1. Data Preparation

1.1. Gather Data

• Ensure you have OHLCV data for all 5000 stocks over the same time period.

• Store data in a structured format (e.g., Pandas DataFrame, CSV files, or databases).

1.2. Data Preprocessing

• Handling Missing Values:

• Use forward-fill, backward-fill, or interpolation for minor gaps.

• For significant gaps, drop the stock or time window.

• Normalization:

• Normalize prices and volume data to make them comparable.

• Common methods:

• Min-Max Scaling: Scale data to [0, 1].

• Z-Score Normalization: Scale data to zero mean and unit variance.

• Log transformation for volume (to reduce skewness).

• Feature Selection:

• Use derived features:

• Log returns: .

• Moving averages or RSI (Relative Strength Index) for trends.

• Volatility measures (e.g., rolling standard deviation).

1.3. Synchronization

• Align all stocks to the same timestamps.

• Handle timezone or holiday differences (e.g., exclude non-trading days).

2. Feature Engineering

2.1. Extract Key Features

You can use the following subsets or combinations:

• OHLC Time Series: Normalize and cluster the entire price series.

• Derived Metrics: Cluster based on:

• Returns: Daily or weekly returns for trends.

• Volatility: Rolling standard deviation or ATR (Average True Range).

• Volume Trends: Rolling volume changes or VWAP (Volume Weighted Average Price).

2.2. Dimensionality Reduction

For high-dimensional data (e.g., 5000 stocks, 252 trading days per year):

• PCA (Principal Component Analysis): Retain dominant patterns.

• Autoencoders: Use deep learning to compress time series into lower-dimensional embeddings.

3. Choosing Similarity Measures

3.1. General Trends

• Use Dynamic Time Warping (DTW):

• Allows for phase shifts (e.g., stocks reacting at different times to news).

• Use tslearn.metrics.dtw or fastdtw.

3.2. Co-Movement Patterns

• Use Correlation-Based Distance:

• Compute pairwise correlations of returns.

• Use as the distance metric.

• Example:

import numpy as np

correlation_matrix = np.corrcoef(return_data.T)

distance_matrix = 1 - correlation_matrix

3.3. Shape-Based Methods

• Segment data into meaningful shapes (e.g., SAX representation from pyts).

• Compare based on symbolic similarity.

4. Clustering

4.1. Select Clustering Algorithm

• k-Means with DTW: Suitable for large datasets with fixed cluster numbers.

• Hierarchical Clustering: Useful for dendrogram analysis.

• DBSCAN or HDBSCAN: For discovering clusters with arbitrary shapes and handling noise.

• Ensemble Methods: Combine multiple clustering results for robust grouping.

4.2. Implementation

Example: Using k-Means with DTW:

from tslearn.clustering import TimeSeriesKMeans

from tslearn.metrics import dtw

# Assuming time_series_data is your preprocessed dataset

model = TimeSeriesKMeans(n_clusters=10, metric=“dtw”)

labels = model.fit_predict(time_series_data)

5. Evaluation and Visualization

5.1. Evaluate Clusters

• Internal Validation Metrics:

• Silhouette Score.

• Davies-Bouldin Index.

• External Metrics (if labels available):

• Adjusted Rand Index (ARI).

5.2. Visualize Results

• Cluster Prototypes: Plot representative time series for each cluster.

• Heatmaps: Show similarity/distance matrices.

• Dendrograms: For hierarchical clustering.

6. Potential Fallbacks and Solutions

6.1. Large Data Volume

• Challenge: Clustering 5000 time series can be computationally expensive.

• Solution:

• Use dimensionality reduction (e.g., PCA) before clustering.

• Parallelize computations (e.g., with joblib or GPU-based libraries).

6.2. Heterogeneous Time Series Length

• Challenge: Some stocks may have incomplete data.

• Solution: Use DTW or truncate/pad time series to the same length.

6.3. Sensitivity to Noise

• Challenge: Stock market data can be noisy.

• Solution: Use smoothing techniques like moving averages or filter outliers.

6.4. Overfitting in DTW

• Challenge: DTW can align noise instead of meaningful trends.

• Solution: Apply smoothing or use weighted DTW to prioritize global trends.

