News - Good or Bad - and Its Impact On Volatility Predictions over Multiple Horizons

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News - Good or Bad - and Its Impact On Volatility Predictions over Multiple Horizons Authors: Xilong Chen Eric Ghysels January 24, 2010 Version

Outline 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Introduciton 1 Motivation: Examine whether the sign and magnitude of intro-daily returns have impact on expected volatlity the next day or over the longer future horizons. 2 Contributions: HAR-S-RV-J: introduce a new model that includes asymmetries in terms of semi-variances. Introduce a new class of semi-parametric/parametric models aplicable to a mixture of high and low frequency data which feature asymmetries. Asymmetry matters for volatility forecasting. Models using intra-daily returns outperform models with daily realized variance and semi-variance measures in terms of out-of-sample forecasting.

Introduciton 1 Motivation: Examine whether the sign and magnitude of intro-daily returns have impact on expected volatlity the next day or over the longer future horizons. 2 Contributions: HAR-S-RV-J: introduce a new model that includes asymmetries in terms of semi-variances. Introduce a new class of semi-parametric/parametric models aplicable to a mixture of high and low frequency data which feature asymmetries. Asymmetry matters for volatility forecasting. Models using intra-daily returns outperform models with daily realized variance and semi-variance measures in terms of out-of-sample forecasting.

pected impact on tomorrow s volatility (with confidence bands) - scaled by lized volatility. The pattern that emerges is interesting. Good news reduces cted volatility, i.e. the expected impact dips below zero. 2 In contrast, very Main Results to increase volatility, as does bad news. This asymmetric pattern has been e past, notably by Engle and Ng (1993). However, here we can carry this fferent horizons using high frequency intra-daily data. Moderate good (intra-daily) news reduce Impact on Tomorrow s RV 4 SP CI of SP 3.5 3 2.5 2 1.5 1 volatility ( the next day ), while both very good news (unusual high intro-daiy positive returns ) and bad news (negative returns) increase volatility, with the latter having a more severe impact. The asymmetries disappear over longer horizons. 0.5 0 0.2 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 S&P 500 Future Market 5 minute Return 2007-2008 crisis. lso reveals that we are essentially dealing with two issues: mis-specification. Mis-specification, because measures of quadratic variation are based on Models featuring asymmetries dominate in terms of out-of-sample forecasting performance, especially during the

Outline Introduction 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Realized Variance (RV): t+k RV t,t+k ( 1 ) j=t 1 i=1 r 2 j,i r j,i : the log asset price difference(return) over short time interval i of length on day j. Bi-power Variation (BPV): t+k BPV t,t+k ( 1 ) r j,i r j,(i 1) j=t 1 i=2

Realized Variance (RV): t+k RV t,t+k ( 1 ) j=t 1 i=1 r 2 j,i r j,i : the log asset price difference(return) over short time interval i of length on day j. Bi-power Variation (BPV): t+k BPV t,t+k ( 1 ) r j,i r j,(i 1) j=t 1 i=2

Semi-variance: t+k SemiV + t+k,t j=t 1 i=1 r 2 j,i 1 r j,i >0 SemiV t+k,t RV t+k,t SemiV + t+k,t

Outline Introduction 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Models with Daily Volatility Generic Equation: τ RV t,t+1 = ψ 0 + ψ j (θ)rv t j 1,t j + ɛ t,t+1 j=0 HAR-RV (HAR: Heterogeneous Autoregressive): RV t,t+k = ψ 0 + ψ D RV t 1,t + ψ W RV t 5,t + ψ M RV t 22,t + ɛ t,t+k

Models with Daily Volatility Generic Equation: τ RV t,t+1 = ψ 0 + ψ j (θ)rv t j 1,t j + ɛ t,t+1 j=0 HAR-RV (HAR: Heterogeneous Autoregressive): RV t,t+k = ψ 0 + ψ D RV t 1,t + ψ W RV t 5,t + ψ M RV t 22,t + ɛ t,t+k

