492 research outputs found
Scaling of the distribution of fluctuations of financial market indices
We study the distribution of fluctuations over a time scale (i.e.,
the returns) of the S&P 500 index by analyzing three distinct databases.
Database (i) contains approximately 1 million records sampled at 1 min
intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily
records for the 35-year period 1962-1996, and database (iii) contains 852
monthly records for the 71-year period 1926-1996. We compute the probability
distributions of returns over a time scale , where varies
approximately over a factor of 10^4 - from 1 min up to more than 1 month. We
find that the distributions for 4 days (1560 mins) are
consistent with a power-law asymptotic behavior, characterized by an exponent
, well outside the stable L\'evy regime . To
test the robustness of the S&P result, we perform a parallel analysis on two
other financial market indices. Database (iv) contains 3560 daily records of
the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649
daily records of the Hang-Seng index for the 18-year period 1980-97. We find
estimates of consistent with those describing the distribution of S&P
500 daily-returns. One possible reason for the scaling of these distributions
is the long persistence of the autocorrelation function of the volatility. For
time scales longer than days, our results are
consistent with slow convergence to Gaussian behavior.Comment: 12 pages in multicol LaTeX format with 27 postscript figures
(Submitted to PRE May 20, 1999). See
http://polymer.bu.edu/~amaral/Professional.html for more of our work on this
are
Multifactor Analysis of Multiscaling in Volatility Return Intervals
We study the volatility time series of 1137 most traded stocks in the US
stock markets for the two-year period 2001-02 and analyze their return
intervals , which are time intervals between volatilities above a given
threshold . We explore the probability density function of ,
, assuming a stretched exponential function, . We find that the exponent depends on the threshold
in the range between and 6 standard deviations of the volatility. This
finding supports the multiscaling nature of the return interval distribution.
To better understand the multiscaling origin, we study how depends on
four essential factors, capitalization, risk, number of trades and return. We
show that depends on the capitalization, risk and return but almost
does not depend on the number of trades. This suggests that relates to
the portfolio selection but not on the market activity. To further characterize
the multiscaling of individual stocks, we fit the moments of , , in the range of by a
power-law, . The exponent is found also to
depend on the capitalization, risk and return but not on the number of trades,
and its tendency is opposite to that of . Moreover, we show that
decreases with approximately by a linear relation. The return
intervals demonstrate the temporal structure of volatilities and our findings
suggest that their multiscaling features may be helpful for portfolio
optimization.Comment: 16 pages, 6 figure
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