7. Using OHLCV Data Specifically

• Create multiple clustering pipelines for specific objectives:

Price-Based Clustering: Use normalized OHLC data.
Volatility-Based Clustering: Use rolling volatility or ATR.
Volume-Based Clustering: Identify high-volume movers.

• Combine results using ensemble clustering or rank-based aggregation to identify overall patterns.

import numpy as np

import pandas as pd

from tslearn.clustering import TimeSeriesKMeans

from tslearn.metrics import dtw

from sklearn.preprocessing import StandardScaler

from sklearn.decomposition import PCA

  

_# Load OHLCV data_

data = pd.read_csv("ohlcv_data.csv")  _# Rows: Timestamps, Columns: Stock OHLCV_

  

_# Step 1: Preprocess Data_

data["log_return"] = np.log(data["Close"] / data["Close"].shift(1)).fillna(0)

normalized_data = StandardScaler().fit_transform(data["log_return"].values.reshape(-1, 1))

  

_# Step 2: Feature Engineering_

_# Use rolling features (e.g., moving averages, volatility)_

data["volatility"] = data["Close"].rolling(window=10).std()

  

_# Step 3: Dimensionality Reduction_

pca = PCA(n_components=10)

compressed_data = pca.fit_transform(normalized_data)

  

_# Step 4: Clustering with DTW_

model = TimeSeriesKMeans(n_clusters=10, metric="dtw")

labels = model.fit_predict(compressed_data)

  

_# Step 5: Analyze and Visualize_

print("Cluster Assignments:", labels)

Preprocessing things

1. Essential Preprocessing Steps for DTW

These steps are critical to ensure that DTW operates on clean, comparable time series data.

1.1. Handling Missing Data

• Why: DTW requires complete time series to compute distances.

• How:

• Interpolate missing values (linear, spline, or nearest neighbor).

• Forward-fill/backward-fill for gaps.

• Drop stocks with excessive missing values.

1.2. Normalization

• Why: DTW is sensitive to the scale of values. Normalization ensures fair comparison across stocks.

• How:

• Min-Max Scaling: Scale all values to [0, 1].

• Z-Score Standardization: Subtract mean and divide by standard deviation for each time series.

1.3. Smoothing

• Why: Stock data is noisy. Smoothing reduces the impact of random fluctuations.

• How:

• Apply a rolling mean or median (e.g., a 5-day moving average).

• Use exponential smoothing for a more responsive approach to recent values.

1.4. Length Alignment

• Why: DTW allows for different lengths, but extreme variations in length can distort alignment.

• How:

• Truncate time series to a fixed length.

• Pad shorter series with zeros or the mean value.

2. Advanced Transformations

These transformations may improve the quality of clustering depending on your objectives.

2.1. Differencing

• Why: Removes trends and focuses on changes, making patterns more comparable.

• How:

• Compute first-order differences: .

• Optionally use second-order differences for more complex patterns.

2.2. Log Transformation

• Why: Reduces the impact of large spikes (e.g., extreme price changes) and stabilizes variance.

• How:

• Apply , where is a small constant to handle zeros.

2.3. Time Series Decomposition

• Why: Decomposition separates a time series into trend, seasonal, and residual components. This helps if you want to focus on specific patterns.

• When to Decompose:

• If your goal is to compare trends or residuals separately.

• For highly seasonal stocks or when noise obscures patterns.

How to Decompose:

Use libraries like statsmodels or seasonal to perform decomposition:

from statsmodels.tsa.seasonal import seasonal_decompose

result = seasonal_decompose(time_series, model=‘additive’, period=252) # 252 trading days

trend = result.trend

seasonal = result.seasonal

residual = result.resid

Decide which component(s) to use for DTW:

• Trend: For long-term comparisons.

• Residual: For pattern-based clustering.

• Seasonal: If you expect stocks to behave similarly in cycles (e.g., quarterly performance).

3. Feature Engineering

Additional transformations can emphasize patterns of interest.

3.1. Rolling Statistics

• Compute rolling means, medians, or volatility (e.g., standard deviation over a 10-day window).

• Example:

data[‘rolling_mean’] = data[‘Close’].rolling(window=10).mean()

data[‘rolling_std’] = data[‘Close’].rolling(window=10).std()

3.2. Aggregation

• Aggregate data into different time scales (e.g., daily, weekly, monthly).

• Useful if daily data is too noisy or if long-term trends are more important.

