A random walk simulation

Stochastic or random movements are used in physics to represent particle and fluid movements, in mathematics to describe fractal behavior, and in finance to describe stock market movements.

Use the np.random.normal() function to model random walk movements of the USO oil ETF with a constant daily average return (mu) and average daily volatility (vol) over the course of T trading days.

This exercise is part of the course

Introduction to Portfolio Risk Management in Python

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Exercise instructions

Set the number of simulated days (T) equal to 252, and the initial stock price (S0) equal to 10.
Calculate T random normal values using np.random.normal(), passing in mu and vol, and T as parameters, then adding 1 to the values and assign it to rand_rets.
Calculate the random walk by multiplying rand_rets.cumprod() by the initial stock price and assign it to forecasted_values.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Set the simulation parameters
mu = np.mean(StockReturns)
vol = np.std(StockReturns)
T = ____
S0 = ____

# Add one to the random returns
rand_rets = ____ + 1

# Forecasted random walk
forecasted_values = ____

# Plot the random walk
plt.plot(range(0, T), forecasted_values)
plt.show()

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