Leptokurtic Stocks
through January 20, 2023
+ new research on 2023 stock price returns
We share US-listed stocks with a leptokurtic distribution and a low variance.
A leptokurtic distribution of daily stock price changes have more results in the tails (or > 2 standard deviations) than a normal distribution, and have a greater number of observations clustered tightly around the mean or expected result. This means the typical market return will be as expected, and there is a greater chance of a big surprise.
We narrow our list to leptokurtic stocks that also have a low variance of daily price changes. Each stock individually has a lower variance than a diversified portfolio of all stocks analyzed, which typically contains hundreds or more than a thousand stocks.
A leptokurtic distribution of daily stock price changes have more results in the tails (or > 2 standard deviations) than a normal distribution, and have a greater number of observations clustered tightly around the mean or expected result. This means the typical market return will be as expected, and there is a greater chance of a big surprise.
We narrow our list to leptokurtic stocks that also have a low variance of daily price changes. Each stock individually has a lower variance than a diversified portfolio of all stocks analyzed, which typically contains hundreds or more than a thousand stocks.
More formally, a Leptokurtic distribution has a standardized kurtosis score that is > 4.5, where a normal distribution = 3.0.
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 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 lifting the bell-shaped curve (or frequency distribution) off the X-axis, giving more room in the tails for observations greater than 2 standard deviations from the mean. Another visualization is that the center of the bell is squeezed to be thinner and taller, fitting more observations within 1 standard deviation of the mean.
A stock that is leptokurtic and low variance appears safer when compared to a normally distributed stock. Options premia may be smaller and this might be a 'flight to safety' stock in highly volatile market situations. We see utilities and consumer products (e.g., food companies) 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 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 lifting the bell-shaped curve (or frequency distribution) off the X-axis, giving more room in the tails for observations greater than 2 standard deviations from the mean. Another visualization is that the center of the bell is squeezed to be thinner and taller, fitting more observations within 1 standard deviation of the mean.
A stock that is leptokurtic and low variance appears safer when compared to a normally distributed stock. Options premia may be smaller and this might be a 'flight to safety' stock in highly volatile market situations. We see utilities and consumer products (e.g., food companies) 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 leptokurtic distribution, the investor sees typical observations closer to the mean. There is also more of a chance that a future observation will be an outlier. When plotted, the peak is taller and narrower (typical observations closer to the mean) and the tails rise up from the x-axis (more frequent outliers).
This provides information for a unique trading opportunity in stocks and stock options.
This way, these stocks will typically have smaller movements, and lower implied volatility, which reduces the cost of stock options, but still have the ability to surprise with a large standard deviation move. We believe the combination of leptokurtic and low variance gives an options trader a chance to invest less money buying an option, predict a direction of surprise, and earn profits as the stock eventually makes its big more.
At least, this is our hypothesis on how it should work. No trading strategy is fool-proof. We have felt foolish on a few of our leptokurtic options bets where the options seemed cheap, but we bet on a move in the wrong direction.
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 leptokurtic distribution, the investor sees typical observations closer to the mean. There is also more of a chance that a future observation will be an outlier. When plotted, the peak is taller and narrower (typical observations closer to the mean) and the tails rise up from the x-axis (more frequent outliers).
This provides information for a unique trading opportunity in stocks and stock options.
This way, these stocks will typically have smaller movements, and lower implied volatility, which reduces the cost of stock options, but still have the ability to surprise with a large standard deviation move. We believe the combination of leptokurtic and low variance gives an options trader a chance to invest less money buying an option, predict a direction of surprise, and earn profits as the stock eventually makes its big more.
At least, this is our hypothesis on how it should work. No trading strategy is fool-proof. We have felt foolish on a few of our leptokurtic options bets where the options seemed cheap, but we bet on a move in the wrong direction.
