how monte carlo simulations work
the monte carlo method acknowledges an issue for any simulation technique the probability of varying outcomes cannot be firmly pinpointed because of random variable interference therefore a monte carlo simulation focuses on constantly repeating random samples a monte carlo simulation takes the variable that has uncertainty and assigns it a random value the model is then run and a result is provided this process is repeated again and again while assigning many different values to the variable in question once the simulation is complete the results are averaged to arrive at an estimate the 4 steps in a monte carlo simulationto perform a monte carlo simulation there are four main steps as an example microsoft excel or a similar program can be used to create a monte carlo simulation that estimates the probable price movements of stocks or other assets there are two components to an asset s price movement drift which is its constant directional movement and a random input which represents market volatility by analyzing historical price data you can determine the drift standard deviation variance and average price movement of a security these are the building blocks of a monte carlo simulation the four steps are as follows step 1 to project one possible price trajectory use the historical price data of the asset to generate a series of periodic daily returns using the natural logarithm note that this equation differs from the usual percentage change formula step 2 next use the average stdev p and var p functions on the entire resulting series to obtain the average daily return standard deviation and variance inputs respectively the drift is equal to alternatively drift can be set to 0 this choice reflects a certain theoretical orientation but the difference will not be huge at least for shorter time frames step 3 next obtain a random input the equation for the following day s price is step 4 to take e to a given power x in excel use the exp function exp x repeat this calculation the desired number of times each repetition represents one day the result is a simulation of the asset s future price movement by generating an arbitrary number of simulations you can assess the probability that a security s price will follow a given trajectory monte carlo simulation results explainedthe frequencies of different outcomes generated by this simulation will form a normal distribution that is a bell curve the most likely return is in the middle of the curve meaning there is an equal chance that the actual return will be higher or lower the probability that the actual return will be within one standard deviation of the most probable expected rate is 68 the probability is 95 that it will be within two standard deviations and 99 7 that it will be within three standard deviations still there is no guarantee that the most expected outcome will occur or that actual movements will not exceed the wildest projections crucially a monte carlo simulation ignores everything not built into the price movement such as macro trends a company s leadership market hype and cyclical factors in other words it assumes a perfectly efficient market advantages and disadvantages of a monte carlo simulationthe monte carlo simulation was created to overcome a perceived disadvantage of other methods of estimating a probable outcome the difference is that the monte carlo method tests a number of random variables and then averages them rather than starting out with an average like any financial simulation the monte carlo method relies on historical price data as the basis for a projection of future price data it then disrupts the pattern by introducing random variables represented by numbers finally it averages those numbers to arrive at an estimate of the risk that the pattern will be disrupted in real life of course no simulation can pinpoint an inevitable outcome the monte carlo method aims at a sounder estimate of the probability that an outcome will differ from a projection 