DOWNSIDE RISK AND LONG TERM INVESTING ROBERT ENGLE NYU 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.

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?

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.

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

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

CONFIDENCE INTERVALS

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 data The 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 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 correlations Berd, 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 Zakoian Volatility 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

MSCI ITALY EWI: Nov 21, 2007

AUSTRIA MSCI : EWO: Nov 21, 2007

MSCI EAFA: EFA: Nov 21, 2007

ALL GARCH VOLATILITIES

ALL GARCH VOLATILITIES 2007

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 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 data Some inappropriate or fraudulent lending Securitization 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 deficits Balance of payments deficit Expensive War going badly Chinese ownership of vast US debt High energy prices Too 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 retirement Fund 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 Studies Engle and Rangel(2007), “The Factor Spline GARCH model for high and low frequency correlations” NYU Discussion Paper Engle(2007) “High Dimension Dynamic Correlations” forthcoming in Volume in honor of David Hendry Berd, Engle and Voronov(2007) "Underlying Dynamics of Credit Correlations," Journal of Credit Risk