DOWNSIDE RISK AND LONG TERM INVESTING

ROBERT ENGLENYU STERN

2007

RISK

A Risk is a bad event that might occur in the future.

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

Finance investigates which risks are worth taking.

NOBEL ANSWERS

Markowitz (1952) and Sharpe(1964) and Tobin (1958) received Nobel awards in 1990 and 1981 for associating risk with the variance of financial returns.

Capital Asset Pricing Model or CAPM answer: Only variances that could not be diversified would be rewarded.

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

DOWNSIDE RISK

The risk of a portfolio is that its value will decline, hence DOWNSIDE RISK is a natural measure of risk.

Many theories and models assume symmetry: c.f. MARKOWITZ, TOBIN, SHARPE AND BLACK, SCHOLES, MERTON and Volatility based risk management systems.

Do we miss anything important?

MEASURING DOWNSIDE RISK

Many measures have been proposed.Skewness - a measure of asymmetry of returns

Value at Risk – number of $ that you can be 99% sure is worse than what you will lose in the next 10 days.

3/ 23 2Skewness= /E r E r

x is the Value at risk if P r x

PREDICTIVE DISTRIBUTION OF PORTFOLIO GAINS

1%$ GAINS ON PORTFOLIO

MULTIVARIATE DOWNSIDE RISK

WHAT IS THE LIKELIHOOD THAT A COLLECTION OF ASSETS WILL ALL DECLINE?

THIS DEPENDS PARTLY ON CORRELATIONS

FOR EXTREME MOVES, OTHER MEASURES ARE IMPORTANT TOO.

MULTIVARIATE DOWNSIDE

“Where are my correlations when I need them?” – a portfolio manager’s lament.When country equity markets decline together more than can be expected from the normal correlation pattern, it is called CONTAGION.Correlations and volatilities appear to move together.

MEASURING JOINT DOWNSIDE RISK

What is the probability that one asset will have a very bad return if another asset has a very bad return?

Tail dependence (lower tail dependence) is defined as the limit as this probability goes to zero. What is the probability that one asset has an extreme down move when another has an extreme down move?

Find x such that i iP r x

i i j j j j i iP r x r x P r x r x

DEFAULT CORRELATIONS

A default is a random event. We can define the correlation between two default events.

For extremes, the default correlation is the same as the tail dependence.

,

2

,

1

/ 1

i i j j

i i j j

Di j r x r x

r x r x

Corr I I

P I I

IMPLEMENTING THESE MODELS

PRACTITIONERS REQUIRED ESTIMATES OF VARIANCES AND COVARIANCES or VOLATILITIES AND CORRELATIONS

PRACTITIONERS REQUIRED METHODS TO COMPUTE VALUE AT RISK and DEFAULT CORRELATIONS

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?

VOLATILITY HISTORY

U.S. BROAD MARKET INDEX S&P500

RETURNS FROM Jan 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

90 91 92 93 94 95 96 97 98 99 00

SPCLOSE SP

800

1000

1200

1400

1600

-.08

-.04

.00

.04

.08

1998 1999 2000 2001 2002 2003

SP500 SPRETURNS

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.

ARCH/GARCH VOLATILITIES

.0

.1

.2

.3

.4

.5

1990 1992 1994 1996 1998 2000 2002

VOL_SP

CONFIDENCE INTERVALS

-.10

-.05

.00

.05

.10

1990 1992 1994 1996 1998 2000 2002

3*GARCHSTD SPRETURNS -3*GARCHSTD

THE ECONOMICS OF VOLATILITY

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?

WHY DO PRICES CHANGE?

BETTER ANSWER

Economic news on future values and risks moves prices

Volatility is the natural response of a financial market to new information.

This news arrives in clusters.

LONG RUN RISKS

Long episodes of high and low volatility are evident in the data

What determines these long run or low frequency risks?

One important measure is the flow of new information on the macro economy

WHAT DETERMINES LONG RUN RISK?

A RECENT STUDY BY GONZALO RANGEL AND MYSELF FOR 50 COUNTRIES FROM 1990-2005 FOUND SOME INTERESTING ANSWERS.

Forthcoming RFS 2008

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

WHAT MAKES CORRELATIONS HIGH?

Correlations generally rise when market volatility rises

Correlations within an industry or sector will generally rise when the volatility of that sector rises.

