Loading the player...

What is the 'Monte Carlo Simulation'

Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables.

BREAKING DOWN 'Monte Carlo Simulation'

Since business and finance are plagued by random variables, Monte Carlo simulations have a vast array of potential applications in these fields. They are used to estimate the probability of cost overruns in large projects and the likelihood that an asset price will move in a certain way. Telecoms use them to assess network performance in different scenarios, helping them to optimize the network. Analysts use them to asses the risk that an entity will default and to analyze derivatives such as options. Insurers and oil well drillers also use them. Monte Carlo simulations have countless applications outside of business and finance, such as in meteorology, astronomy and particle physics.

Monte Carlo simulations are named after the gambling hot spot in Monaco, since chance and random outcomes are central to the modeling technique, much as they are to games like roulette, dice and slot machines. The technique was first developed by Stanislaw Ulam, a mathematician who worked on the Manhattan Project. After the war, while recovering from brain surgery, Ulam entertained himself by playing countless games of solitaire. He became interested in plotting the outcome of each of these games in order to observe their distribution and determine the probability of winning. He mentioned this to John Von Neumann, and the two collaborated to develop the Monte Carlo simulation.

Asset Price Modeling

One way to employ a Monte Carlo simulation is to model possible movements of asset prices using Excel or a similar program. There are two components to an asset's price movements: drift, which is a constant directional movement, and a random input, representing market volatility. By analyzing historical price data, you can determine the drift, standard deviation, variance and average price movement for a security. These are the building blocks of a Monte Carlo simulation.

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):

periodic daily return = ln (day's price ÷ previous day's price)

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:

drift = average daily return - (variance ÷ 2)

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.

Next obtain a random input:

random value = standard deviation * NORMSINV(RAND())

The equation for the following day's price is:

next day's price = today's price * e ^ (drift + random value)

To take e to a given power in Excel, use the EXP function: EXP(x). Repeat this calculation the desired number of times (each repetition represents one day) to obtain a simulation of future price movement. By generating an arbitrary number of simulations, you can assess the probability that a security's price will follow given trajectory. Here is an example, showing around 30 projections for the Time Warner Inc's (TWX) stock for the remainder of November 2015:

The frequencies of different outcomes generated by this simulation will form a normal distribution, that is, a bell curve. The most likely return is at the middle of the curve, meaning there is an equal chance that the actual return will be higher or lower than that value. The probability that the actual return will be within one standard deviation of the most probable ("expected") rate is 68%; that it will be within two standard deviations is 95%; and that it will be within three standard deviations is 99.7%. Still, there is no guarantee that the most expected outcome will occur, or that actual movements will not exceed the wildest projections.

Crucially, Monte Carlo simulations ignore everything that is not built into the price movement (macro trends, company leadership, hype, cyclical factors); in other words, they assume perfectly efficient markets. For example, the fact that Time Warner lowered its guidance for the year on November 4 is not reflected here, except in the price movement for that day, the last value in the data; if that fact were accounted for, the bulk of simulations would probably not predict a modest rise in price.

RELATED TERMS
  1. Look-Ahead Bias

    Bias created by the use of information or data in a study or ...
  2. Random Factor Analysis

    A statistical analysis performed to determine the origin of random ...
  3. Stochastic Modeling

    A method of financial modeling in which one or more variables ...
  4. Random Variable

    A variable whose value is unknown or a function that assigns ...
  5. Standard Deviation

    1. A measure of the dispersion of a set of data from its mean. ...
  6. Stress Testing

    A simulation technique used on asset and liability portfolios ...
Related Articles
  1. Investing

    Explaining the Monte Carlo Simulation

    Monte Carlo simulation is an analysis done by running a number of different variables through a model in order to determine the different outcomes.
  2. Investing

    What Can The Monte Carlo Simulation Do For Your Portfolio?

    A Monte Carlo simulation allows analysts and advisors to convert investment chances into choices. The advantage of Monte Carlo is its ability to factor in a range of values for various inputs.
  3. Investing

    Multivariate Models: The Monte Carlo Analysis

    This decision-making tool integrates the idea that every decision has an impact on overall risk.
  4. Investing

    Monte Carlo Simulation With GBM

    Learn to predict future events through a series of random trials.
  5. Investing

    Create a Monte Carlo Simulation Using Excel

    How to apply the Monte Carlo Simulation principles to a game of dice using Microsoft Excel.
  6. Trading

    How To Convert Value At Risk To Different Time Periods

    Volatility is not the only way to measure risk. Learn about the "new science of risk management".
  7. Trading

    Stimulate Your Skills With Simulated Trading

    Think you can beat the Street? We'll show you how to test your abilities without losing your shirt.
  8. Small Business

    Disadvantages Of Stock Simulators

    Stock simulators enable one to practice trading, but they have some disadvantages that you should be aware of, before transitioning to actual trading.
  9. Personal Finance

    Stock Market Simulators: Play Your Way To Profits

    Online stock simulators make learning about stocks as fun and easy as playing a game.
  10. Investing

    Bet Smarter With The Monte Carlo Simulation

    This technique can reduce uncertainty in estimating future outcomes.
RELATED FAQS
  1. What percentage of a diversified portfolio should be exposed to the insurance sector?

    Learn how it is critical to innovate and improve financial models and techniques used in quantitative analysis, and understand ... Read Answer >>
  2. What is the minimum number of simulations that should be run in Monte Carlo Value ...

    Find out how many simulations should be run at minimum for an accurate value at risk when using the Monte Carlo method of ... Read Answer >>
  3. How can I use systematic sampling in finance?

    Learn about systematic sampling, how it works and how it can be used in finance, including Monte Carlo simulations that model ... Read Answer >>
  4. What technical skills must one possess to trade options?

    Learn about the technical skills required to trade options and how mathematical and computer science skills give you a better ... Read Answer >>
  5. What is stress testing in Value at Risk (VaR)?

    Discover the difference between Value at Risk, or VaR, and stress testing, and learn how the two concepts might be used together ... Read Answer >>
  6. What is the difference between standard deviation and average deviation?

    Understand the basics of standard deviation and average deviation, including how each is calculated and why standard deviation ... Read Answer >>
Hot Definitions
  1. Cash Flow

    The net amount of cash and cash-equivalents moving into and out of a business. Positive cash flow indicates that a company's ...
  2. PLUS Loan

    A low-cost student loan offered to parents of students currently enrolled in post-secondary education. With a PLUS Loan, ...
  3. Graduate Record Examination - GRE

    A standardized exam used to measure one's aptitude for abstract thinking in the areas of analytical writing, mathematics ...
  4. Graduate Management Admission Test - GMAT

    A standardized test intended to measure a test taker's aptitude in mathematics and the English language. The GMAT is most ...
  5. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  6. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
Trading Center