Monte Carlo Backtesting: A Trader's Ace

In the world of trading, "fail to prepare, prepare to fail" - and this applies to testing strategies too. Monte Carlo backtesting is a powerful tool to ensure a strategy can withstand the volatility of the market. By simulating multiple market scenarios, traders can evaluate their approach and make data-driven decisions. In this article, we delve into the details of Monte Carlo backtesting and its use in assessing the reliability of trading strategies.

To harness the power of Monte Carlo simulation, traders can follow these four steps:

• First, choose a probability distribution that best describes the behavior of the input variables you want to simulate. This could be a normal distribution to simulate the daily returns of a coin’s price.
• Second, generate random values for each input variable for each time step in your simulation using the chosen probability distribution.
• Third, calculate the new value of each input variable for each time step in your simulation using the random values generated in step?two.
• Fourth, repeat steps two and three for a large number of time steps to generate a vast number of possible paths for the asset price.

Once you have generated numerous possible paths for the asset price using Monte Carlo simulation, you can use these paths to simulate the execution of your strategy under a wide variety of market conditions.

One useful method to analyse the results of the simulations is to run the strategy using those paths and draw the distribution of the return, volatility, Sharpe, and other metrics. The less standard deviation these distributions have, the better it is, as it indicates a smaller variance in the performance metrics.

Now let’s take a closer look at the code snippet for Monte Carlo simulations. This code will help you understand how to generate random variations in the input variables and simulate the possible paths that the asset price could take in the future.

import numpy as np

# Define input variables

price = 100 # initial price

daily_return = 0.01 # average daily return

volatility = 0.2 # daily volatility

num_simulations = 1000 # number of simulations

num_days = 30 # number of days to simulate

# Calculate daily drift and diffusion

drift = daily_return - 0.5 * volatility ** 2

diffusion = volatility * np. random. normal (0, 1, – num_days, num_simulations)

# Initialize price matrix

price_matrix = np. zeros num_days, num_simulations)

price_matrix [0,:] = price

# Simulate price paths

for i in range (1, num_days):

price_matrix [i,:] = price_matrix [i-1,:] * np.exp (drift + diffusion [i,:])

# Plot price paths

import matplotlib. pyplot as plt

plt.plot (price_matrix)

plt. xlabel (‘Time – days – ’)

plt. ylabel (‘Asset Price’)

plt. title (‘Monte Carlo Simulation for the asset’)

plt.show ()

This code is a Python implementation of the Monte Carlo simulation for asset prices. It generates a simulated path for the price of an asset over a specified number of days, based on the input variables of initial price, average daily return, daily volatility, number of simulations, and number of days to simulate.

The first step is to define the input variables: price is the initial price of the asset, daily_return is the average daily return of the asset, volatility is the daily volatility of the asset, num_simulations is the number of simulations to run, and num_days is the number of days to simulate.

Next, the daily drift and diffusion are calculated. drift is the difference between the average daily return and half of the square of the daily volatility, while diffusion is a matrix of random values generated using the normal distribution with mean 0 and standard deviation?1.

A price matrix is then initialized with the initial price and populated with the simulated price paths, calculated using the drift and diffusion values. The for loop iterates over the specified number of days, and the price_matrix array is updated at each iteration with the new simulated price path.

Finally, the price paths are plotted using Matplotlib to visualise the simulated paths. The plot function is used to plot the price_matrix array, with xlabel, ylabel, and title used to label the axes and give the plot a title. The show function is then called to display the plot.

Let’s take a look at a real-world example from DFi Labs. We simulated 100 paths for each coin in the universe using Monte Carlo simulation, and ran a strategy over 100 sets of universes. This allowed us to evaluate the robustness of our strategy under a wide range of market conditions.

By generating numerous possible paths for the asset price, we were able to simulate the execution of our trading strategy and analyze important metrics such as returns, volatility, and Sharpe ratio.

• Returns distribution

• Sharpe ratio distribution

• Volatility distribution

The proof is in the pudding – the Monte Carlo backtesting results revealed that the evaluated strategy was a force to be reckoned with, showing robustness and the potential for generating consistent returns across diverse market conditions. This goes to show the power of Monte Carlo simulation in enabling traders to assess the effectiveness of their trading strategies and make informed decisions. By simulating multiple possible paths for the asset price, traders can truly grasp how their strategy would perform under different market scenarios and adapt their approach accordingly.