3.3. Feature Scaling Across Time Series

• Scale all time series together (global normalization) if relative differences between stocks matter.

4. Decision: Should You Decompose?

• Yes, Decompose If:

• You want to analyze specific components (e.g., trend or residuals).

• The time series has strong seasonality or noise obscuring patterns.

• Clustering objectives focus on identifying long-term behavior or separating noise.

• No, Decomposition May Not Be Necessary If:

• You’re analyzing overall similarity.

• Patterns are already clear after basic preprocessing.

5. Handling Potential Fallbacks

Scaling Mismatches: Normalize or rescale to avoid outlier bias.
Noise Sensitivity: Apply smoothing or decomposition to isolate meaningful components.
Computational Cost: For large datasets, downsample or use approximate DTW algorithms like fastdtw.

Example Pipeline for Preprocessing and DTW

import numpy as np

from tslearn.metrics import dtw

from tslearn.preprocessing import TimeSeriesScalerMeanVariance

from statsmodels.tsa.seasonal import seasonal_decompose

import pandas as pd

# Step 1: Load Data

data = pd.read_csv(“ohlcv_data.csv”) # Assume ‘Close’ is the target series

# Step 2: Preprocessing

# Normalize

scaler = TimeSeriesScalerMeanVariance()

normalized_data = scaler.fit_transform(data[‘Close’].values.reshape(-1, 1))

# Smooth (Rolling Mean)

data[‘smoothed’] = data[‘Close’].rolling(window=5).mean()

# Optional: Decompose

result = seasonal_decompose(data[‘smoothed’], model=‘additive’, period=252)

trend = result.trend.dropna()

# Step 3: DTW

distance_matrix = np.array([[dtw(ts1, ts2) for ts2 in trend] for ts1 in trend])

Summary of Required Transformations

Normalize (Min-Max or Z-Score).
Handle missing values (interpolation or removal).
Smooth data to reduce noise.
Align lengths or truncate/pad as needed.
Optionally decompose to isolate trends, seasonality, or residuals.

Things to look out for.

End-to-End Process for Clustering Stocks

1. Define the Objective

• Goal: Group stocks into clusters for representation and diversification.

• Criteria:

• Clusters should reflect stocks with similar risk/return or price movement patterns.

• Stocks within a cluster should avoid redundancy, ensuring meaningful diversification.

2. Data Preparation

This stage is critical for ensuring high-quality input data.

2.1. Data Collection

• Collect OHLCV data for all 5000 stocks.

• Metrics to Calculate:

• Price-Based Features: Closing prices, log returns, volatility.

• Volume-Based Features: Average daily volume, changes in volume.

• Technical Indicators: RSI, MACD, Bollinger Bands, etc.

2.2. Data Cleaning

• Potential Errors:

• Missing Data: Gaps in price or volume data.

• Solution: Interpolate missing values or drop incomplete data.

• Outliers: Sudden spikes/drops due to errors or rare events.

• Solution: Winsorize or use robust statistical methods to handle outliers.

2.3. Feature Scaling

• Normalize or standardize features.

• Error to Watch: Inconsistent scaling across stocks leads to biased clustering.

• Solution: Use global normalization (e.g., Z-score scaling across all stocks).

2.4. Align Time Frames

• Ensure all stocks have data for the same time period.

• Error to Watch: Different lengths of time series (e.g., newly listed stocks).

• Solution: Truncate or pad shorter time series.

2.5. Denoising

• Apply smoothing to reduce noise (e.g., moving averages or exponential smoothing).

• Error to Watch: Over-smoothing may remove meaningful signals.

• Solution: Use a moderate smoothing window (e.g., 5–10 days).

3. Feature Engineering

3.1. Statistics-Based Features

• Compute summary statistics for clustering:

• Mean log returns, standard deviation, skewness, kurtosis.

• Rolling features (e.g., 15-day mean return, 15-day volatility).

3.2. Time Series Features

• Use raw price series or log returns for DTW or correlation-based clustering.

• Error to Watch: Overemphasis on high-volatility stocks in similarity metrics.

• Solution: Normalize time series before applying similarity measures.

3.3. Technical Indicators

• Calculate indicators like RSI, MACD, or moving averages.

• Error to Watch: Redundant or correlated features.

• Solution: Use PCA or feature selection to reduce dimensionality.