Models with Daily Volatility (cont.) HAR-RV-J (J: Jump): RV t,t+k = ψ 0 + ψ D BPV t 1,t + ψ W BPV t 5,t +ψ M BPV t 22,t + ψ J J t + ɛ t,t+k HAR-S-RV-J (S: Semi): RV t,t+k = ψ 0 + ψ + D SemiV + t 1,t + ψ D SemiV t 1,t +ψ + W SemiV + t 5,t + ψ W SemiV t 5,t +ψ + M SemiV + t 22,t + ψ M SemiV t 22,t +ψ J J t + ɛ t,t+k

Models with Daily Volatility (cont.) HAR-RV-J (J: Jump): RV t,t+k = ψ 0 + ψ D BPV t 1,t + ψ W BPV t 5,t +ψ M BPV t 22,t + ψ J J t + ɛ t,t+k HAR-S-RV-J (S: Semi): RV t,t+k = ψ 0 + ψ + D SemiV + t 1,t + ψ D SemiV t 1,t +ψ + W SemiV + t 5,t + ψ W SemiV t 5,t +ψ + M SemiV + t 22,t + ψ M SemiV t 22,t +ψ J J t + ɛ t,t+k

Models with Intro-daily Returns: Semi-parametric SP: Semi-parametric MIDAS regression τ 1 RV t,t+1 = ψ 0 + ψ ij (θ)nic(r t j,i ) + ɛ t,t+1 j=1 i=1 MIDAS: MIxed DAta Sampling ψ ij (θ): polynomial lag structure parameterized by θ NIC(.): the news impact curve Semi-parametric: a parametric estimation of ψ ij (θ) and a non-parametric NIC(.) SP model nests the generic equation when setting ψ ij = ψ i j = 1,..., 1, and NIC(r) r 2

Models with Intro-daily Returns: Parametric SYMM: Symmetric NIC NIC(r) = br 2 ASYMGJR: Asymmetric GJR NIC(r) = br 2 + cr 2 1 r<0 GJR Model: Glosten, Jagannathan, and Runkle(1993) ASYMLS: Asymmetric Location Shift NIC(r) = b(r c) 2

Models with Intro-daily Returns: Parametric SYMM: Symmetric NIC NIC(r) = br 2 ASYMGJR: Asymmetric GJR NIC(r) = br 2 + cr 2 1 r<0 GJR Model: Glosten, Jagannathan, and Runkle(1993) ASYMLS: Asymmetric Location Shift NIC(r) = b(r c) 2

Models with Intro-daily Returns: Parametric SYMM: Symmetric NIC NIC(r) = br 2 ASYMGJR: Asymmetric GJR NIC(r) = br 2 + cr 2 1 r<0 GJR Model: Glosten, Jagannathan, and Runkle(1993) ASYMLS: Asymmetric Location Shift NIC(r) = b(r c) 2

Polynomial lag structure ψ ij (θ) To Nest models based on RV and SP τ RV t,t+1 = ψ 0 + ψ j (θ)rv t j 1,t j + ɛ t,t+1 j=0 τ 1 RV t,t+1 = ψ 0 + ψ ij (θ)nic(r t j,i ) + ɛ t,t+1 j=1 i=1

Polynomial lag structure ψ ij (θ) (cont.) Let ψ ij (θ) ψj D (θ) ψi ID (θ) ψj D (θ): a daily weighting scheme ψi ID (θ): the intra-daily weights With equal intro-daily weights and quadratic NIC, the above two models are the same the authors adopt the following specification of polynomials ψ D j (θ) ψ ID i (θ) = Beta(j, τ, θ 1, θ 2 ) Beta(i, 1, θ 3, θ 4 )

Estimation Issues The top part of the table provides the details of the data used in our study. We an consist of intra-day returns of respectively Dow Jones and S&P 500 cash and futures 1 Estimation summarizes allof models, parametric showing models the equation numbers, the models acronyms and som specification appears in equation (3.1), namely: RV OLS for HAR-RV, HAR-RV-J, and HAR-S-RV-J t,t+1 = ψ 0 + τ j=1 [ 1 i=1 ψ ij(θ) wherenonlinear τ 1 j=1 i=1least ψ ij = squares 1 and NIC(r) for models stands for those news use impact intra-daily curve. returns, SYMM, ASYMGJR, and ASYMLS 2 Estimation of the semi-parametric MIDAS regression model and non parametric estimation of the NIC function 3 Data Table 1: Details of the Data Series and Model Acro Period Days Trading Hours (EST) Full Sample Dow Jones Cash DJC 04/01/1993 12/31/2008 3969 Futures DJF 10/06/1997 12/31/2008 2834 S&P 500 Cash SPC 09/30/1985 12/31/2008 5668 Futures SPF 04/21/1982 12/31/2008 6764 News Impact Acronym Explanation

