Saturday, February 13, 2016

Downside Price Volatility of QQQ Compared to the NASDAQ 100

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 intra-day 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 t-test on whether the difference in ratio is less than zero gives a p-value 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 8-24.  



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 8-24-2015 QQQ deviated fairly widely from its underlying index.

Also, on January 27, 2015 there was a non-trivial 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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