Wednesday, May 2, 2012

What is Monte Carlo Simulation?

4:10 PM

Monte Carlo simulation is a mathematical method used to estimate the most likely outcome and the odds that certain events will occur, given a mathematical model of the problem.

Like the roulette wheels associated with the casinos of Monte Carlo, Monte Carlo simulation reproduces random outcomes by generating random numbers to obtain results. Unlike a roulette wheel, the Monte Carlo method uses random numbers to measure and quantify uncertainty and chance events.

The program generates random rates of return and develops a large number of potential future outcomes in the capital markets, assuming that past averages and standard deviations will hold in the future.

Expected returns from equity asset classes (such as Canadian, US or international equities) are typically higher than returns from low risk or risk-free investments (e.g., cash, GICs and fixed income). But higher equity returns also have greater risk, that is a greater range of outcomes, from complete loss of capital to appreciation many times over the initial purchase price. And they also experience greater volatility.

Probability of success

The probability (or chance) of success is the number of times that your plan is successful, i.e. the number of illustrations in which you have enough money to sustain your lifestyle until the end of your life, divided by the number of all simulations. For example, if the portfolio does not run out of money 800 times out of 1,000 scenarios, we can say that the probability of success is 80%.

As a benchmark, a probability of success of 75% or more is good.

Rates of return fluctuate from year to year and are based on the expected return and volatitlity (as measured by the standard deviation) of each asset class.

The chart below shows sample simulations for somone age 45, retiring at age 65 and with a life expectancy of 90. The variability of outcomes results from the degree of volatility, which increases with the proportion of assets invested in equities.

Sample simulations

Why is it useful?

The goal is to raise the comfort level knowing the odds of achieving pragmatic financial lifestyle goals, and feel comfortable with a financial plan, even in periods of negative market performance.

If a probability of 80% percent seems too risky and you would like to increase the odds to 85% or 90% , you can adjust your annual savings, retire later, reduce your income requirements or change your portfolio allocation.

The risk of hitting a string of bad years early on can easily upset a retirement plan. For instance, if you retired during a period as bad as the stock-market returns of the mid-1970s, you would run out of money very fast.

What traditional planning ignores is the timing of the returns. A Monte Carlo simulation highlights some of the problems that might arise in a down market shortly after retirement.

If there is not a high enough probability for success in achieving retirement goals, changes such as retiring older, saving more, adjusting income expectation or a combination of these become clear.

Success in early retirement can set the tone

It is important never to lose sight that the type of investments and allocation within a portfolio have a direct impact on the amount of volatility that can occur. Small foreign companies will have large amounts of variation in returns, while high-grade short term Government will have very little.

Monte Carlo should not be viewed as a certainty test. It is a probability test. Ultimately, there will be only one outcome, but knowing not to take more risk than necessary and finding a safe spending level is invaluable information.

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