Lecture 1: Empirical Properties of Returns

Transcription

1 Lecture 1: Empirical Properties of Returns Econ 589 Eric Zivot Spring 2011 Updated: March 29, 2011 Daily CC Returns on MSFT -0.3 r(t)

2 Daily CC Returns on S&P Distribution of Daily CC Returns on MSFT Percent of Total Daily CC Returns on MSFT Sample Quantiles: min 1Q median 3Q max Sample Moments: mean std skewness kurtosis Number of Observations: x 2

3 Distribution of Daily CC Returns on S&P 500 Percent of Total Daily CC Returns on S&P 500 Sample Quantiles: min 1Q median 3Q max Sample Moments: mean std skewness kurtosis Number of Observations: x Normal QQ-Plot Test for Normality /26/ Daily CC Returns on MSFT 10/19/2000 Test for Normality: Jarque-Bera Null Hypothesis: data is normally distributed MSFT Test Stat p.value 0 Dist. under Null: chi-square with 2 degrees of freedom Total Observ.: /19/

4 QQ-Plot: Student-t with 4 degrees of freedom Daily CC Returns on MSFT /30/ /17/ /14/ Skew Normal Distribution shape=5 shape=-5 pdf pdf shape=0 shape=1000 pdf pdf ξ = 0, ω = 1 4

5 Skew t Distribution shape=5 shape=-5 St St pdft Sn pdft Sn shape=0 shape=1000 pdft St Sn pdft St Sn ξ = 0, ω = 1, ν = 5 QQ-Plot: MLE of Skew-t for MSFT location = -04, scale = 20, shape = 0.298, df = msft mle computed with R package sn, qqplot() from R package car st quantiles 5

6 Normal QQ-Plot Test for Normality Daily CC Returns on S&P /21/1987 Test for Normality: Jarque-Bera Null Hypothesis: data is normally distributed -5 10/26/ SP500 Test Stat p.value Dist. under Null: chi-square with 2 degrees of freedom Total Observ.: /19/ QQ-Plot: Student-t with 4 degrees of freedom 0.1 Daily CC Returns on S&P /30/ /17/ /14/

7 QQ-Plot: MLE of Skew-t for SP500 location = 01, scale = 07, shape = -99, df = sp mle computed with R package sn, qqplot() from R package car st quantiles Monthly CC Returns on MSFT r(t)

8 Monthly CC Returns on S&P Distribution for Monthly Returns on MSFT 30 Monthly CC Returns on MSFT Sample Quantiles: min 1Q median 3Q max Percent of Total 20 Sample Moments: mean std skewness kurtosis Number of Observations: x 8

9 Distribution for Monthly Returns on S&P Monthly CC Returns on S&P500 Sample Quantiles: min 1Q median 3Q max Percent of Total Sample Moments: mean std skewness kurtosis Number of Observations: x Normal QQ-Plot Tests for Normality /01/ /01/2001 Test for Normality: Shapiro-Wilks MSFT Test Stat p.value Dist. under Null: normal Total Observ.: 208 Test for Normality: Jarque-Bera MSFT Test Stat p.value /01/ Dist. under Null: chi-square with 2 degrees of freedom Total Observ.: 208 9

10 QQ-Plot: Student s t with 10 df /01/ /01/ /01/ Normal QQ-Plot Tests for Normality 0.1 Monthly CC Returns on S&P500 01/01/1987 Test for Normality: Shapiro-Wilks SP500 Test Stat p.value 154 Dist. under Null: normal Total Observ.: 208 Test for Normality: Jarque-Bera /01/ /01/ SP500 Test Stat p.value 000 Dist. under Null: chi-square with 2 degrees of freedom Total Observ.:

11 QQ-Plot: Student s t with 7 df Monthly CC Returns on S&P /01/ /01/ /01/ Testing for Autocorrelation Test for Autocorrelation: Ljung-Box Daily CC Returns on MSFT Null Hypothesis: no autocorrelation Daily CC Returns on S&P SP500 Test Stat p.value 191 Dist. under Null: chi-square with 20 degrees of freedom Total Observ.: 4365 Test for Autocorrelation: Ljung-Box Null Hypothesis: no autocorrelation MSFT Test Stat p.value 019 Dist. under Null: chi-square with 20 degrees of freedom Total Observ.:

12 Stylized Facts of Daily Asset Returns Microsoft Returns S & P 500 Returns Microsoft Squared Returns S & P 500 Squared Returns Volatility clustering Microsoft Absolute Returns S & P 500 Absolute Returns Sample Autocorrelations of Daily Returns Microsoft Returns S&P 500 Returns Microsoft Squared Returns Dependence in volatility S&P 500 Squared Returns Microsoft Absolute Returns Microsoft Absolute Returns

13 Stylized Facts for Monthly Asset Returns Microsoft Returns S&P 500 Returns Microsoft Squared Returns Less volatility clustering S&P 500 Squared Returns Microsoft Squared Returns Less volatility dependence S&P 500 Squared Returns MSFT and S&P 500 Daily Returns SP Sample covariance matrix MSFT SP500 MSFT SP MSFT Sample correlation matrix MSFT SP500 MSFT SP

14 EWMA Volatilities and Correlations EWMA Conditional Volatilities EWMA Conditional Correlation SP MSFT Correlations