FitGallery

Fit Gallery

The graphics below show the lognormal-normal mixture (LNN) fits to the logarithmic returns to the stocks in the Dow Jones Industrial Average for ten years of data. The fits are shown for the empirical density data points and the LNN distribution function in green, with the same configuration we have been using for stable distributions. The ticker symbol, start date, and end date for the data along with the starting and ending price for the time-series of the fit are shown for each plot. In the log-log plot every tail point in the ten-year data set is represented.

Graphics:Log Log Left Tail Blue, Right Red, (Lognormal Normal Green)

The LNN fit parameters are shown for each ticker.

Ticker	γ	σ	δ
AA	0.0143776	0.379748	0.0000811193
AIG	0.0105503	0.546865	-0.000128683
AXP	0.012167	0.526956	0.0000873189
BA	0.0122332	0.382974	0.000273366
BAC	0.0100915	0.592507	0.00025833
C	0.0114741	0.570884	-0.000146885
CAT	0.012411	0.404011	0.000526981
CVX	0.00997108	0.28126	0.000473874
DD	0.0105449	0.452357	-0.0000605811
DIS	0.0121173	0.46576	-0.000164497
GE	0.0100534	0.500971	-0.000209129
GM	0.0143105	0.411722	-0.00035456
HD	0.0127974	0.486911	-0.000185893
HPQ	0.0145468	0.531354	0.000371338
IBM	0.0105728	0.501313	0.000356852
INTC	0.0168842	0.393565	0.000139461
JNJ	0.00771572	0.507225	0.000296962
JPM	0.0119605	0.605455	0.0000658679
KO	0.00830957	0.540472	-0.0000826663
MCD	0.0106858	0.395635	0.000297342
MMM	0.00884088	0.47815	0.000326877
MRK	0.0105157	0.451994	-0.000104989
MSFT	0.0115218	0.561703	-0.000107142
PFE	0.0107934	0.443709	-0.000206686
PG	0.00794587	0.558387	0.000232795
T	0.0111047	0.490385	0.000182797
UTX	0.0107953	0.441281	0.000506665
VZ	0.0108119	0.455917	-0.0000204924
WMT	0.010947	0.447005	0.000314356
XOM	0.0101004	0.258761	0.0004501

The lognormal density plots of the {log(γ), σ} are shown for each stock. This presents a two dimensional visualization of risk.

Graphics:A Gallery of Risk The Lognormal Plots For the DJIA Stocks