Platykurtic Stocks
through January 20, 2023
We share US-listed stocks with a platykurtic distribution and a low variance.
Stocks that are platykurtic, or that have a platykurtic distribution with a standardized kurtosis score </= a parameter and a variance that is </= the variance of the total population in this run (multiplied by a parameter ~ 1.0). In other words, stocks that are platykurtic with a low variance.
A platykurtic distribution of daily stock price changes have fewer results in the tails (or > 2 standard deviations) than a normal distribution. They have a flatter frequency distribution than a normal distribution, so their typical results are spread across the high potential scores and are not as frequently returning the expected return, or mean.
A perfect example of a platykurtic distribution is the results of rolling a fair, 6-sided dice, or flipping a fair coin. There are no outliers because there are few, knowable scores (discrete scores), and no possible outliers. These are a uniform distribution.
For stocks, this could be returns that are in the typical range (say within one standard deviation), and fewer surprises.
Stocks that are platykurtic, or that have a platykurtic distribution with a standardized kurtosis score </= a parameter and a variance that is </= the variance of the total population in this run (multiplied by a parameter ~ 1.0). In other words, stocks that are platykurtic with a low variance.
A platykurtic distribution of daily stock price changes have fewer results in the tails (or > 2 standard deviations) than a normal distribution. They have a flatter frequency distribution than a normal distribution, so their typical results are spread across the high potential scores and are not as frequently returning the expected return, or mean.
A perfect example of a platykurtic distribution is the results of rolling a fair, 6-sided dice, or flipping a fair coin. There are no outliers because there are few, knowable scores (discrete scores), and no possible outliers. These are a uniform distribution.
For stocks, this could be returns that are in the typical range (say within one standard deviation), and fewer surprises.
More formally, a platykurtic distribution has a standardized kurtosis score that is < 1.250, where a normal distribution = 3.0. These stocks also have a variance that is </= the variance of the population, held evenly. You may notice that money-losing stock populations have a much higher variance, so their resulting platykurtic results likely do too.
Kurtosis is the fourth central movement of a distribution. It is one way to measure whether a random variable has a normal distribution. We use the kurtosis of a year's worth of adjusted, daily stock price changes, along with the variance of those changes, to better understand how a stock might perform in the future.
If you can visualize it, the distribution is flattening the bell-shaped curve (or frequency distribution) down onto the X-axis, giving less room in the tails for observations greater than 2 standard deviations from the mean. In some cases, the tails seem longer, but there are fewer outliers in the expected observations. Another visualization is that the center of the bell is stretched out to be fatter and shorter than a bell shaped curve, which seems to spread out the observations around the mean.
A stock that is platykurtic and low variance are safer when compared to a normally distributed stock. Options premia may be higher than fair value since it prices in a normal occurance of outliers. This is actually a safer stock in highly volatile market situations. We see energy services companies, healthcare, financial services and industrial companies that are not economically sensitive, nor do they seem to be subject to normal business cycles in this category.
Kurtosis is the fourth central movement of a distribution. It is one way to measure whether a random variable has a normal distribution. We use the kurtosis of a year's worth of adjusted, daily stock price changes, along with the variance of those changes, to better understand how a stock might perform in the future.
If you can visualize it, the distribution is flattening the bell-shaped curve (or frequency distribution) down onto the X-axis, giving less room in the tails for observations greater than 2 standard deviations from the mean. In some cases, the tails seem longer, but there are fewer outliers in the expected observations. Another visualization is that the center of the bell is stretched out to be fatter and shorter than a bell shaped curve, which seems to spread out the observations around the mean.
A stock that is platykurtic and low variance are safer when compared to a normally distributed stock. Options premia may be higher than fair value since it prices in a normal occurance of outliers. This is actually a safer stock in highly volatile market situations. We see energy services companies, healthcare, financial services and industrial companies that are not economically sensitive, nor do they seem to be subject to normal business cycles in this category.
Investor Expectations & Possible Trading Implications
Investors may expect a normal distribution of stock prices. Stocks go up and down seemingly randomly along with expectedly random new information. However, with a stock with a platykurtic distribution, the investor sees typical observations grouped into a typical range, although that range may be slightly wider than a normal distribution. There is also a smaller chance that a future observation will be an outlier. When plotted, the peak is shorter and wider (typical observations spread more widely around the mean) and the tails are pushed flat into the x-axis (less frequent outliers).
This provides information for a unique trading opportunity in stocks and stock options.
These stocks will typically have a wider range of daily price changes, and potentially higher actual and implied volatility, which increases the cost of stock options. However, it will be less likely to surprise with a large standard deviation move.
We believe the combination of platykurtic and low variance gives an options trader a chance to sell options and have less chance of making a big payout from any one daily move.
At least, this is our hypothesis on how it should work. No trading strategy is fool-proof, and this discussion does not take into account fundamental performance of the company or the markets...only the distribution of 1 year of daily price changes. Do your own due diligence.
Investors may expect a normal distribution of stock prices. Stocks go up and down seemingly randomly along with expectedly random new information. However, with a stock with a platykurtic distribution, the investor sees typical observations grouped into a typical range, although that range may be slightly wider than a normal distribution. There is also a smaller chance that a future observation will be an outlier. When plotted, the peak is shorter and wider (typical observations spread more widely around the mean) and the tails are pushed flat into the x-axis (less frequent outliers).
This provides information for a unique trading opportunity in stocks and stock options.
These stocks will typically have a wider range of daily price changes, and potentially higher actual and implied volatility, which increases the cost of stock options. However, it will be less likely to surprise with a large standard deviation move.
