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Skew Lognormal Cascade DistributionStephen Lihn / research archive

Quantitative finance
2008 to 2026

Data atlas / stock index

Russell 2000 Daily Log Return

Twenty years of the small cap index fit with eta near 0.56, in line with other major equity series.

Kurtosis 5 to 101988 to 2008Eta near 0.56
Russell 2000 daily log return with a skew lognormal cascade fit.
The Russell 2000 fit over 20 years.

Twenty years of Russell 2000 index data fit well with eta near 0.56, a level similar to that of other major stock indices over the same period.

The series is useful as a small cap comparison with the Dow and the Nasdaq. The tail shape is close even when the market segment is different.

Data source: Yahoo Finance.

Related fits

Compare the shape.

Nikkei 225 Daily Log ReturnStock index / 1984 to 2009Blue Chip Stock Daily Log Return FitsUS stocks / 1980 to 2010

Source shelf

Data and further reading

12 entries
  1. Yahoo FinanceMarket data and historical quotes used for several series.
  2. Nasdaq CompositeOfficial index information for the Nasdaq Composite.
  3. Federal Reserve Economic DataEconomic time series from the Federal Reserve Bank of St. Louis.
  4. Lihn 2008 on SSRNThe 2008 working paper on the scale invariant Brownian motion model.
  5. Lihn 2009 on SSRNThe working paper on higher order lognormal cascade distributions.
  6. Clark 1973Subordinated stochastic process model for speculative prices.
  7. Fernholz 2002Stochastic portfolio theory and the diversity index.
  8. Heavy tailed distributionsA reference overview of distributions with heavy tails.
  9. Lognormal distributionDefinition and properties of the lognormal distribution.
  10. Mandelbrot 1963The variation of certain speculative prices.
  11. Fat tailed distributionsA reference overview of heavy tailed probability distributions.
  12. Stochastic portfolio theoryA reference overview of stochastic portfolio theory.