Quant And Machine Learning Portfolio Construction: Pairs Trading, Mean Reversion, Slope Weights

We construct a stock portfolio based on the assumption that stocks will revert to a given index represented by an ETF. In the example here, we use the entire stock market and VTI, the total stock market ETF. Slopes of zsore prices are the measure of deviation from VTI as well as the basis for computing weights.

We construct the portfolio as follows:

1. Cluster stocks using 126 days of data, transformed into fractional return series, with Dynamic Time Warping and the K-Medoids algorithm (See K-Medoids Clusters With Dynamic Time Warping Distances Have Been Added To Daily Asset Analysis).
2. Using stocks only, select those with volume >= 100,000 shares.
3. For 126 days, transform all prices to zscores and compute slopes (See Standard Deviation And Slopes Have Been Added To Daily Asset Analysis).
4. Divide stocks into two groups: those with slopes greater and lesser than VTI slope. Randomly choose 5 from each such that each stock is in a unique K-Medoids cluster.
5. Compute two types of weights. Aggressive weights are proportional to |stock slope – VTI slope|, while conservative weights are proportional to 1/|stock slope – VTI slope|.
6. For stocks whose slopes are greater than VTI slope, weights are negative. For stocks whose slopes are less than VTI slope, weights are positive. Thus mean reversion.
7. Select and quantify a directional bias. Neutral means 1/2 of the portfolio is long and 1/2 short. Long means 2/3 long and 1/3 short. Short means 1/3 long and 2/3 short. This information is used to normalize the weights.

1/2 Long 1/2 Short

	Name	Trade Direction	Slope	Delta Slope	1/Delta Slope	Cluster Number	Aggressive Weights	Conservative Weights
TWST	Twist Bioscience	Long	0.0045	0.0189	52.9101	64	0.1849	0.0194
RRC	Range Resources	Long	0.0224	0.001	1000.0	4	0.0098	0.366
NCMI	National CineMedia	Long	0.009	0.0144	69.4444	86	0.1409	0.0254
ATAI	atai Life Sciences	Long	0.0137	0.0097	103.0928	20	0.0949	0.0377
NSIT	Insight Enterprises	Long	0.0163	0.0071	140.8451	10	0.0695	0.0515
SHAK	Shake Shack	Short	0.0245	0.0011	909.0909	77	-0.0705	-0.1178
DFH	Dream Finders Homes	Short	0.026	0.0026	384.6154	60	-0.1667	-0.0498
LII	Lennox International	Short	0.0244	0.001	1000.0	18	-0.0641	-0.1296
HUBB	Hubbell	Short	0.0243	0.0009	1111.1111	47	-0.0577	-0.144
FOR	Forestar Group	Short	0.0256	0.0022	454.5455	31	-0.141	-0.0589

1/3 Long 2/3 Short

	Name	Trade Direction	Slope	Delta Slope	1/Delta Slope	Cluster Number	Aggressive Weights	Conservative Weights
TWST	Twist Bioscience	Long	0.0045	0.0189	52.9101	64	0.1233	0.0129
RRC	Range Resources	Long	0.0224	0.001	1000.0	4	0.0065	0.244
NCMI	National CineMedia	Long	0.009	0.0144	69.4444	86	0.0939	0.0169
ATAI	atai Life Sciences	Long	0.0137	0.0097	103.0928	20	0.0633	0.0252
NSIT	Insight Enterprises	Long	0.0163	0.0071	140.8451	10	0.0463	0.0344
SHAK	Shake Shack	Short	0.0245	0.0011	909.0909	77	-0.094	-0.157
DFH	Dream Finders Homes	Short	0.026	0.0026	384.6154	60	-0.2222	-0.0664
LII	Lennox International	Short	0.0244	0.001	1000.0	18	-0.0855	-0.1727
HUBB	Hubbell	Short	0.0243	0.0009	1111.1111	47	-0.0769	-0.1919
FOR	Forestar Group	Short	0.0256	0.0022	454.5455	31	-0.188	-0.0785

2/3 Long 1/3 Short

	Name	Trade Direction	Slope	Delta Slope	1/Delta Slope	Cluster Number	Aggressive Weights	Conservative Weights
TWST	Twist Bioscience	Long	0.0045	0.0189	52.9101	64	0.2466	0.0258
RRC	Range Resources	Long	0.0224	0.001	1000.0	4	0.013	0.4879
NCMI	National CineMedia	Long	0.009	0.0144	69.4444	86	0.1879	0.0339
ATAI	atai Life Sciences	Long	0.0137	0.0097	103.0928	20	0.1265	0.0503
NSIT	Insight Enterprises	Long	0.0163	0.0071	140.8451	10	0.0926	0.0687
SHAK	Shake Shack	Short	0.0245	0.0011	909.0909	77	-0.047	-0.0785
DFH	Dream Finders Homes	Short	0.026	0.0026	384.6154	60	-0.1111	-0.0332
LII	Lennox International	Short	0.0244	0.001	1000.0	18	-0.0427	-0.0864
HUBB	Hubbell	Short	0.0243	0.0009	1111.1111	47	-0.0385	-0.096
FOR	Forestar Group	Short	0.0256	0.0022	454.5455	31	-0.094	-0.0393

We note that all of the data was directly taken from data that we compute each market day (available at our Proton Drive). Specifically, data was from:

• Dynamic Time Warping Nearest Neighbors And K-Medoids Clusters 2023-08-04.zip: Dynamic Time Warping Nearest Neighbors Fractional Return 126 Days Stocks.csv
• Analysis 2023-08-04.zip: Slope Zscore Arrays.csv

We could have performed a fresh clustering at the end of step 4 above for each of the two divisions of stocks, but we wanted to highlight a use case for the data that we compute each market day.

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