Machine Learning and Deep Learning Algorithm Trading, Mean Variance Optimization

Hello! Welcome to the course for those interested in quantitative trading. In this course, we will delve deeply into machine learning and deep learning algorithm trading as well as mean-variance optimization. To understand this content, a basic knowledge of statistics and programming skills are required. However, do not worry, I will explain it as simply as possible.

1. Basic Concepts of Machine Learning and Deep Learning

Machine learning is a technique that uses data to recognize patterns and make predictions. Deep learning, a subset of machine learning, uses artificial neural networks to solve even more complex problems.

1.1 Types of Machine Learning

Machine learning can be broadly categorized into three types:

  • Supervised Learning: Used when input data and correct output data are provided. For example, a model that predicts future stock prices based on past stock prices falls into this category.
  • Unsupervised Learning: In cases where only input data is given and no output data is provided. Techniques like clustering fall under this category.
  • Reinforcement Learning: An agent learns strategies to maximize rewards by interacting with the environment. It is commonly used in stock trading systems.

1.2 Structure of Deep Learning

Deep learning is based on artificial neural networks and consists of multiple layers of nodes (neurons). Each layer receives signals from the previous layer, applies weights, and then passes the signals to the next layer through an activation function.

2. What is Algorithm Trading?

Algorithm trading is a method that automatically executes trading transactions based on predefined trading rules. Through machine learning and deep learning algorithms, market data can be collected and analyzed to develop more sophisticated strategies.

2.1 Advantages of Algorithm Trading

  • Accurate data analysis
  • Exclusion of emotional factors
  • Rapid order execution
  • Validation of strategies through backtesting

2.2 Implementation Process of Algorithm Trading

The process of implementing an algorithm trading system is as follows:

  1. Market data collection
  2. Data preprocessing and exploratory data analysis (EDA)
  3. Model selection and training
  4. Backtesting and strategy optimization
  5. Real trading

3. Mean-Variance Optimization

Mean-variance optimization is a methodology that serves as the foundation for portfolio theory, used to balance the returns and risks of assets. It is a theory proposed by Harry Markowitz in 1952.

3.1 Basic Principles of Mean-Variance Optimization

Mean-variance optimization is based on two key elements:

  • Expected Return: The average return that an asset is expected to yield over the long term.
  • Risk: Represents the volatility of asset returns and is generally measured by standard deviation.

3.2 Portfolio Construction

Portfolio construction is the process of determining the proportions of each asset. In this process, the correlations between each asset play an important role.

3.3 Mean-Variance Optimization Formula

    Minimize: 1/2 * w' * Σ * w
    Subject to: μ' * w >= r
                 1' * w = 1

Where:

  • w: Proportions of the assets
  • Σ: Covariance matrix of the assets
  • μ: Expected return vector of the assets
  • r: Target return
  • 1: A vector with all elements equal to 1

3.4 Implementation of Mean-Variance Optimization Using Python

import numpy as np
import pandas as pd
from scipy.optimize import minimize

def mean_variance_optimization(return_data, target_return):
    returns = return_data.mean()
    cov_matrix = return_data.cov()
    
    num_assets = len(returns)
    
    def objective(weights):
        return 0.5 * np.dot(weights.T, np.dot(cov_matrix, weights))
    
    constraints = (
        {'type': 'eq', 'fun': lambda x: np.sum(x) - 1},
        {'type': 'eq', 'fun': lambda x: np.dot(returns, x) - target_return}
    )
    
    bounds = tuple((0, 1) for asset in range(num_assets))
    initial_weights = num_assets * [1. / num_assets]
    
    optimization_results = minimize(objective, initial_weights, method='SLSQP', bounds=bounds, constraints=constraints)
    
    return optimization_results.x

# Example data
data = pd.DataFrame({
    'Asset1': [0.1, 0.12, 0.15],
    'Asset2': [0.08, 0.1, 0.09],
    'Asset3': [0.15, 0.14, 0.2],
})

optimized_weights = mean_variance_optimization(data, target_return=0.1)
print(optimized_weights)

3.5 Results Analysis

The optimal asset proportions calculated from the code above constitute a structure that minimizes risk while satisfying the portfolio’s expected return to meet the target return. The optimized weights can also be applied in the process of portfolio rebalancing.

4. Building Machine Learning and Deep Learning Models

Now we will implement algorithm trading using machine learning and deep learning. The model supports trading decisions based on historical market data predictions.

4.1 Data Collection and Preprocessing

Data collection can be performed through API or web scraping, and the collected data is sorted over time, handling missing values before calculating metrics.

4.2 Feature Engineering

This is the process of creating various features to improve the model. For example, considering past prices, trading volume, moving averages, etc.

4.3 Training the Machine Learning Model

from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor

# Splitting the data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Training the model
model = RandomForestRegressor()
model.fit(X_train, y_train)

4.4 Model Evaluation and Optimization

The performance of the model can be evaluated using various metrics such as RMSE, MAE, etc., which can be used to proceed with hyperparameter tuning to optimize the model.

4.5 Building the Deep Learning Model

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense

# Constructing the deep learning model
model = Sequential()
model.add(Dense(units=64, activation='relu', input_dim=X.shape[1]))
model.add(Dense(units=32, activation='relu'))
model.add(Dense(units=1, activation='linear'))

model.compile(optimizer='adam', loss='mean_squared_error')

# Training the model
model.fit(X_train, y_train, epochs=100, batch_size=10)

5. Backtesting and Strategy Evaluation

We analyze the results by testing the performance of the built algorithm against historical data. This allows us to evaluate the profitability and safety of the strategy.

5.1 Establishing a Backtesting Framework

Backtesting an algorithm involves generating trading signals based on given historical data and executing them to measure performance.

5.2 Performance Metrics

Several performance metrics are used to evaluate backtesting results:

  • Sharpe Ratio
  • Maximum Drawdown
  • Annualized Return

6. Conclusion

In this course, we covered algorithm trading using machine learning and deep learning, as well as mean-variance optimization. Based on the knowledge gained in this process, we encourage you to build your own trading system. The world of quantitative trading is continuously evolving, and through this, you can also aim for high profitability!

We will prepare more courses and details in the future. Thank you!