What Is a Monte Carlo Simulation?

Analysts can assess possible portfolio returns in many ways. The historical approach, which is the most popular, considers all the possibilities that have already happened. However, other forecasting methods can be consulted, too, with one option being the 澳洲幸运5官方开奖结果体彩网:Monte Carlo simulation.

The Monte Carlo method is a stochastic (random sampling of inputs) method to solve a statistical problem, and a simulation is a virtual representation of a problem. The Monte Carlo simulation combines the two to give us a powerful tool that allows us to obtain a distribution (array) of results for any 澳洲幸运5官ꦗ方开奖结果体彩网:statistical problem wiܫth numerous inputs sampled over and over again.

Monte Carlo Simulation Demystified

Monte Carlo simulations can be best understood by thinking about a person throwing dice. A novice gambler who plays craps for the first time will have no clue what the odds are to roll a six in any combination (for example, four and two, three and three, one and five). What are the odds of rolling two threes, also known as a "hard six?"

Throwing the dice many times, ideally several million times, would provide a representative distribution of results, which will tell us how likely a roll of six will be a hard six. Ideally, we should run these tests efficiently and quickly, which is exactly what a 澳洲幸运5官方开奖结果体彩网:Monte Carlo simulation offers.

Asset prices or portfolios' 澳洲幸运5官方开奖结果体彩网:future values don't depend on dice rolls, but sometimes asset prices do resemble a 澳洲幸运5官方开奖结果体彩网:random walk. The problem with looking at history alone is that it represents, in effect, just one roll, or probable outcome, which may or may not be applicable in the future. A M⛄onte Carlo simulation considers a ꦑwide range of possibilities and helps us reduce uncertainty.

A Monte Carlo simulation is very flexible; it 澳洲幸运5官方开奖结果体彩网:allows us to vary risk assumptions under all paramete▨rs and thus model a range of possible outcomes. One can compare multiple future outcomes and customize the model to various assets and portfolios under review.

Applying the Monte Carlo Simulation

The Monte Carlo simulation has numerous applications in finance and other fields. Monte Carlo is used in corporate finance to model components of project 澳洲幸运5官方开奖结果体彩网:cash flow, which are impacted by uncertainty. The result is a range of 澳洲幸运5官方开奖结果体彩网:net present values (NPVs) along with observations on the average NPV of the investment under analysis and its vol𝔍atility. The investor can, thus, estim💛ate the probability that NPV will be greater than zero.

Monte Carlo is used for option pricing where numerous random paths for the price of an 澳洲幸运5官方开奖结果体彩网:underlying asset are generated, each having an associated payoff. These payoffs are then discounted back to the present and averaged to get 澳洲幸运5官方开奖结果体彩网:the option price.

It is similarly used for pricing 澳洲幸运5官方开奖结果体彩网:fixed income securities and interest rate 澳洲幸运5官方开奖结果体彩网:derivatives. But the Monte Carlo simulation is used most extensively in 澳洲幸运5官方开奖结果体彩网:portfolio management and personal financial planning.

Uses in Portfolio Management

A Monte Carlo simulation allows an analyst to determine the size of the portfolio a client would need at retirement to support their desired retirement lifestyle and other desired gifts and bequests. It factors in various important factors including 澳洲幸运5官方开奖结果体彩网:reinvestment rates, 澳洲幸运5官方开奖结果体彩网:inflation rates, 澳洲幸运5官方开奖结果体彩网:asset class returns, 澳洲幸运5官方开奖结果体彩网:tax rates, and even possible lifespans. The result is a distribution of portfolio sizes with the probabilitieꦫs of supporting the client's desired spending nee🐲ds.

The analyst next uses the Monte Carlo simulation to determine the 澳洲幸运5官方开奖结果体彩网:expected value and distribution of a portfolio at the 澳洲幸运5官方开奖结果体彩网:owner's retirement date. The simulation allows the analyst to take a multi-period view and factor in 澳洲幸运5官方开奖结果体彩网:path dependency; the portfolio value🌳 and asset allocation at every period depend on the returns and volatility in the preceding period.

The analyst uses various 澳洲幸运5官方开奖结果体彩网:asset allocations with varying degrees of risk, different correlations between assets, and distribution of a large number of factors—including the savings in each period and the retirement date—to arrive at a distribution of portfolios along with the probability of arriving at the desired portfolio value at retirement. The client's different spending rates and lifespan can be factored in to determine the probability that the client will run out of funds (the probability of ruin or 澳洲幸运5官方开奖结果体彩网:longevity risk) before their death. 

A client's risk and return profile is the most important factor influencing portfolio management decisions. The client's required returns are a function of their retirement and spending goals; the client's risk profile is determined by their ability and willingness😼 to take risks.

More often than not, the desired return and the risk profile of a client are not in sync with each other. For example, the level of risk acceptable to a client may make it impossible or very difficult to attain the desired return. Moreover, a minimum amount may be needed before retirement to achieve the client's goals, but the client's lifestyle would not allow for the savings or the client may be reluctant to change it.

Monte Carlo Simulation Example

Let's consider an example of a young working couple who works very hard and has a lavish lifestyle including expensive holidays every year. They have a retirement objective of spending $170,000 per year (approx. $14,000/month) and leaving a $1 million estate to their children.

An analyst runs a simulation and finds that their savings-per-period is insufficient to build the desired portfolio value at retirement; however, it is achievable if the 澳洲幸运5官方开奖结果体彩网:allocation to small-cap stocks is doubl꧅ed (up to 50% to 70% from 25% to 35%), which will increase their risk considerably.

None of the above alternatives (higher savings or increased risk) ꧟are acceptable to the client. Thus, the analyst factors in other adjustments before running the simulation again.

The analyst delays their retirement by two years and decreases their monthly spend post-retirement ꧅to $12,500. The resulting distribution shows that the desired portfolio value is achievable by increasing allocation to small-cap stock by only 8%. With the available insight, the ana꧅lyst advises the clients to delay retirement and decrease their spending marginally, to which the couple agrees. 

The Bottom Line

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; this is also its greatest disa🀅dvantage in the sense that assumptions need to be fair because the output is only as good as the inputs.

Another great disadvantage is that the Monte Carlo simulation tends to underestimate the probability of extreme bear events like a 澳洲幸运5官方开奖结果体彩网:financial crisis. In fact, experts argue that a simulation like the Monte Carlo ꦬis unable ꦉto factor in the behavioral aspects of finance and the irrationality exhibited by market participants. It is, however, a useful tool for advisors.