4. Clustering

4.1. Statistics-Based Clustering

• Algorithm: k-Means, DBSCAN, or Gaussian Mixture Models.

• Steps:

• Use features like mean return, variance, and kurtosis.

• Identify the optimal number of clusters using:

• Elbow method (for k-Means).

• Silhouette score (for all methods).

• Visualize clusters in 2D using t-SNE or PCA.

• Error to Watch:

• Poorly separated clusters due to high-dimensional data

Features that might be useful

1. Goals of Feature Engineering

Features should:

Represent Risk-Return Dynamics:

• Capture mean returns, volatility, and other risk measures.

Incorporate Temporal Patterns:

• Reflect trends or seasonal behaviors in stock performance.

Enable Clustering Separability:

• Distinguish meaningful groups using diverse metrics.

2. Categories of Features

2.1. Return Features

These capture the profit potential of a stock.

Simple Returns:

• Definition: Percentage change between consecutive prices.

• Use: Short-term clustering.

Log Returns:

• Definition: Natural log of the ratio of consecutive prices.

• Use: Better for handling compounding effects.

Rolling Metrics:

• Rolling mean return over a window (e.g., 15 or 30 days).

• Rolling cumulative return:

Excess Returns:

• Subtract the market index return (benchmark-adjusted returns).

2.2. Risk Features

Quantify the variability or downside risk of stock performance.

Volatility:

• Rolling standard deviation of returns:

• Longer rolling windows (30–90 days) smooth short-term spikes.

Downside Deviation:

• Focuses only on negative deviations from the mean:

Beta:

• Measures sensitivity to the overall market:

Value at Risk (VaR):

• Quantifies potential loss over a period at a confidence level (e.g., 5%):

Skewness and Kurtosis:

• Skewness captures the asymmetry of return distribution.

• Kurtosis reflects extreme values (fat tails).

2.3. Performance Ratios

Combine risk and return into interpretable metrics.

Sharpe Ratio:

• Captures risk-adjusted returns:

Sortino Ratio:

• Penalizes only downside risk:

Information Ratio:

• Measures excess return per unit of tracking error relative to a benchmark:

2.4. Technical Indicators

Incorporate momentum, trend, and mean-reversion signals.

Momentum Indicators:

• Relative Strength Index (RSI): Measures overbought/oversold conditions.

• Moving Average Convergence Divergence (MACD): Difference between short-term and long-term moving averages.

Trend Indicators:

• Moving Averages: SMA, EMA (e.g., 15-day, 50-day, 200-day).

• Average True Range (ATR): Measures volatility.

Reversal Indicators:

• Bollinger Bands: Identify price relative to a moving average.

• Stochastic Oscillator: Measures position within a recent high-low range.

2.5. Correlation Features

Assess relationships between stocks for diversification.

Pairwise Correlations:

• Compute rolling correlations between stocks and indices.

Clustered Correlations:

• Use hierarchical clustering on correlation matrices.

Autocorrelation:

• Measures the lagged relationship of a stock with itself:

2.6. Macro and Sector Features

Broaden context with external factors:

• Macro Indicators: Interest rates, inflation, GDP growth.

• Sector Membership: Group stocks by industries or sectors.

3. Steps to Validate Features

Correlation Matrix:

• Identify highly correlated features and drop redundant ones.

• Use dimensionality reduction techniques (e.g., PCA).

Feature Importance:

• Use tree-based models (e.g., Random Forest) to rank feature importance.

Clustering Quality:

• Evaluate clusters using silhouette score or Davies-Bouldin Index.

4. Errors to Watch For

Feature Overload:

• Too many features dilute clustering quality.

• Solution: Focus on the most interpretable and impactful metrics.

Multicollinearity:

• High correlation between features can mislead clustering algorithms.

• Solution: Drop correlated features or use PCA.

Temporal Instability:

• Features may not generalize across different market conditions.

• Solution: Use rolling windows and validate across multiple periods.

Outlier Influence:

• Outliers in returns or technical indicators can skew clusters.

• Solution: Winsorize or cap extreme values.

Normalization Issues:

• Features on different scales affect clustering results.

• Solution: Normalize features using Z-score scaling.

5. Advanced Extensions

Automated Feature Selection

• Use algorithms like Recursive Feature Elimination (RFE) or AutoML tools to automate feature selection.

