1. Financial Stylized Facts Fin250f: Lecture 3.3 Fall 2005 Reading: Taylor, chapter 4

2. Outline  Measuring returns  Summary stats  Distributions Skewness Kurtosis  Calendar effects  Autocorrelations Returns Volatility  Early thoughts on efficiency

3. Returns: fixed horizons

4. Continuously Compounded Returns

5. Reminder  That last formula only really works if returns are Gaussian

6. Multiperiod Returns

7. Multiperiod Returns: Continuous Compounding

8. Summary Stats and Shape  Mean, Variance, Skewness, Kurtosis  Distribution shape

9. Summary Stats

11. Matlab code  genret.m  annret.m  sumstat.m  quantratio.m

12. Risk Premia  Annual returns relative to risk free  5-10% for equity  Depends on risk measures  Often thought “too high” Equity premium puzzle

13. Standard Deviations  Currency 10-14%  Stock portfolio 11-21%  Stock of large US firm 19-32%  Commodities 16-32%

14. Return Distributions  Normal  Student-t  Mixture of normal  Stable  Other  Time scales

15. Calendar Effects  Day of the week Monday negative (-0.2%, -0.1%)  Day of the month High returns for 4 trading days starting at end of month  Month of the year (Jan) January returns large Not important anymore

16. Astronomy  Lower in fall and higher in winter  Larger around new moons 5-8% (annualized) differences Insignificant

17. Return Autocorrelations  Very low  No patterns  Simultaneous tests Q-stat Qtest.m Variance ratios

18. Q-statistic: Combining autocorrelations

19. Absolute Return Autocorrelations  Volatility persistence  Large/positive/persistent  Similar for squared returns

20. Summary  Volatile  Not normal (fat tails)  Nearly uncorrelated  Some weak calendar effects  Strong persistent volatility