# Monte Carlo¶

The Monte Carlo method is implemented in finquant.monte_carlo.

The module provides a class MonteCarlo which is an implementation of the Monte Carlo method and a class MonteCarloOpt which allows the user to perform a Monte Carlo run to find optimised financial portfolios, given an intial portfolio.

class finquant.monte_carlo.MonteCarlo(num_trials=1000)

An object to perform a Monte Carlo run/simulation.

__init__(num_trials=1000)
Input:
num_trials: int (default: 1000), number of iterations of the Monte Carlo run/simulation.
run(fun, **kwargs)
Input:
fun: Function to call at each iteration of the Monte Carlo run. (optional) Additional arguments that are passed to fun.
Output:
result: List of quantities returned from fun at each iteration.
class finquant.monte_carlo.MonteCarloOpt(returns, num_trials=1000, risk_free_rate=0.005, freq=252, initial_weights=None)

An object to perform a Monte Carlo run/simulation for finding optimised financial portfolios.

Inherits from MonteCarlo.

__init__(returns, num_trials=1000, risk_free_rate=0.005, freq=252, initial_weights=None)
Input:
returns: num_trials: A pandas.DataFrame which contains the returns of stocks. Note: If applicable, the given returns should be computed with the same risk free rate and time window/frequency (arguments risk_free_rate and freq as passed down here. int (default: 1000), number of portfolios to be computed, each with a random distribution of weights/allocation in each stock float (default: 0.005), the risk free rate as required for the Sharpe Ratio int (default: 252), number of trading days, default value corresponds to trading days in a year list/numpy.ndarray (default: None), weights of initial/given portfolio, only used to plot a marker for the initial portfolio in the optimisation plot.
Output:
opt: pandas.DataFrame with optimised investment strategies for maximum Sharpe Ratio and minimum volatility.
optimisation()

Optimisation of the portfolio by performing a Monte Carlo simulation.

Output:
opt_w: pandas.DataFrame with optimised investment strategies for maximum Sharpe Ratio and minimum volatility. pandas.DataFrame with Expected Return, Volatility and Sharpe Ratio for portfolios with minimum Volatility and maximum Sharpe Ratio.
plot_results()

Plots the results of the Monte Carlo run, with all of the randomly generated weights/portfolios, as well as markers for the portfolios with the minimum Volatility and maximum Sharpe Ratio.

properties()

Prints out the properties of the Monte Carlo optimisation.