Downside Price Volatility of QQQ Compared to the NASDAQ 100
A previous post presented evidence indicating that on August
24, 2015 several ETFs exhibited price volatility substantially larger than the
volatility of the major stock indices.
This post examines the relationship between the price
volatility of QQQ and the volatility of its underlying index the NASDAQ 100.
Issue: The allegation has been made that on August
24, 2015 ETF prices fell by much more than the underlying index for a couple of
indices. The news articles suggest that
price irregularities were not widespread.
QQQ is a major broadly traded ETF. This post tracks the relationship between
QQQ and its underlying index between January 1,2015 to February 12, 2016.
In general, how
closely did the price of QQQ deviate from the value of NASDAQ 100 on the down
side?
Downside price volatility is measured by taking the ratio of
the low price to the close price for both the ETF and the index.
Assessment of
Downside Price Volatility: Summary
statistics for the ratio of Low QQQ price to close QQQ price and low NASDAQ100
price to close NASDAQ100 price are presented in the table below.
Ratio of Low Price to
Close Price


Mean

STD

Min

Max


QQQ

0.99254

0.010

0.861

1.000

NASDAQ100

0.99299

0.071

0.937

1.000

Observations:
On average the ratio of the low to close for QQQ and NASDAQ100
are really close.
There was at least one day where the ratio of QQQ low to
close was a lot lower than the ratio of NASDAQ 100 to close. We know this because the min of the ratio is
a lot lower for QQQ than for its index.
How did the difference between downside volatility of QQQ
and NASDAQ100 vary over time?
Summary Statistics on the
Difference in Downside Measures
for QQQ and NASDAQ100


Percentile

Difference QQQLOW over
QQQCLOSE  NASDAQLOW/NASDAQ CLOSE

Min

0.0777

1%

0.0011

10%

0.0006

25%

0.0004

Median

0.0002

75%

0

90%

0.0002

95%

0.0005

99%

0.0009

100%

0.0011

Mean

0.0004

Standard Deviation

0.0046

Skewness

16.5

Kurtosis

274.4

Observations:
·
From this chart it is apparent that on at least
one day QQQ fell a lot more intraday than its underlying index.
·
I printed out the data. The downside fall of QQQ was a lot more than
the downside fall of NASDAQ100 on two days during this sample. The two days were August 24, 2015 and
January 27, 2016.
·
The difference in downside risk measures was
negative on 72% of days in this sample but on the overwhelming majority of days
this difference was very small.
·
A paired ttest on whether the difference in
ratio is less than zero gives a pvalue of 0.0517. The test is not significant for this sample
at a significance level of 0.05.
However, I suspect that if if one increases the sample to cover all
years since the creation of QQQ the difference in these ratios will be significantly
different from zero.
Concluding Thoughts: The WSJ article that I cited in my discussion
of the choice between ETFs and underlying index mentioned pricing problems for
some ETFs on 824.
Potential problems with QQQ were not measured.
QQQ is a widely held fund.
On most days it and the NASDAQ100 move in tandem. However, on 8242015 QQQ deviated fairly
widely from its underlying index.
Also, on January 27, 2015 there was a nontrivial deviation
between price of QQQ and the underlying index.
My preliminary analysis suggests that pricing problems with
ETFs are more widespread than the industry acknowledges.
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