All stock run
The stocks that are leptokurtic and low variance:
The stocks that are leptokurtic and low variance:
This is the minimum Leptokurtic score and variance of all stocks: 5.0 0.0002891
AMGN 5.33 0.0001882
CAG 8.87 0.0002444
CFFN 10.90 0.0002547
CHD 5.58 0.0002582
CPB 5.89 0.0002316
CVS 8.06 0.0002773
EIG 6.09 0.0002753
FLO 5.81 0.0002374
GILD 12.71 0.0002547
GIS 5.65 0.0002074
HMN 7.14 0.0002883
HONE 7.08 0.0002410
HRL 9.88 0.0001898
HSY 5.48 0.0001855
INGR 6.55 0.0002525
JBSS 14.10 0.0002751
K 6.40 0.0002035
KHC 7.33 0.0002746
KRNY 6.43 0.0002708
LHCG 6.54 0.0002036
MGRC 10.25 0.0002855
MKC 5.68 0.0002854
MO 9.76 0.0002504
PFS 16.33 0.0002749
PINC 6.61 0.0002045
SHBI 12.62 0.0001895
SJM 12.33 0.0002267
STZ 7.30 0.0002578
TGNA 6.41 0.0001747
UVV 8.04 0.0002732
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AMGN 5.33 0.0001882
CAG 8.87 0.0002444
CFFN 10.90 0.0002547
CHD 5.58 0.0002582
CPB 5.89 0.0002316
CVS 8.06 0.0002773
EIG 6.09 0.0002753
FLO 5.81 0.0002374
GILD 12.71 0.0002547
GIS 5.65 0.0002074
HMN 7.14 0.0002883
HONE 7.08 0.0002410
HRL 9.88 0.0001898
HSY 5.48 0.0001855
INGR 6.55 0.0002525
JBSS 14.10 0.0002751
K 6.40 0.0002035
KHC 7.33 0.0002746
KRNY 6.43 0.0002708
LHCG 6.54 0.0002036
MGRC 10.25 0.0002855
MKC 5.68 0.0002854
MO 9.76 0.0002504
PFS 16.33 0.0002749
PINC 6.61 0.0002045
SHBI 12.62 0.0001895
SJM 12.33 0.0002267
STZ 7.30 0.0002578
TGNA 6.41 0.0001747
UVV 8.04 0.0002732
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This church represents a leptokurtic distribution. The peak is high and narrow, and the tails are wide, sloping and obscured in this photo.
A short film to describe our service and current picks as of market close January 5, 2023
New Research on 2023 Returns
We are running a 'public' test to see whether a set of leptokurtic stocks and platykurtic stocks behave differently than each other. Our hypothesis is that they will act very differently around range of daily returns, median return, number of stocks that advance in price). We will control for overall market returns based on the daily return of the S&P 500 Index.
Starting on January 13, we will change our population. We will start collecting new data.
We will use the leptokurtic and low variance stocks, along with the platykurtic and low variance stocks that we find in the model. We want to isolate the impact that high variance was having on the data set. Both populations will have the same variance (</= the variance of the population they were measured from), and the standardized kurtosis test.
Over the weekend before Jan 16, we will review the setting to create a more even set of stocks to compare. The sample sizes may cause anomalies (e.g., one set is 2x the other set, and could explain greater range of daily price change values).
LEPTOKURTIC AND LOW VARIANCE STOCKS (37 ON FRI JAN 13)
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 37), S&P 500 daily performance (%)
Jan 17: -2.48, 4.28, -0.21, 16, -0.20,
Jan 18: -4.21, 2.60, -1.96, 5, -1.56
Jan 19: -5.88, 2.58, -0.47, 7, -0.76
Jan 23: -2.70, 3.83, 0.29, 23, 1.20
Jan 24: -4.06, 2.52, -0.08, 17, -0.07
PLATYKURTIC AND LOW VARIANCE STOCKS (72 ON FRI JAN 13)
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 72), S&P 500 daily performance (%)
Jan 17: -4.60, 6.15, -0.27, 30, -0.20,
Jan 18: -4.06, 1.0, -1.60, 5, -1.56
Jan 19: -3.40, 1.71, -0.74, 15, -0.76
Jan 23: -2.51, 4.32, 0.40, 46, 1.20
Jan 24: -6.71, 3.70, 0.22, 43, -0.07
We will use the leptokurtic and low variance stocks, along with the platykurtic and low variance stocks that we find in the model. We want to isolate the impact that high variance was having on the data set. Both populations will have the same variance (</= the variance of the population they were measured from), and the standardized kurtosis test.
Over the weekend before Jan 16, we will review the setting to create a more even set of stocks to compare. The sample sizes may cause anomalies (e.g., one set is 2x the other set, and could explain greater range of daily price change values).