Dynamic Feature Sets

• Adjust feature importance dynamically based on market conditions (e.g., using regime-switching models).

6. Sample Implementation

Here’s a Python snippet for feature engineering:

import pandas as pd

import numpy as np

from scipy.stats import skew, kurtosis

# Load data

data = pd.read_csv(“stock_data.csv”)

returns = data.pivot(index=“Date”, columns=“Stock”, values=“Close”).pct_change()

# Rolling metrics

window = 15

features = pd.DataFrame()

features[‘mean_return’] = returns.rolling(window=window).mean().mean(axis=1)

features[‘volatility’] = returns.rolling(window=window).std().mean(axis=1)

features[‘skewness’] = returns.rolling(window=window).apply(skew).mean(axis=1)

features[‘kurtosis’] = returns.rolling(window=window).apply(kurtosis).mean(axis=1)

# Performance ratios

risk_free_rate = 0.01 / 252 # Annualized to daily

features[‘sharpe_ratio’] = (features[‘mean_return’] - risk_free_rate) / features[‘volatility’]

# Normalize

from sklearn.preprocessing import StandardScaler

scaler = StandardScaler()

scaled_features = scaler.fit_transform(features.dropna())

Next Steps

Evaluate Clustering Quality:

• Use silhouette scores or visualization (e.g., t-SNE).

Experiment with Different Features:

• Combine risk, return, and technical indicators.

Iterate:

• Continuously refine based on clustering performance and backtesting results.

Risk Return profile

If your goal is to cluster stocks based on similar risk-return profiles, here’s an in-depth approach tailored to your objective.

1. What is a Risk-Return Profile?

A stock’s risk-return profile captures:

Return: Measures the average return over a period (e.g., 15–30 days).
Risk: Measures the variability (volatility) of returns.
Higher-Order Risk Metrics: Skewness, kurtosis, and tail risks to capture unusual behaviors.
Other Considerations: Downside risk, Sharpe ratio, and historical drawdowns.

2. Workflow for Clustering Based on Risk-Return Profiles

Step 1: Data Preparation

1.1. Time Frame

• Focus on a rolling window of 15–30 days to align with your target horizon.

• If using long-term historical data, calculate rolling statistics for short-term returns and risk.

1.2. Return Calculation

• Use log returns for robust comparisons:

• Compute rolling metrics:

• Mean Log Return over 15 or 30 days.

• Standard Deviation (Volatility) of returns over the same period.

1.3. Risk Metrics

• Higher-Order Statistics:

• Skewness: Asymmetry of return distribution (positive indicates higher likelihood of gains).

• Kurtosis: Extreme movements (higher kurtosis indicates more outliers).

• Downside Risk: Focus on negative returns using semi-deviation or Sortino ratio.

• Drawdowns: Maximum percentage decline from a peak during a rolling window.

Step 2: Feature Engineering

The features should comprehensively represent risk-return profiles:

• Returns:

• Average return (mean log return).

• Rolling cumulative return over 15–30 days.

• Risk:

• Rolling standard deviation of returns (volatility).

• Downside deviation.

• Beta (sensitivity to market movements).

• Performance Ratios:

• Sharpe ratio:

• Sortino ratio: Penalizes downside risk more heavily.

• Tail Risk:

• Skewness and kurtosis of return distribution.

Step 3: Clustering

3.1. Select Clustering Algorithm

• Use clustering algorithms that handle mixed feature spaces (numerical and statistical metrics):

• k-Means: Works well for standardized numerical features.

• DBSCAN: Identifies clusters of arbitrary shapes and outliers.

• Gaussian Mixture Models (GMM): Clusters based on probabilistic distributions.

• Agglomerative Clustering: Good for hierarchical relationships.

3.2. Preprocessing

• Normalize or standardize all features to ensure they contribute equally:

3.3. Determine the Number of Clusters

• Use methods like:

• Elbow Method: Plot inertia (sum of squared distances) versus the number of clusters.

• Silhouette Score: Measures separation between clusters.

Step 4: Stock Selection for Diversification

Representative Stocks:

• Pick one stock from each cluster based on criteria like lowest volatility or highest Sharpe ratio.

Diversification Check:

• Ensure clusters are distinct in terms of risk-return characteristics by plotting key metrics (e.g., mean return vs. volatility).

