Financial Stylized Facts

1
Financial Stylized Facts

• Fin250f Lecture 3.3
• Fall 2005
• Reading Taylor, chapter 4

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Outline

• Measuring returns
• Summary stats
• Distributions
• Skewness
• Kurtosis
• Calendar effects
• Autocorrelations
• Returns
• Volatility
• Early thoughts on efficiency

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Returns fixed horizons
4
Continuously Compounded Returns
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Reminder

• That last formula only really works if returns
  are Gaussian

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Multiperiod Returns
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Multiperiod Returns Continuous Compounding
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Summary Stats and Shape

• Mean, Variance, Skewness, Kurtosis
• Distribution shape

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Summary Stats
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Summary Stats
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Matlab code

• genret.m
• annret.m
• sumstat.m
• quantratio.m

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Risk Premia

• Annual returns relative to risk free
• 5-10 for equity
• Depends on risk measures
• Often thought too high
• Equity premium puzzle

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Standard Deviations

• Currency
• 10-14
• Stock portfolio
• 11-21
• Stock of large US firm
• 19-32
• Commodities
• 16-32

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Return Distributions

• Normal
• Student-t
• Mixture of normal
• Stable
• Other
• Time scales

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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

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Astronomy

• Lower in fall and higher in winter
• Larger around new moons
• 5-8 (annualized) differences
• Insignificant

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Return Autocorrelations

• Very low
• No patterns
• Simultaneous tests
• Q-stat
• Qtest.m
• Variance ratios

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Q-statistic Combining autocorrelations
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Absolute Return Autocorrelations

• Volatility persistence
• Large/positive/persistent
• Similar for squared returns

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Summary

• Volatile
• Not normal (fat tails)
• Nearly uncorrelated
• Some weak calendar effects
• Strong persistent volatility