A Practical Guide to Volatility Forecasting in a Crisis

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1 A Practical Guide to Volatility Forecasting in a Crisis Christian Brownlees Robert Engle Bryan Kelly Volatility NYU Stern Volatilities and Correlations in Stressed Markets April 3, 2009 BEK (2009) 1 / 18

2 Setting Introduction What is the best way to implement a recursive volatility forecasting strategy? Which models should we consider? How does forecasting ability vary across different horizons?... and... How did these models perform in Fall 08? Did these models predict what we have seen? BEK (2009) 2 / 18

3 Status Questionis Introduction Relatively large literature on (volatility) forecast evaluation Andersen and Bollerslev (1998), Hansen and Lunde (2005), Hansen and Lunde (2006), Patton (2009), Sheppard and Patton (2009) Relatively small literature on multi step ahead forecasting ability Christoffersen and Diebold (2000), Ghysels et al. (2009) In Fall 08 big drop in forecasting performance comes from forecasting volatility over longer horizons! BEK (2009) 3 / 18

4 Approach Introduction Detailed S&P 500 volatility forecasting exercise. We use battery of different volatility forecasting methods in order to 1 assess which model/forecasting design option works best and 2 analyze predictive ability across different horizons. Summary evidence from other asset classes: Equity Sectors, International Equities, Exchange Rates BEK (2009) 4 / 18

5 Findings Introduction Identify which models and ingredients lead to successful volatility forecasting performance. Best forecasting recipe persists across forecasting horizons. The recent episodes of extreme volatility do not change our conclusions and may not be as extreme as one might think. BEK (2009) 5 / 18

6 Forecasting Design Forecasting Design Methods: Model: GARCH, TGARCH, EGARCH, APARCH Error Distribution: Normal or Student t Estimation Window: 2y, 4y, 8y, all Estimation Update Frequency: daily, weekly, monthly we consider all 96 = ( ) combinations Predictions: Horizons: 1 day, 1 week, 2 weeks, 3 weeks, 1 month Sample Period: Forecast: January 2001 to December 2008 Initial Training: January 1990 to December 2000 BEK (2009) 6 / 18

7 Forecasting Design Forecast Evaluation Let ˆσ 2 be a variance proxy and h and the variance forecast. We evaluate forecasts using the Quasi Likelihood loss QLike(ˆσ 2, h) = ˆσ2 h log ˆσ2 h 1 We focus on predicting the cumulative τ horizon variance τ ht τ = i=1 h t+i t We employ both realized volatility and squared returns as proxies. τ τ ˆσ rv 2 τ t = c adj rt+i 2 j ˆσ2 r2 τ t = rt+i 2 i=1 intra daily return frequency: 5 minutes j BEK (2009) 7 / 18 i=1

8 QLike Loss Forecasting Design QLike has several appealing properties: robust (Patton (2009), scale invariant, iid under correct specification (if τ = 1). BEK (2009) 8 / 18

9 Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 Predicting S&P500 Volatility from 2001 to 2008 BEK (2009) 9 / 18

10 Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 Predicting S&P500 Volatility from 2001 to 2008 BEK (2009) 9 / 18

11 Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 Error Distribution, Estimation Window, Frequency Error Distribution Window Student t assumption doesn t lead to better forecasts GARCH often does well with small forecasting windows. Asymmetric Specifications the more data the better. APARCH poor performance with short estimation windows. Frequency The more frequent the updating, the better the predictions. BEK (2009) 10 / 18

12 Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 A Closer Look at TGARCH horizon 1 d 1 w 2 w 3 w 1 m Small Medium Large All Monthly Weekly Daily Normal Student t Bigger is Better (Losses are relative to 60 days rolling variance) BEK (2009) 11 / 18

13 What Model? Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 QLike Loss Realized Volatility Full Sample horizon 1 d 1 w 2 w 3 w 1 m GARCH TGARCH EGARCH APARCH Sept Dec 08 horizon 1 d 1 w 2 w 3 w 1 m GARCH TGARCH EGARCH APARCH Bigger is Better (Losses are relative to 60 days rolling variance) BEK (2009) 12 / 18

14 What Model? Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 QLike Loss Squared Returns Full Sample horizon 1 d 1 w 2 w 3 w 1 m GARCH TGARCH EGARCH APARCH Sept Dec 08 horizon 1 d 1 w 2 w 3 w 1 m GARCH TGARCH EGARCH APARCH Bigger is Better (Losses are relative to 60 days rolling variance) BEK (2009) 13 / 18

15 QLike Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 Jan 01 Aug 08 Sept Dec 08 BEK (2009) 14 / 18

16 Empirical Findings Predicting S&P500 Volatility from 2001 to 2008 Predictive Ability Across Horizons: Patterns Jan 01 Aug 08 Forecasting ability hardly deteriorates as the horizon increases. Dispersion between different losses decreases with the horizon. Sept Dec 08 Deterioration in forecasting ability is pronounced. At a 1 day horizon out of sample loss is not far from normal times. Dispersion between different losses increases with the horizon. Even if predictive ability deteriorates, large relative gains can be obtained by picking up the right forecasting method. BEK (2009) 15 / 18

17 Other Asset Classes Empirical Findings What happens to other assets? SPDR Equity Sectors Jan 01 Aug 08 Sept 08 Dec 08 horizon 1d 1w 2w 3w 1m 1d 1w 2w 3w 1m GARCH TGARCH EGARCH APARCH XLF, XLE, XLI, XLK, XLV International Equities horizon 1d 1w 2w 3w 1m 1d 1w 2w 3w 1m GARCH TGARCH EGARCH APARCH MSCIWRLD, MSCIBRIC, MSCIEM, MSCIDE, MSCIHK FX horizon 1d 1w 2w 3w 1m 1d 1w 2w 3w 1m GARCH TGARCH EGARCH APARCH USD2GBP, USD2YEN, USD2EUR, USD2SFR, USD2SID Smaller is Better BEK (2009) 16 / 18

18 Did we predict this? Empirical Findings What happens to other assets? Consider the in sample Forward QLike loss QLike(σ 2 t+τ, h t+τ t ) on the S&P 500 between 1927 to 2008 (TGARCH / Student Innovations) What are the means of the QLike losses accros horizons? horizon 1d 1w 2w 3w 1m How frequent are the Fall 08 losses? horizon 1d 1w 2w 3w 1m Historical Simulated BEK (2009) 17 / 18

19 Conclusions Empirical Findings Conclusions We ve engaged a forecasting exercises aiming at finding successful ingredients for volatility forecasting at different horizons with a special focus on the recent period financial distress. Results show that Best forecasting recipe persists across forecasting horizons. Recent period of financial distress has deteriorated volatility prediction at long horizons but most ARCH specification did not performed badly at short horizons. BEK (2009) 18 / 18

Amath 546/Econ 589 Univariate GARCH Models: Advanced Topics

Amath 546/Econ 589 Univariate GARCH Models: Advanced Topics Eric Zivot April 29, 2013 Lecture Outline The Leverage Effect Asymmetric GARCH Models Forecasts from Asymmetric GARCH Models GARCH Models with