1. Evidences of Risk-Return Trade-Off in IBOVESPA Using High Frequency Data Breno Pinheiro Néri bneri@fgvmail.br www.fgv.br/aluno/bneri Hilton Hostalácio Notini hilton@fgvmail.br Escola de Pós-Graduação em Economia Fundação Getúlio Vargas

2. June 25, 2015 Risk-Return Trade-Off2 ICAPM Introduction Omnibus Definitions Data Results Merton (1973)

3. June 25, 2015 Risk-Return Trade-Off3 Actually, is there a trade-off? Introduction Omnibus Definitions Data Results  Positive but not statistically significant:  Baillie and DeGennaro (1990)  French, Schwert and Stambaugh (1987)  Campbell and Hentschel (1992)  Negative and statistically significant:  Campbell (1987)  Nelson (1991)  Depends on the method:  Glosten, Jagannathan and Runkle (1993)  Harvey (2001)  Turner, Startz and Nelson (1989)

4. June 25, 2015 Risk-Return Trade-Off4 Mixed Data Sampling (MIDAS) Introduction Omnibus Definitions Data Results Ghysels, Santa-Clara and Valkanov (2002)

5. June 25, 2015 Risk-Return Trade-Off5 Note on notation Introduction Omnibus Definitions Data Results

6. June 25, 2015 Risk-Return Trade-Off6 Note on notation Introduction Omnibus Definitions Data Results

7. June 25, 2015 Risk-Return Trade-Off7 High Frequency Data Introduction Omnibus Definitions Data Results  São Paulo Stock Exchange Index (IBOVESPA)  01/02/1998 – 07/19/2001 (T=867)  Russian and Latin American crises, 1998  Blast of the technology-stock market bubble, 1999  10h00 – 18h15, each 15 min  Max N t =34  Typical values: 29 – 33  350 days (more than 40%) with 29 observations  Total of observations: 26,030

8. June 25, 2015 Risk-Return Trade-Off8 Histogram of N Introduction Omnibus Definitions Data Results

9. June 25, 2015 Risk-Return Trade-Off9 Typos Treating Introduction Omnibus Definitions Data Results  Inverted Digits: 48xx.xx -> 84xx.xx  Missing Digits: 14xx.xx -> 174xx.xx  Missing Decimal Point: 10xxxxx -> 10xxx.xx  Atypical Digit: 67xx.xx -> 97xx.xx

10. June 25, 2015 Risk-Return Trade-Off10 Unit Root ADF test Introduction Omnibus Definitions Data Results SeriesTest StatisticP-Value P 1,t -1.50620.7873 P Nt,t -1.52780.7782 R t+1 -8.2384<0.01 Rt*Rt* -8.5292<0.01 [σ]t2[σ]t2 -5.8074<0.01 [σ]t[σ]t -4.6115<0.01

11. June 25, 2015 Risk-Return Trade-Off11 Descritive Statistics Introduction Omnibus Definitions Data Results SeriesR t+1 Rt*Rt* [σ]t2[σ]t2 [σ]t[σ]t Mean0.00030.00020.00050.0195 Variance0.00800.0078<0.00010.0014 Skewness1.14991.20146.93873.1003 Excess Kurtosis15.937317.540666.787214.3488 Minimum-0.1723 <0.00010.0048 1 st Quartil-0.0144-0.01380.00020.0128 Median0.00070.00000.00030.0163 3 rd Quartil0.01470.01400.00050.0219 Maximum0.28820.29190.01390.1178 Observations866867

12. June 25, 2015 Risk-Return Trade-Off12 Histograms Introduction Omnibus Definitions Data Results

13. June 25, 2015 Risk-Return Trade-Off13 No Serial Correlation Introduction Omnibus Definitions Data Results RegressionR t+1 =β 0 +β 1 R t +ε t+1 R t * =β 0 +β 1 R t-1 * +ε t F-Statistic (P-Value)0.309 (0.579)0.003 (0.960) OLS Estimatorβ0β0 β1β1 β0β0 β1β1 Estimative0.0000.0190.000-0.002 Standard Error0.0010.0340.0010.034 T-Statistic0.3060.5560.125-0.051 P-Value0.7600.5780.9000.960

