1. Robert Engle and Jose Gonzalo Rangel NYU and UCSD
Spline Garch as a Measure of Unconditional Volatility and its Global Macroeconomic Causes
Robert Engle and Jose Gonzalo Rangel
NYU and UCSD

2. GOALS ESTIMATE THE DETERMINANTS OF GLOBAL EQUITY VOLATILITY
How are long run volatility forecasts affected by macroeconomic conditions?
What volatility can be expected for a newly opened financial market?
MEASURE AND MODEL CHANGING UNCONDITIONAL VOLATILITY

3. WHAT MOVES ASSET PRICES AND VOLATILITY?
NEWS vs OTHER THINGS
RESEARCH STRATEGIES
VOLATILITY MODELS
e.g.Officer(1973), Schwert(1989)
ANNOUNCEMENT + NEWS MODELS
e.g.Roll(1988), Cutler Poterba and Summers(1990)
In all cases, macro effects appear small

4. A MODEL CAMPBELL(1991), CAMPBELL& SHILLER(1988) LOG LINEARIZATION
Decompose into Innovations to the present discounted value of future dividends or expected returns

5. MULTIPLICATIVE EFFECTS
The impact of a news event may depend upon the macro economy.
Eg. News about a firm will have a bigger effect in a recession or close to bankruptcy

6. NEWS EVENTS Return is a function of news times its impact
e = observable news
z = macro or deterministic events
if news is not observable, then there is just an innovation, u

7. NEWS VARIANCE
The variance of the news also depends upon macro and other deterministic elements both through the intensity and the magnitude of the news.

8. REALIZED VARIANCE
Realized Variance is the unconditional variance plus an error. Assuming mean zero returns:

9. HISTORY OF THE US EQUITY MARKET VOLATILITY: S&P500
PLOT PRICES AND RETURNS
HOW MUCH DO RETURNS FLUCTUATE?

14. MEAN REVERSION QUOTES “Volatility is Mean Reverting”
no controversy
“The long run level of volatility is constant”
very controversial
“Volatility is systematically lower now than it has been in years”
Very controversial. Cannot be answered by simple GARCH

15. DEFINITIONS
rt is a mean zero random variable measuring the return on a financial asset
CONDITIONAL VARIANCE
UNCONDITIONAL VARIANCE

16. GARCH(1,1)
The unconditional variance is then

17. GARCH(1,1) If omega is slowly varying, then
This is a complicated expression to interpret

18. SPLINE GARCH Instead, use a multiplicative form
Tau is a function of time and exogenous variables

19. UNCONDITIONAL VOLATILTIY
Taking unconditional expectations
Thus we can interpret tau as the unconditional variance.

20. SPLINE
ASSUME UNCONDITIONAL VARIANCE IS AN EXPONENTIAL QUADRATIC SPLINE OF TIME
For K knots equally spaced

21. ESTIMATION FOR A GIVEN K, USE GAUSSIAN MLE
CHOOSE K TO MINIMIZE BIC FOR K LESS THAN OR EQUAL TO 15

22. EXAMPLES FOR US SP500 DAILY DATA FROM 1963 THROUGH 2004
ESTIMATE WITH 1 TO 15 KNOTS
OPTIMAL NUMBER IS 7

23. RESULTS LogL: SPGARCH Method: Maximum Likelihood (Marquardt)
Date: 08/04/04 Time: 16:32
Sample:
Included observations: 12455
Evaluation order: By observation
Convergence achieved after 19 iterations
Coefficient Std. Error z-Statistic Prob.
C(4) E
W(1) -1.89E E
W(2) 2.71E E
W(3) -4.35E E
W(4) 3.28E E
W(5) -3.98E E
W(6) 6.00E E
W(7) -8.04E E
C(5)
C(1)
C(2)
Log likelihood Akaike info criterion
Avg. log likelihood Schwarz criterion
Number of Coefs Hannan-Quinn criter

31. PATTERNS OF VOLATILITY
ASSET CLASSES
EQUITIES
EQUITY INDICES
CURRENCIES
FUTURES
INTEREST RATES
BONDS
PUT TOGETHER AN EVIEWS WORKFILE WITH ALL SIX TYPES OF ASSET CLASSES. FOR THE BONDS USE A LONG BOND YIELD SO THAT PRICE IS COUPON/YIELD. THEN FIGURE OUT RETURN. SIMILARLY FOR SHORT TERM INTEREST RATES – APPROXIMATELY TAKE FIRST DIFFERENCES. SHOULD I THINK ABOUT THE VOLATILITY OF PRICE DIFFERENCES VS LOG DIFFERENCES?

32. VOLATILITY BY ASSET CLASS

34. PATTERNS OF EQUITY VOLATILITY
COUNTRIES
DEVELOPED MARKETS
EUROPE
TRANSITION ECONOMIES
LATIN AMERICA
ASIA
EMERGING MARKETS
Calculate Median Annualized Unconditional Volatility using daily data

38. MACRO VOLATILITY
Macro volatility variables measure the size of the surprises in macroeconomic aggregates over the year.
If y is the variable (cpi, gdp,…), then:

42. EXPLANATORY VARIABLES

43. ESTIMATION
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

44. ONE VARIABLE REGRESSIONS

45. MULTIPLE REGRESSIONS

47. CPI VOLATILITY T-STAT

48. DROP ARGENTINA?
OUTLIER?
HIGHLY INFORMATIVE?
ESTIMATE BOTH WAYS.

49. PANEL ESTIMATE RANDOM COUNTRY EFFECTS AR(1) DYNAMIC COUNTRY EFFECTS
TIME FIXED EFFECTS

51. ANNUAL REALIZED VOLATILITY

53. CONCLUSIONS AND IMPLICATIONS
Unconditional volatility changes in systematic ways.
Macro volatility and growth are important determinants of financial volatility.
Unconditional volatility and realized volatility give similar results but the former fits better.
Big swings in financial volatility are common across the globe.