Outline Introduction Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Table 2: Asymmetry and Parameter Estimates Is News Impact Asymmetric? ession appearing in (2.7) Volatility involving Measurement semi-variances. and Entries Model pertain Specifications to tests of the single restrictions Out-of-sample that either Forecasting the Performance mi-variances have equal coefficients. The final column contains Empirical a jointresults test of the null with all three restrictions. to compute the tests use HAC standard errors with lag lengths that Are the Forecasting Gains Statistically Significant? match the inference recommendations of iebold (2007). Panel B pertains to parametric models using intra-daily returns and featuring asymmetries. The er estimates of the lag polynomials involving parameters θ1 through θ4, see equation (3.2). The parameters a, b, impact, where c relates to asymmetries, since for the ASYMGJR model NIC(r) = (br 2 + c1r<0r 2 ), and for the (b(r c) 2 ). The parameter estimates are reported for one representative series, the S&P 500 Futures contract, at ast horizons. Entries in Panel A are p-values, since joint and single restriction tests feature different asymptotic e results in the table pertain to full sample estimates. The latter differ across series due to data availability - see Is News Impact Asymmetric using Semi-variances? ge... Panel A Regressors Daily Weekly Monthly Joint Dow Jones - Cash Horizon Daily 0.49 0.35 0.92 0.37 Weekly 0.06 0.29 0.01 0.00 Monthly 0.00 0.42 0.00 0.00 Dow Jones - Futures Daily 0.13 0.16 0.02 0.00 Weekly 0.09 0.01 0.66 0.00 Monthly 0.02 0.83 0.00 0.00 S&P Cash Daily 0.05 0.09 0.81 0.00 Weekly 0.16 0.41 0.04 0.00 Monthly 0.00 0.12 0.73 0.00 S&P Futures Daily 0.11 0.25 0.03 0.00 Weekly 0.00 0.02 0.12 0.00 Monthly 0.10 0.63 0.00 0.00 HAR-S-RV-J model Entries are p-values The first three columns test ψ + D = ψ D, ψ + W = ψ W, ψ+ M = ψ M, respectively. The final column reports joint tests. The daily lag coeffiecient do not seem to feature asymmetries for predicting future daily volatility, yet it does for weekly and monthly forecasts. The asymmetries are present at all forecast horizons based on the final column, except for DJC.

Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? Is News Impact Asymmetric using Intro-daily Returns? Table 2 continued Panel B θ1 θ2 θ3 θ4 a b c S&P 500 Futures Market - One-day horizon ASYMGJR 2.337e-014 3.051 1.360 1.955-0.008254-125.9 428.5 (std. dev.) (0.005456) (0.03413) (0.001195) (0.004495) (0.01655) (4.728) (10.08) ASYMLS 2.337e-014 1.974 1.239 2.825-39.18 67.61 0.7621 (std. dev.) (0.004674) (0.0215) (0.002814) (0.01108) (0.4254) (0.7221) (0.001995) S&P 500 Futures Market - One-week horizon ASYMGJR 0.6527 2.672 1.740 1.347-0.01653-272.3 727.2 (std. dev.) (0.02066) (0.1054) (0.01897) (0.01655) (0.02881) (16.51) (34.28) ASYMLS 1.614e-013 0.6246 78.65 148.1-0.08167 80.52 0.05015 (std. dev.) (0.01403) (0.01892) (1.300) (2.554) (0.02946) (1.580) (0.004611) RV t,t+1 = ψ 0 + τ j=1 1 i=1 ψ ij(θ)nic(r t j,i )+ ɛ t,t+1 ψ ij (θ) = Beta(j, τ, θ 1, θ 2 ) Beta(i, 1, θ 3, θ 4 ) ASYMGJR: NIC(r) = br 2 + cr 2 1 r<0 ASYMLS: NIC(r) = b(r c) 2 The intro-daily asymmetries is present based on the significance of parameter c.