14. June 25, 2015 Risk-Return Trade-Off14 Risk-Return Trade-Off Introduction Omnibus Definitions Data Results RegressionR t+1 =β 0 +β 1 [σ] t 2 +ε t+1 R t+1 =β 0 +β 1 [σ] t +ε t+1 F-Statistic (P-Value)8.181 (0.004)5.294 (0.022) OLS Estimatorβ0β0 β1β1 β0β0 β1β1 Estimative-0.0012.876-0.0030.188 Standard Error0.0011.0060.0020.082 T-Statistic-1.0762.860-1.8032.301 P-Value0.2820.0040.0720.022

15. June 25, 2015 Risk-Return Trade-Off15 Risk-Return Trade-Off Introduction Omnibus Definitions Data Results RegressionR t * =β 0 +β 1 [σ] t-1 2 +ε t R t * =β 0 +β 1 [σ] t-1 +ε t F-Statistic (P-Value)7.725 (0.006)4.918 (0.027) OLS Estimatorβ0β0 β1β1 Β0Β0 β1β1 Estimative-0.0012.765-0.0040.179 Standard Error0.0010.9950.0020.081 T-Statistic-1.2152.779-1.8362.218 P-Value0.2250.0060.0670.027

16. June 25, 2015 Risk-Return Trade-Off16 Risk-Return Trade-Off Introduction Omnibus Definitions Data Results Regressions 1 and 2R t+1 =β 0 +β 1 [σ] t-1 2 +ε t+1 R t * =β 0 +β 1 [σ] t-2 2 +ε t F-Statistic (P-Value)18.270 (0.000)18.320 (0.000) OLS Estimatorβ0β0 β1β1 Β0Β0 β1β1 Estimative-0.0024.276-0.0024.234 Standard Error0.0011.0000.0010.989 T-Statistic-1.7624.275-1.9444.280 P-Value0.0780.0000.0520.000

17. June 25, 2015 Risk-Return Trade-Off17 Analyses of Residuals Introduction Omnibus Definitions Data Results

18. June 25, 2015 Risk-Return Trade-Off18 Other Analyses Introduction Omnibus Definitions Data Results  We cannot reject (even at 10%) the Ljung-Box and the Box-Pierce tests for independence of the residuals.  Regression of the residuals on its lags are not significant.  Regression of the residuals on the square of its lags are not significant (no ARCH effect).  We reject, at 5%, Teräsvirta and White neural-network tests for nonlinearity.  Information Criteria: two covariates, maximum.  No correlation between R t+1 e R t * nor R t e R t+1 *.

19. June 25, 2015 Risk-Return Trade-Off19 Leverage Effect Introduction Omnibus Definitions Data Results Regression[σ] t+1 =β 0 +β 1 I{R t <0}+ε t+1 [σ] t+1 =β 0 +β 1 I{R t * <0}+ε t+1 F-Statistic (P-Value)21.070 (0.000)17.330 (0.000) OLS EstimatorΒ0Β0 β1β1 Β0Β0 β1β1 Estimative0.0180.0040.0180.003 Standard Error0.001 T-Statistic32.0304.59031.9904.163 P-Value0.000

20. June 25, 2015 Risk-Return Trade-Off20 Conclusion  It has been difficult to find a positive correlation between risk and return in the literature.  MIDAS Regression has been used to find this correlation.  In Brazil, we could find this trade-off by applying OLS to high frequence data.  This maybe due to both the lack of liquidity and the lack of access to intra day data.  The leverage effect is also present.  Next step: is it possible to beat IBOVESPA using this correlation?

21. Thank you! Breno Pinheiro Néri bneri@fgvmail.br www.fgv.br/aluno/bneri Hilton Hostalácio Notini hilton@fgvmail.br Escola de Pós-Graduação em Economia Fundação Getúlio Vargas