L.S.:
I am a graduate student (Drs degree) in finance & investments.
I have the following problems and I got stuck.
My data are the returns on a quarterly basis of leveraged buyout funds in
the USA from 1989 to 1999 (40 quarters). I have bought this data in two
groups with in one group funds smaller (in terms of capital under
management) then a certain size; in the other funds larger then that certain
size (I did this for 5 cut off points). This way I can test whether the
returns of the smaller funds behave differently from those of the larger
funds.
My hypothesis is that the smaller funds have higher returns. Not just that,
even better for their investors, they also have a lower risk level (standard
deviation of returns).
The hypothesis of lognormal distributions is made more often in the
financial world. This for stock returns, option valuations of Black Scholes
(as I applied in a previous chapter assuming lognormal already there), and
other cases. The data is telling the following (not supporting this
assumption I think) cutting of at a low cut off point skewdness is slightly
negative for large funds, high cut off point skewdness is 0.89; for the
smaller funds this goes from 2.2 to 1.5. The Kurtosis goes from 2.2 to 4.3
for larger funds and from 6.5 to 3.4 for smaller funds. Apparently, the
more numbers of funds this data is comprised of it keeps changing. Or: the
more larger funds in the original set the data behaves differently...
Oh, yes, in the statistical program Eviews 3.1 I tested for serial
correlation (something found often in stock data). There was none.
Problem I
There are way more smaller buyout firms then there are large ones. The
returns of the smaller funds are the combined results of about 150 firms
(from 80 in 1989 to 225 in 1999); the results of the large buyout firms are
the combined results of 8 in 1989 to 63 in 1999. Since I only have the
returns of the combined funds as observations I do only have N=40. One can
imagine that the standard deviation of returns is a lot lower for the
smaller funds this way in the first place... [4.63 vs. 5.15] . I of
course also found this at other "split off points" changing the above
numbers to 86 to 251 funds (small); 4 to 38 funds (large) and the stand.
dev. to 4.08 vs. 8.56.
How can I approach this problem: correcting for the larger number the
data is comprised of for smaller funds (or: correcting for the smaller
numbers the data is comprised of for the larger funds) if I want to test for
return level & standard deviation?
Problem II
There are relatively many negative numbers in the data, especially for
larger funds. Since the standard deviation is quite large for this data
(buyout funds are risky investments) negative numbers deviate significantly
from zero. A transformation from lognormal to normal seems not possible
therefore without "applying some tricks". Is this number large enough to
just use tests that are assuming normal distribution? What "tricks" are at
my service?
Well, I hope this is enough information so people can help me out....
Please do when you can as I am really stuck...
Help is therefore highly appreciated!!
Yours sincerely & kind regards,
edzo wisman
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