isplay of 1 3 results, the news impact is scaled by0 the mean Introduction pact is in terms of fraction of average horizon volatility. 0 2 Volatility Measurement and Model 2 Specifications returns are displayed. They are: (a) Dow Jones Cash 1 0 Cash Market; and (d) S&P 500 Futures Market. The 1 4 a (A.15) appearing 2 in the Appendix. 0.15 0.1 0.05 0 0.05 0.1 0.15 0 43 0.15 0.1 0.05 0 0.05 0.1 0.15 Is News Impact Asymmetric? (cont.) 0.2 0.1 0 0.1 0.2 (b) 6 (c) 5 6 Weekly NIC (d) Weekly CI 46 5 Monthly NIC Monthly CI Daily NIC 3 5 4 Daily CI 2 4 3 1 03 2 1 1 2 2 0 0 1 0.2 0.1 0 0.1 Figure 0.2 3: One-week and one-month ahead news impact curves for semiparametric 1 1 and parametric MIDAS models 0 The plots represent estimates of semi-parametric and parametric news impact curves for different horizons. The results pertain to the S&P 500 Futures Market. Hence, the SP part is a repeat of plot (b) of Figure 2 2 and the confidence 2 bands are again computed according to formula (A.15) appearing in the Appendix. 0.15 0.1 0.05 0 0.05 0.1 0.15 0 0.05 0.15 0.15 0.2 0.1 0.05 0.1 (d) 0 0.1 0.1 0.2 (a) 6 6 5 Weekly NIC SP Weekly CI 5 CIs of SP ASYMGJR 4 ASYMLS 4 3 2 1 0 1 2 46 0.2 0.1 0 0.1 0.2 Impact on Next Week s RV 6 5 4 3 2 1 3 2 1 0 1 (d) Monthly NIC Monthly CI 0.15 0.1 0.05 0 0.05 0.1 0.15 S&P 500 Futures Market 5 minute Return Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? SPF news impact curve via the SP estimation. X-axis: annualized intra-daily returns. Y-axis: Impact on next day, week, and month s RV scaled by the mean of RV for each horizon. Daily and weekly NIC: asymmetry. Monthly NIC: symmetric. Bad news has more acute impact than positive news.

Outline Introduction Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? ut-of-sample performance of Semi-Parametric and Parametric MIDAS regression models s the out-of-sample MSFE the SP, i.e. the semi-parametric MIDAS model, and parametric models SYMM, ASYMGJR, nd models Out-of-sample that use daily volatility measures HAR-RV, Forecasting HAR-RV-J, and HAR-S-RV-J. Performance The MSFE of the SP model is the l other models are reported relative to the benchmark, namely values below one outperform the benchmark. We consider figurations, one ending in 2004 and out-of-sample appraisal 2005-2006, the other ending in 2006 and out-of-sample appraisal stands for Dow Jones Cash Market, DJF for Dow Jones Futures Market, SPC for S&P 500 Cash Market, and SPF for S&P rket. Out-of-sample Period One-day ahead forecasts One-week ahead forecasts DJC DJF SPC SPF DJC DJF SPC SPF Semi-Parametric Intra-daily returns SP 2005-2006 0.04 0.05 0.04 0.07 0.02 0.05 0.03 0.08 2007-2008 19.99 9.63 16.32 11.28 16.94 4.60 20.52 6.96 Parametric Intra-daily returns SYMM 2005-2006 1.00 1.00 1.00 0.57 1.50 1.40 0.67 0.25 2007-2008 0.95 1.10 1.79 2.88 0.79 1.19 0.60 3.67 ASYMGJR 2005-2006 0.75 0.60 075 0.72 1.00 1.40 0.67 0.25 2007-2008 0.95 1.41 1.11 1.29 0.67 1.11 0.42 6.72 ASYMLS 2005-2006 1.25 1.20 0.57 1.29 1.50 1.40 0.67 0.38 2007-2008 0.91 1.02 1.01 1.12 0.73 0.95 0.48 3.67 Parametric Daily Volatility Measures HAR-RV 2005-2006 1.25 1.00 1.75 0.57 3.00 1.60 3.00 0.63 2007-2008 1.04 1.13 1.08 1.17 1.06 1.17 0.59 1.00 HAR-RV-J 2005-2006 1.00 0.80 0.86 2.00 1.20 0.80 2.33 0.63 2007-2008 1.02 1.09 1.12 1.22 1.02 0.85 0.60 0.99 HAR-S-RV-J 2005-2006 1.00 0.60 1.00 0.43 1.50 0.40 1.00 0.50 2007-2008 1.08 0.98 1.02 1.04 1.03 0.84 0.53 0.97 MSFE m k = 1 N k Nk i=1 (um t+(i 1)k,t+ik) 2 u m t,t+k = RV t,t+k ˆ RV m t,t+k Out-of-sample MSFE of the SP model is the benchmark. Values below one outperform the benchmark. The level of MSFE are different. The best models always feature asymmetries, but not the same model.