3. Example Pipeline

Here’s how you can implement this in Python:

import pandas as pd

import numpy as np

from sklearn.cluster import KMeans

from sklearn.preprocessing import StandardScaler

from scipy.stats import skew, kurtosis

# Step 1: Load Data

data = pd.read_csv(“stock_data.csv”) # OHLCV data

returns = data.pivot_table(index=‘Date’, columns=‘Stock’, values=‘Close’).pct_change()

# Step 2: Compute Risk-Return Metrics

rolling_window = 15

features = pd.DataFrame()

# Mean Return

features[‘mean_return’] = returns.rolling(window=rolling_window).mean().mean(axis=1)

# Volatility (Standard Deviation)

features[‘volatility’] = returns.rolling(window=rolling_window).std().mean(axis=1)

# Skewness

features[‘skewness’] = returns.rolling(window=rolling_window).apply(skew).mean(axis=1)

# Kurtosis

features[‘kurtosis’] = returns.rolling(window=rolling_window).apply(kurtosis).mean(axis=1)

# Step 3: Preprocessing

scaler = StandardScaler()

scaled_features = scaler.fit_transform(features.dropna())

# Step 4: Clustering

kmeans = KMeans(n_clusters=5, random_state=42)

clusters = kmeans.fit_predict(scaled_features)

features[‘cluster’] = clusters

# Step 5: Analyze and Select Stocks

# Group by clusters and find representative stocks

representative_stocks = returns.groupby(features[‘cluster’]).apply(

lambda x: x.idxmin(axis=1) # Example: Pick stock with lowest volatility

)

4. Errors and Pitfalls to Watch For

High Dimensionality:

• Too many features dilute clustering quality.

• Solution: Use dimensionality reduction (e.g., PCA) to retain the most important features.

Overlapping Clusters:

• Stocks may not cleanly fall into distinct clusters.

• Solution: Use soft clustering methods (e.g., GMM) to handle overlaps.

Outliers and Noise:

• Extreme returns or atypical stocks can skew clusters.

• Solution: Apply robust methods (e.g., DBSCAN) or Winsorize extreme values.

Feature Selection Bias:

• Poorly chosen features might miss key patterns.

• Solution: Experiment with different combinations of risk-return metrics.

Temporal Instability:

• Clusters based on short-term data may not generalize.

• Solution: Use rolling windows to validate consistency.

5. Visualization

After clustering, visualize clusters to confirm separability:

• Scatter Plots:

• Plot mean return vs. volatility, colored by cluster.

• Cluster Centroids:

• Compare centroids to understand cluster profiles.

• Time Series Plots:

• Overlay representative stocks from each cluster.

6. Advanced Extensions

Dynamic Clustering:

• Update clusters periodically as new data becomes available.

Hybrid Clustering:

• Combine statistics-based clustering with time series similarity measures.

Portfolio Optimization:

• Use the clusters to select a diversified portfolio with constraints like maximum volatility.

Risk Return Profile In depth

Risk-Return Profile: A Comprehensive Guide

The risk-return profile approach seeks to group stocks or assets based on their ability to balance returns and risk, tailoring it to your desired rebalancing timeline of 7–15 days. Here’s a deep dive into how you can implement this strategy effectively.

1. Understanding Risk and Return Metrics

1.1 Return Metrics

• Mean Return (Short-Term):

• Measures the average return over the desired period (e.g., 7 or 15 days).

• Formula:

where is the return on day .

• Cumulative Return:

• Measures total return over a fixed period.

where and are prices at the start and end of the period.

• Rolling Returns:

• Calculates returns over a moving window (e.g., every 15 days).

1.2 Risk Metrics

• Volatility (Standard Deviation):

• Quantifies daily return fluctuations.

• Maximum Drawdown (MDD):

• Captures the largest peak-to-trough loss during the period.

• Value at Risk (VaR):

• Estimates the potential loss in value under normal market conditions.

• Beta:

• Measures sensitivity to market movements. A lower beta reduces market exposure.

1.3 Risk-Adjusted Return Metrics

• Sharpe Ratio:

• Measures return per unit of risk. Higher is better.

where is the risk-free rate.

• Sortino Ratio:

• Similar to Sharpe but penalizes only downside volatility.

• Treynor Ratio:

• Focuses on systematic risk using beta.

