Portfolio Random Walk Simulation
A random walk is a sequence of steps where each step is determined by chance, and the direction and size of each move are unpredictable. In portfolio modeling, you can use a random walk to represent how the value of a portfolio might evolve over time if each period's return is random and independent of previous returns. This approach helps you visualize the possible paths a portfolio's value could take and analyze cumulative returns, which is crucial for understanding risk and uncertainty in investments.
1234567891011121314151617181920212223import numpy as np import matplotlib.pyplot as plt # Set simulation parameters np.random.seed(42) n_steps = 252 # Number of trading days in a year initial_value = 1000 # Starting portfolio value # Simulate daily returns as a normal random variable (mean=0, std=1%) daily_returns = np.random.normal(0, 0.01, n_steps) # Calculate cumulative returns (random walk) portfolio_values = initial_value * np.cumprod(1 + daily_returns) # Plot the results plt.figure(figsize=(10, 5)) plt.plot(portfolio_values, label="Simulated Portfolio Value") plt.title("Portfolio Value Random Walk Simulation") plt.xlabel("Day") plt.ylabel("Portfolio Value ($)") plt.legend() plt.grid(True) plt.show()
The code begins by importing the required libraries and setting a random seed to ensure reproducibility. You specify the number of steps, representing trading days, and the initial portfolio value. The daily returns are simulated using a normal distribution with a mean of zero and a standard deviation of 1%, reflecting the idea that returns can be both positive and negative with no expected drift. Each day's portfolio value is calculated by multiplying the previous value by one plus the daily return, which models compounding. The np.cumprod function applies this compounding across all days, producing a simulated path for the portfolio's value. Finally, the code plots the resulting time series, allowing you to visualize how the random walk leads to fluctuations in the portfolio's cumulative return over time.
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Can you explain how changing the standard deviation affects the simulation?
What does it mean if the mean of daily returns is not zero?
How can I interpret the results of the random walk simulation?
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A random walk is a sequence of steps where each step is determined by chance, and the direction and size of each move are unpredictable. In portfolio modeling, you can use a random walk to represent how the value of a portfolio might evolve over time if each period's return is random and independent of previous returns. This approach helps you visualize the possible paths a portfolio's value could take and analyze cumulative returns, which is crucial for understanding risk and uncertainty in investments.
1234567891011121314151617181920212223import numpy as np import matplotlib.pyplot as plt # Set simulation parameters np.random.seed(42) n_steps = 252 # Number of trading days in a year initial_value = 1000 # Starting portfolio value # Simulate daily returns as a normal random variable (mean=0, std=1%) daily_returns = np.random.normal(0, 0.01, n_steps) # Calculate cumulative returns (random walk) portfolio_values = initial_value * np.cumprod(1 + daily_returns) # Plot the results plt.figure(figsize=(10, 5)) plt.plot(portfolio_values, label="Simulated Portfolio Value") plt.title("Portfolio Value Random Walk Simulation") plt.xlabel("Day") plt.ylabel("Portfolio Value ($)") plt.legend() plt.grid(True) plt.show()
The code begins by importing the required libraries and setting a random seed to ensure reproducibility. You specify the number of steps, representing trading days, and the initial portfolio value. The daily returns are simulated using a normal distribution with a mean of zero and a standard deviation of 1%, reflecting the idea that returns can be both positive and negative with no expected drift. Each day's portfolio value is calculated by multiplying the previous value by one plus the daily return, which models compounding. The np.cumprod function applies this compounding across all days, producing a simulated path for the portfolio's value. Finally, the code plots the resulting time series, allowing you to visualize how the random walk leads to fluctuations in the portfolio's cumulative return over time.
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