LEPTOKURTIC AND LOW VARIANCE STOCKS (37 ON FRI JAN 13)
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 37), S&P 500 daily performance (%)
Jan 17: -2.48, 4.28, -0.21, 16, -0.20,
Jan 18: -4.21, 2.60, -1.96, 5, -1.56
Jan 19: -5.88, 2.58, -0.47, 7, -0.76
Jan 23: -2.70, 3.83, 0.29, 23, 1.20
Jan 24: -4.06, 2.52, -0.08, 17, -0.07
PLATYKURTIC AND LOW VARIANCE STOCKS (72 ON FRI JAN 13)
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 72), S&P 500 daily performance (%)
Jan 17: -4.60, 6.15, -0.27, 30, -0.20,
Jan 18: -4.06, 1.0, -1.60, 5, -1.56
Jan 19: -3.40, 1.71, -0.74, 15, -0.76
Jan 23: -2.51, 4.32, 0.40, 46, 1.20
Jan 24: -6.71, 3.70, 0.22, 43, -0.07
Initial observations with new dataset (Day 1).
1. The platykurtic and leptokurtic stock populations both had median returns in line with return of the S&P 500 Index.
2. The ranges of these stock samples was 6.76% for the Leptokurtic stocks, and 10.75% for the platykurtic stocks.
3. Both populations had fewer stocks rise than fall today.
Day 3: I realize that we have different sample sizes, so these findings should be taken with a grain of salt.
1. It looks like platykurtic stocks at the median perform more similarly to the S&P 500, and the leptokurtic stocks median over-shoots or under-shoots it more.
2. The platykurtic range may be smaller than the leptokurtic range, despite having ~ 2x the number of stocks.
1. The platykurtic and leptokurtic stock populations both had median returns in line with return of the S&P 500 Index.
2. The ranges of these stock samples was 6.76% for the Leptokurtic stocks, and 10.75% for the platykurtic stocks.
3. Both populations had fewer stocks rise than fall today.
Day 3: I realize that we have different sample sizes, so these findings should be taken with a grain of salt.
1. It looks like platykurtic stocks at the median perform more similarly to the S&P 500, and the leptokurtic stocks median over-shoots or under-shoots it more.
2. The platykurtic range may be smaller than the leptokurtic range, despite having ~ 2x the number of stocks.
We have 24 stocks that passed our test for being Leptokurtic (Standardized Kurtosis > 4.5) and Low Variance for the year through 12/30/2022. They are both profitable and unprofitable companies. All are US listed common stocks. We exclude stocks that fail data validation.
LEPTOKURTIC AND LOW VARIANCE STOCKS
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 24), S&P 500 daily performance (%)
Jan 3: -2.22, 3.29, 0.07, 13, -0.4
Jan 4: -0.76, 3.89, 0.62, 18, 0.75
Jan 5: -2.04, 3.42, 0.18, 12, -1.16
Jan 6: -7.08, 3.13,1.90 , 21, 2.28
Jan 9: -7.74,-1.71, -1.29, 2, -0.08
Jan 10: -2.31,2.40,0.06,9, 0.70
Jan 11: -2.14, 5.37, 0.12, 14, 1.28
Jan 12: -3.31, 7.02, 0.00, 9, 0.34
Jan 13: -1.13, 1.53, 0.33, 13 0.40
FINAL DATA COLLECTED
LEPTOKURTIC AND LOW VARIANCE STOCKS
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 24), S&P 500 daily performance (%)
Jan 3: -2.22, 3.29, 0.07, 13, -0.4
Jan 4: -0.76, 3.89, 0.62, 18, 0.75
Jan 5: -2.04, 3.42, 0.18, 12, -1.16
Jan 6: -7.08, 3.13,1.90 , 21, 2.28
Jan 9: -7.74,-1.71, -1.29, 2, -0.08
Jan 10: -2.31,2.40,0.06,9, 0.70
Jan 11: -2.14, 5.37, 0.12, 14, 1.28
Jan 12: -3.31, 7.02, 0.00, 9, 0.34
Jan 13: -1.13, 1.53, 0.33, 13 0.40
FINAL DATA COLLECTED
We have 105 stocks* that passed our test for being Platykurtic (standardized kurtosis < 1.5) and High Variance for the year through 12/30/2022. They are both profitable and unprofitable companies. All are US listed common stocks. We exclude stocks that fail data validation.