Outline Introduction Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant? 1 Introduction 2 3 Is News Impact Asymmetric? Out-of-sample Forecasting Performance Are the Forecasting Gains Statistically Significant?

Table 5: Tests of Improved Predictability: HAR-S-RV-J Benchmark The table reports the conditional forecasting ability test Introduction of Giacomini and White for each model against the benchmark HAR-S-RV-J model Is News Impact Asymmetric? appearing Volatility in equation Measurement (2.7). The model andacronyms Model appear Specifications in lower panel of Table 1. The tests involve the sample MSFE appearing in equation (4.1), computed for each forecasting horizon k, Out-of-sample Forecasting Performance Empirical and each Results forecasting model/method m. The null hypothesis appears in equation (4.2) with instruments a constant and u b t k,t )2., The entries are test statistic will beare χ the Forecasting Gains Statistically Significant? 2 (1). DJC stands for Dow Jones Cash Market, DJF for Dow Jones Futures Market, SPC for S&P 500 Cash Market, and SPF for S&P 500 Futures Market. All entries are p-values. Whenever an entry is boldfaced, the benchmark model is better than the alternative model, implying that the benchmark model significantly outperforms the alternative model. Normal-faced entries with low p-values mean that the alternative model significantly outperforms the benchmark. The tests involve rolling 5-year samples for estimation and 2-year out-of-sample forecast performances rolling over one month at the time - starting with the 1997-2001 estimation sample. Are the Forecasting Gains Statistically Significant? One-day ahead forecasts One-week ahead forecasts One-month ahead forecasts DJC DJF SPC SPF DJC DJF SPC SPF DJC DJF SPC SPF Evaluation sample: 2001-2006 41 SYMM 0.00 0.00 0.00 0.00 0.01 0.16 0.10 0.14 0.21 0.26 0.18 0.13 ASYMGJR 0.00 0.00 0.00 0.00 0.01 0.11 0.01 0.03 0.19 0.19 0.19 0.13 ASYMLS 0.00 0.00 0.00 0.00 0.07 0.15 0.11 0.15 0.21 0.19 0.21 0.13 Evaluation sample: 2001-2008 SYMM 0.03 0.00 0.11 0.00 0.01 0.06 0.02 0.06 0.09 0.15 0.11 0.21 ASYMGJR 0.03 0.06 0.03 0.04 0.01 0.02 0.02 0.06 0.15 0.13 0.11 0.25 ASYMLS 0.02 0.00 0.04 0.09 0.02 0.07 0.03 0.06 0.11 0.14 0.12 0.26 Giacomini and White(2006) test: H 0 : E[((u b t,t+k) 2 (u m t,t+k) 2 ) I t 1 ] = 0 b: HAR-S-RV-J Benchmark; m: model m; I t 1 : information set(constant and (u b t k,t) 2 here); the test statistic will be χ 2 1 All entries are p-values. Boldfaced: the benchmark model id better than the alternative model. For one-day ahead forecasts: ASYMGJR outperform the benchmark for both periods; SYMM is inferior. Adding the crisis, the evidence weakens the evidence againest ASYMLS.

1 New impact curve is asymmetric for short term horizons and the asymmetries disappear over longer horizons. 2 Asymmetry matter for volatility forecasting. 3 Models using intra-daily returns outperfrom models with daily realized variance and semi-variance measures in terms of out-of-sample forecasting.

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