Question: Consider data on daily fund returns over the
2004 to 2105 time period for FVPU and FVINX.
What are the mean and standard deviation of daily returns for the two
funds over this time period? Do paired
versus unpaired tests reveal significant differences in the return of FVPU and
FVINX? Do nonparametric tests reveal
evidence that the returns from the two funds differ in a significant way?
Description of Data:
The data on daily returns for FPU and FVINX involve adjusted closing stock
price for all days from 2/2/04 to 12/8/15.
The sample has 2985 observations.
The return variable is the ln(Stock Price at period t/Stock
Price at t1).
The mean and standard deviation of the stock prices are as
presented below.
Mean

STD


ret_ut

0.0003371

0.0002067

ret_sp

0.0002791

0.0002249

Observations:
·
The mean return is slightly higher for the
utility stocks.
·
The standard deviation of returns for the
utility stocks is slightly lower.
It is also worth looking at the correlation of daily returns
between the two stock funds.
Observations:
·
The correlation between ret_sp and ret_ut is
0.7379.
This is pretty high but it may be the case that some
diversification across funds is better than no diversification across funds, a
topic for a future post.
Results from four
statistical tests: Are the
difference in returns from the two funds statistically different from zero?
I address this issue with STATA software. Four tests are considered – (1) the two
sample test with equal variances, (2) a paired mean test, (3) A Wilcoxon signed
rank test on difference between two medians, and (4) a paired sign rank test.
The twotailed pvalues for the four tests are presented
below.
Test

TwoTailed pvalue

unparied ttest

0.8493

paired ttest

0.7119

Unpaired Wilcoxon Test

0.2982

Paired Sign Test

0.2001

Observations:
·
None of the four statistical tests reveal a
significant difference between daily returns from the S&P fund and daily
returns from the utility fund.
·
The pvalues are lower for the nonparametric
tests but still the evidence does not reveal significant differences in returns
from the two securities.
Comment on this
result: Previous research found that
the person who invested in the utility fund earned more money over the 2004 to
2015 time period than the person who purchased the S&P fund.
Profit opportunities may temporarily exist even when return
differences are not significantly different from zero.
This result may not persist.
Returns from the utility fund started to fall in early 2015. Also, both funds fell precipitously during the
crisis of 2008 and diversification across funds would not have protected
investors in that turbulent time period.
(Really the only thing that would have minimized risk in that period was
a lot of cash.)
Additional Research: I have at least two additional questions
related to these two funds. First, what
are the potential gains from diversifying between the two funds?
Second, what is the expected return and standard deviation
of return from purchasing funds some time in second quarter of 2004 and selling
the stock sometime in the second quarter of 2015? A method of measuring expected return and
variability of return for stocks purchased and sold over particular time
intervals strikes me as a useful return measure compared to more common return measures
that pick a single purchase date and a single sale date.
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