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 24), S&P 500 daily performance (%)
Jan 3: -12.24, 10.35, -3.15, 18, -0.4
Jan 4: -6.07, 24.12, 2.12, 88, 0.75
Jan 5: -11.31, 4.96, -1.06, 32, -1.16
Jan 6: -3.92, 32.08, 2.46, 86, 2.28
Jan 9: -8.37, 19.80, 2.13, 80, -0.08
Jan 10: -3.63,17.35,1.92,79,0.70
Jan 11: -6.61, 12.52, 1.53, 78,1.28
Jan 12: -4.32, 11.08, 0.76, 68, 0.34
Jan 13: -10.64, 14.20, 0.72, 69, 0.40
FINAL DATA COLLECTED
* We may reduce the number of platykurtic and high variance stocks in future work.
** We are completing this analysis, and replacing it with a new run of stocks and a new platykurtic stock definition.
Date, largest daily loss (%), largest daily gain (%), median daily return (%), number of gainers (out of 24), S&P 500 daily performance (%)
Jan 3: -12.24, 10.35, -3.15, 18, -0.4
Jan 4: -6.07, 24.12, 2.12, 88, 0.75
Jan 5: -11.31, 4.96, -1.06, 32, -1.16
Jan 6: -3.92, 32.08, 2.46, 86, 2.28
Jan 9: -8.37, 19.80, 2.13, 80, -0.08
Jan 10: -3.63,17.35,1.92,79,0.70
Jan 11: -6.61, 12.52, 1.53, 78,1.28
Jan 12: -4.32, 11.08, 0.76, 68, 0.34
Jan 13: -10.64, 14.20, 0.72, 69, 0.40
FINAL DATA COLLECTED
* We may reduce the number of platykurtic and high variance stocks in future work.
** We are completing this analysis, and replacing it with a new run of stocks and a new platykurtic stock definition.
FINAL DATA COLLECTED
Initial observations:
1. There are 75% fewer Leptokurtic stocks with low variance (based on our conditions) than platykurtic stocks with high variance
2. Leptokurtic stocks have smaller range in daily price changes than platykurtic stocks
3. Leptokurtic stocks have a smaller median price change than platykurtic stocks
4. Platykurtic stocks had a higher percentage of stocks that declined in value. Our first day of the 2023 trading year saw 83% of platykurtic and high variance stocks fall.
5. Leptokurtic stocks did better than the platykurtic stocks on down days, and worse on up days.
Secondary observations (Jan 9):
The range of daily price moves in platykurtic and high variance stocks is enormous, and even the daily median move is quite high at an average over 2% per day. These stocks really move, and there is a large sample of them (105).
The leptokurtic stocks did not do well on January 9, and underperformed the market.
On Jan 11, we see that this market favors the riskiest stocks with a significant upside bias.
On Jan 13, we realize the range on the 105 stocks with platykurtic and high variance are significant. This 'breaks' our hypothesis that platykurtic stocks are less risky, even with higher variance. It also suggests that the variance characteristic vastly outweighs the kurtosis characteristic in today's market.
Initial observations:
1. There are 75% fewer Leptokurtic stocks with low variance (based on our conditions) than platykurtic stocks with high variance
2. Leptokurtic stocks have smaller range in daily price changes than platykurtic stocks
3. Leptokurtic stocks have a smaller median price change than platykurtic stocks
4. Platykurtic stocks had a higher percentage of stocks that declined in value. Our first day of the 2023 trading year saw 83% of platykurtic and high variance stocks fall.
5. Leptokurtic stocks did better than the platykurtic stocks on down days, and worse on up days.
Secondary observations (Jan 9):
The range of daily price moves in platykurtic and high variance stocks is enormous, and even the daily median move is quite high at an average over 2% per day. These stocks really move, and there is a large sample of them (105).
The leptokurtic stocks did not do well on January 9, and underperformed the market.
On Jan 11, we see that this market favors the riskiest stocks with a significant upside bias.
On Jan 13, we realize the range on the 105 stocks with platykurtic and high variance are significant. This 'breaks' our hypothesis that platykurtic stocks are less risky, even with higher variance. It also suggests that the variance characteristic vastly outweighs the kurtosis characteristic in today's market.
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