2. Key Steps in Risk-Return Optimization

Step 1: Feature Engineering

Create features that capture risk-return metrics for each stock:

• Return-Based Features:

• Rolling mean return, cumulative return, 7-day and 15-day return.

• Risk-Based Features:

• Rolling volatility, beta, and max drawdown.

• Risk-Adjusted Features:

• Sharpe and Sortino ratios.

Step 2: Normalize and Scale Features

Standardize features to ensure comparability:

• Mean-center and scale using Z-scores:

Step 3: Clustering Stocks

• Apply clustering algorithms (e.g., k-means, DBSCAN, or hierarchical clustering) using the engineered features.

• Choose the number of clusters based on metrics like the silhouette score or elbow method.

Step 4: Portfolio Construction

• Select stocks from different clusters to ensure diversification.

• Optimize weights using mean-variance optimization (e.g., Markowitz Portfolio Theory) or Risk Parity.

Step 5: Backtesting and Rebalancing

• Backtest cluster performance over rolling 7–15 day windows.

• Rebalance periodically by re-evaluating clusters and portfolio weights.

3. Portfolio Rebalancing: Why 7–15 Days?

Short-term rebalancing aligns with your goal of capturing market opportunities while minimizing exposure. Here’s how this timeline works:

• 7-Day Rebalance:

• Captures short-term price movements and trends.

• Suitable for volatile markets or event-driven strategies.

• 15-Day Rebalance:

• Provides a balance between transaction costs and capturing medium-term trends.

4. Implementation Workflow

Feature Engineering Workflow in Python

import pandas as pd

import numpy as np

# Load stock price data

prices = pd.read_csv(“stock_prices.csv”)

returns = prices.pct_change()

# Feature Engineering

features = pd.DataFrame()

features[‘mean_return_7d’] = returns.rolling(window=7).mean()

features[‘volatility_7d’] = returns.rolling(window=7).std()

features[‘sharpe_ratio_7d’] = features[‘mean_return_7d’] / features[‘volatility_7d’]

features[‘mean_return_15d’] = returns.rolling(window=15).mean()

features[‘volatility_15d’] = returns.rolling(window=15).std()

features[‘sharpe_ratio_15d’] = features[‘mean_return_15d’] / features[‘volatility_15d’]

features = features.dropna()

Clustering Workflow

from sklearn.cluster import KMeans

from sklearn.preprocessing import StandardScaler

# Normalize features

scaler = StandardScaler()

scaled_features = scaler.fit_transform(features)

# Apply k-means clustering

kmeans = KMeans(n_clusters=5, random_state=42)

features[‘Cluster’] = kmeans.fit_predict(scaled_features)

# Analyze clusters

print(features.groupby(‘Cluster’).mean())

Portfolio Construction

from pypfopt.efficient_frontier import EfficientFrontier

from pypfopt.risk_models import CovarianceShrinkage

from pypfopt.expected_returns import mean_historical_return

# Calculate expected returns and covariance matrix

expected_returns = mean_historical_return(prices)

cov_matrix = CovarianceShrinkage(prices).ledoit_wolf()

# Optimize portfolio for maximum Sharpe ratio

ef = EfficientFrontier(expected_returns, cov_matrix)

weights = ef.max_sharpe()

cleaned_weights = ef.clean_weights()

print(cleaned_weights)

5. Common Challenges to Address

5.1 Overfitting Clusters

• Avoid overly complex features or too many clusters.

• Solution: Use cross-validation to test cluster robustness.

5.2 Transaction Costs

• Frequent rebalancing increases costs.

• Solution: Limit turnover by capping stock weight changes.

5.3 Changing Market Regimes

• Risk-return profiles can vary across market cycles.

• Solution: Monitor cluster consistency over different time periods.

5.4 Outlier Impact

• Sudden price spikes can distort metrics.

• Solution: Winsorize returns to cap extreme values.

6. Advanced Tips

Combine Risk-Return and Event-Based Approaches:

• Overlay event-driven insights (e.g., earnings sensitivity) on risk-return clusters.

Dynamic Clustering:

• Update clusters adaptively as new data arrives, especially during volatile periods.

Factor Analysis:

• Decompose returns into common factors (e.g., size, value) for deeper clustering insights.

🪴 Prakritidev Verma

Explorer

"Time Series - Clustering"

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Risk Return profile

Risk Return Profile In depth

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