Thus falling markets and macro volatility predict higher correlations

See Engle and Rangel(2007) and Engle(2007) for evidence.

CDO PRICING

The value of tranches of collateralized debt obligations depend upon default correlations.Senior tranches become riskier when default correlations rise.Default correlations and tail dependence rise when market volatility rises just as do ordinary correlationsBerd, Engle, Voronov(2007) Journal of Credit Risk

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 today than it was yesterday, its price should fall.Volatility news predicting higher future risks should be accompanied by falling prices.

ASYMMETRIC VOLATILITY

Asset Price declines today predict higher volatility in the future than do equal price increases.

Nelson and ZakoianVolatility responds asymmetrically to price moves

TARCH and EGARCH are popular specifications

PRICING LONG RUN RISKS

When long run risks look greater, prices today are lower.

Solving long run risks will increase asset prices today

Macroeconomic policy is important

FINANCIAL RISKS TODAY

S&P 500 Nov 21, 2007

600

800

1,000

1,200

1,400

1,600

-.08

-.04

.00

.04

.08

00 01 02 03 04 05 06 07

ADJ_CLOSE SP

MSCI ITALY EWI: Nov 21, 2007

10

15

20

25

30

35

40

-.10

-.05

.00

.05

.10

.15

00 01 02 03 04 05 06 07

ADJ_CLOSE_EWI EWI

AUSTRIA MSCI : EWO: Nov 21, 2007

0

10

20

30

40

50

-.08

-.04

.00

.04

.08

00 01 02 03 04 05 06 07

ACLOSE_EW O EWO

MSCI EAFA: EFA: Nov 21, 2007

20

40

60

80

100

-.06

-.04

-.02

.00

.02

.04

.06

.08

2002 2003 2004 2005 2006 2007

ADJ_CLOSE_EFA EFA

ALL GARCH VOLATILITIES

.0

.1

.2

.3

.4

.5

2002 2003 2004 2005 2006 2007

VOLAUSTRIA VOLITALYVOLUS VOLEFA

ALL GARCH VOLATILITIES 2007

.05

.10

.15

.20

.25

.30

.35

.40

VOLAUSTRIA VOLITALYVOLUS VOLEFA

WHY ARE VOLATILITIES SO HIGH -- WILL THEY STAY HIGH?

For most assets, they are high relative to the last several years but not high relative to 2000-2002.

In the US, I think this is due A) Macroeconomic uncertainty

B) Credit problems particularly associated with subprime mortgages

MACROECONOMIC UNCERTAINTY

Will the housing slowdown bring a recession or will the export industries keep the economy growing?

Is recession or inflation the greater threat?

What will the FED do?

CREDIT INDUSTRY

Subprime mortgage holders generally expect some defaults. They are now predicted to be greater than historically observed. Why is this a surprise?

Our last housing crisis was in the early 90’s before subprime lending was important so there is little useful dataSome inappropriate or fraudulent lendingSecuritization of these contracts has made it difficult to know the risks. Senior tranches were rated AAA and are now downgraded.

A related argument applies to the large credit needs of private equity.

WHY WERE US VOLATILITIES SO LOW UNTIL SUMMER 2007?

MANY REASONS TO THINK THE RISKS WERE HIGH:

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

But volatility remained low because these risks were in the future and there was little information on their outcomes.

WERE WE PREPARED?

VERY LONG RUN RISKS!ARE WE READY FOR THESE?

TWO VERY LONG RUN RISKS

CLIMATE CHANGE

PUBLIC PENSION FUND SOLVENCY

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

A PROPOSED SOLUTION

Most Economists believe the best solution to climate change is a comprehensive tax on carbon emissions and other greenhouse gases.

Only if it is comprehensive will it encourage alternative energy solutions

Only if it is comprehensive will efforts to avoid the tax be socially beneficial.

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

Policy makers remember: reducing long run risks gives benefits today

REFERENCES

Engle and Rangel(2008) “The Spline Garch Model of Low Frequency Volatility and its Global Macroeconomic Causes”, forthcoming Review of Financial StudiesEngle and Rangel(2007), “The Factor Spline GARCH model for high and low frequency correlations” NYU Discussion PaperEngle(2007) “High Dimension Dynamic Correlations” forthcoming in Volume in honor of David HendryBerd, Engle and Voronov(2007) "Underlying Dynamics of Credit Correlations," Journal of Credit Risk