Get the Drift
In the last exercise, you simulated stock prices that follow a random walk. You will extend this in two ways in this exercise.
- You will look at a random walk with a drift. Many time series, like stock prices, are random walks but tend to drift up over time.
- In the last exercise, the noise in the random walk was additive: random, normal changes in price were added to the last price. However, when adding noise, you could theoretically get negative prices. Now you will make the noise multiplicative: you will add one to the random, normal changes to get a total return, and multiply that by the last price.
This exercise is part of the course
Time Series Analysis in Python
Exercise instructions
- Generate 500 random normal multiplicative "steps" with mean 0.1% and standard deviation 1% using
np.random.normal(), which are now returns, and add one for total return. - Simulate stock prices
P:- Cumulate the product of the steps using the numpy
.cumprod()method. - Multiply the cumulative product of total returns by 100 to get a starting value of 100.
- Cumulate the product of the steps using the numpy
- Plot the simulated random walk with drift.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Generate 500 random steps
steps = np.random.normal(loc=___, scale=___, size=___) + ___
# Set first element to 1
steps[0]=1
# Simulate the stock price, P, by taking the cumulative product
P = ___ * np.cumprod(___)
# Plot the simulated stock prices
plt.plot(___)
plt.title("Simulated Random Walk with Drift")
plt.show()