We believe the combination of platykurtic and low variance gives an options trader a chance to sell options and have less chance of making a big payout from any one daily move.
At least, this is our hypothesis on how it should work. No trading strategy is fool-proof, and this discussion does not take into account fundamental performance of the company or the markets...only the distribution of 1 year of daily price changes. Do your own due diligence.
All stocks
The stocks that are platykurtic and low variance:
The stocks that are platykurtic and low variance:
This is the minimum Platykurtic score and variance of all stocks: 0.725 0.0002891
AAAU 0.51 0.0000924
ABT 0.71 0.0002789
ADC 0.46 0.0002041
AFG 0.60 0.0002791
AFL 0.26 0.0002214
AME 0.12 0.0002421
ATR 0.66 0.0002801
AWK 0.48 0.0002872
BKH 0.72 0.0002534
BUSE 0.42 0.0002546
BY 0.42 0.0002577
CBOE 0.51 0.0002444
CBSH 0.54 0.0002115
CBU 0.61 0.0002199
CBZ 0.68 0.0002731
CFB 0.19 0.0002495
CHCO 0.63 0.0001690
CVBF 0.39 0.0001913
DCI 0.13 0.0002729
EFSC 0.41 0.0002607
EQC 0.38 0.0001211
FCF 0.29 0.0002404
FRME 0.45 0.0002806
GGG -0.10 0.0002795
GL 0.25 0.0002369
GPC 0.10 0.0002402
HFWA 0.38 0.0002774
HIG 0.16 0.0002665
HTLF 0.44 0.0002670
IBCP 0.51 0.0002721
IDA 0.69 0.0002148
IEP 0.54 0.0001059
IEX 0.15 0.0002669
INDB 0.54 0.0002442
L 0.35 0.0002176
LECO 0.20 0.0002342
LKFN -0.03 0.0002400
LNT 0.32 0.0002447
LTC 0.51 0.0002412
MET 0.43 0.0002509
MKL 0.36 0.0002471
MMP 0.72 0.0002295
MSM 0.71 0.0002260
NFG 0.07 0.0002825
NJR 0.62 0.0002543
NSIT 0.62 0.0002263
NWBI 0.49 0.0001938
OTIS 0.24 0.0002783
PB 0.48 0.0002423
PFE 0.10 0.0002889
PGC 0.05 0.0002868
PRAA 0.34 0.0001906
ROP 0.42 0.0002639
RSG 0.72 0.0002057
RTX 0.58 0.0002678
SAFT 0.04 0.0002055
SLGN 0.57 0.0002445
SNA 0.65 0.0002716
SPY 0.33 0.0002328
SR 0.29 0.0002631
SRE 0.60 0.0002296
TCBK 0.52 0.0002815
TLT -0.25 0.0001702
TR 0.63 0.0002565
UBSI 0.18 0.0002749
UNF 0.45 0.0002832
VICI 0.53 0.0002869
WEC 0.59 0.0002177
WRB 0.68 0.0002490
YORW 0.34 0.0002498
YUM 0.22 0.0002280
71
AAAU 0.51 0.0000924
ABT 0.71 0.0002789
ADC 0.46 0.0002041
AFG 0.60 0.0002791
AFL 0.26 0.0002214
AME 0.12 0.0002421
ATR 0.66 0.0002801
AWK 0.48 0.0002872
BKH 0.72 0.0002534
BUSE 0.42 0.0002546
BY 0.42 0.0002577
CBOE 0.51 0.0002444
CBSH 0.54 0.0002115
CBU 0.61 0.0002199
CBZ 0.68 0.0002731
CFB 0.19 0.0002495
CHCO 0.63 0.0001690
CVBF 0.39 0.0001913
DCI 0.13 0.0002729
EFSC 0.41 0.0002607
EQC 0.38 0.0001211
FCF 0.29 0.0002404
FRME 0.45 0.0002806
GGG -0.10 0.0002795
GL 0.25 0.0002369
GPC 0.10 0.0002402
HFWA 0.38 0.0002774
HIG 0.16 0.0002665
HTLF 0.44 0.0002670
IBCP 0.51 0.0002721
IDA 0.69 0.0002148
IEP 0.54 0.0001059
IEX 0.15 0.0002669
INDB 0.54 0.0002442
L 0.35 0.0002176
LECO 0.20 0.0002342
LKFN -0.03 0.0002400
LNT 0.32 0.0002447
LTC 0.51 0.0002412
MET 0.43 0.0002509
MKL 0.36 0.0002471
MMP 0.72 0.0002295
MSM 0.71 0.0002260
NFG 0.07 0.0002825
NJR 0.62 0.0002543
NSIT 0.62 0.0002263
NWBI 0.49 0.0001938
OTIS 0.24 0.0002783
PB 0.48 0.0002423
PFE 0.10 0.0002889
PGC 0.05 0.0002868
PRAA 0.34 0.0001906
ROP 0.42 0.0002639
RSG 0.72 0.0002057
RTX 0.58 0.0002678
SAFT 0.04 0.0002055
SLGN 0.57 0.0002445
SNA 0.65 0.0002716
SPY 0.33 0.0002328
SR 0.29 0.0002631
SRE 0.60 0.0002296
TCBK 0.52 0.0002815
TLT -0.25 0.0001702
TR 0.63 0.0002565
UBSI 0.18 0.0002749
UNF 0.45 0.0002832
VICI 0.53 0.0002869
WEC 0.59 0.0002177
WRB 0.68 0.0002490
YORW 0.34 0.0002498
YUM 0.22 0.0002280
71
This mushroom represents a platykurtic distribution. The peak is low and wide, and the tails are non-existent.
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