOME INVESTORS WILL INVEST HEAVILY NOW BECAUSE SHORT RUN RISK IS LOW.MORE SOPHISTICATED INVESTORS WILL BE MORE CAUTIOUS BECAUSE RISING RISK WILL LOWER THE VALUE OF SHARES JUST WHEN THE MANAGER WANTS TO SELL THEM.

IF LONG RUN RISKS ARE PRICED

Then asset prices are now lower as a consequence of the long run riskNew information on the long run risk will influence returnsLow volatility simply means that we have little information on the long run risksEventually, as the risks approach, market volatility will rise.

WHAT DETERMINES LONG RUN RISK?

A RECENT STUDY BY GONZALO RANGEL AND MYSELF FOR 50 COUNTRIES FROM 1990-2005 FOUND SOME INTERESTING ANSWERS.WHAT MAKES FINANCIAL MARKET VOLATILITY HIGH?

MULTIPLE REGRESSIONS

0

0.05

0.1

0.15

0.2

0.25

1990 1994 1998 2002

Time EffectsAll Countries

emerging 0.0376( 0.0131 )**

transition -0.0178( 0.0171 )

log(mc) -0.0092( 0.0055 )*

log(gdpus) 0.0273( 0.0068 )**

nlc -1.8E-05( 5.4E-06 )**

grgdp -0.1603( 0.1930 )

gcpi 0.3976( 0.1865 )**

vol_irate 0.0020( 0.0008 )**

vol_gforex 0.0222( 0.0844 )

vol_grgdp 0.8635( 0.1399 )**

vol_gcpi 0.9981( 0.3356 )**

VERY LONG RUN RISKS!DO THESE HAVE ANY EFFECT?

VERY LONG RUN RISKS

CLIMATE CHANGE

PUBLIC PENSION FUND SOLVENCY

BOTH OF THESE ISSUES WILL REQUIRE TAXES AND EXPENDITURES AT SOME TIME IN THE FUTURE.PRESUMABLY BOTH ARE RESPONSIBLE FOR SOME REDUCTION IN ASSET PRICES TODAY AND INVESTOR CAUTION.

A PROPOSED SOLUTION

The best solution to climate change is a comprehensive tax on carbon emissions.

Only if it is comprehensive will it encourage alternative energy solutionsOnly if it is comprehensive will efforts to avoid the tax be socially beneficial.

But is it politically and economically possible?

SOLVE BOTH PROBLEMS AT ONCE!!

Establish a fund as many countries have done to support long run social costs such as retirementFund it with a carbon tax.Both risks are reduced as they offset each other.Tax a “bad” rather than income or other “good”.Delay implementation to reduce initial impact but still get benefit.

CONCLUSION

Make sure you take only the risks you intend to take

Keep an eye on long run risks as well as long run returns

Reducing long run risks gives benefits today