Boost your portfolio performance with Monte Carlo simulation

When it comes to evaluating the performance of an investment portfolio, most people (and financial institutes) use the historical approach. This means to look at how the portfolio would (should) perform in the future if the market conditions were the same as in the past. This is normally wrong because there is a multitude of events that can affect investments, not only in the present but also in the future: the occasional geopolitical conflict or pandemic, added to the social dynamics of investors, always make sure to shake things up. This is where Monte Carlo method comes into play.

The Monte Carlo method uses computer simulations to evaluate potential future outcomes of an investment portfolio (among other things). It takes into account random events and market conditions, which makes it a more accurate way to predict performance than its traditional counterparts.

What is Monte Carlo simulation and how does it work

The Monte Carlo method, or Monte Carlo simulation, was first developed by the mathematician Stanislaw Ulam and John von Neumann in the 1940s while they were working on nuclear weapons projects. The name Monte Carlo simulation comes from the casino resort located in Monaco, as the method itself is derived from the same concepts used by gamblers. As with gambling, Monte Carlo simulations involve randomly generating multiple outcomes from a given set of assumptions and then aggregating the results to get an overall picture.

For example, if you want to estimate the first month's sales of a new product, you can provide the Monte Carlo simulation program with historical sales data. The program will estimate various sales values based on factors such as general market conditions, product price and advertising budget. When it comes to investing, the output of the model can be used to make informed decisions about where and when to invest, as well as how much money should be allocated for each asset class in order to maximize returns while minimizing risks.

This means that rather than expecting a certain result, investors can prepare for all possible outcomes and make better decisions about how to optimize their portfolios. In practice, it is done by creating a model portfolio with different asset allocations, and running it over different scenarios—such as different market conditions or varying time horizons—to calculate expected returns. The result is an understanding of the potential range of outcomes, as well as their likelihood.

The Monte Carlo method also helps investors to understand the risk-return tradeoff of a particular investment. It allows them to assess the potential rewards and risks associated with any given asset allocation, as well as its expected returns for different time horizons. This information can be used to inform decisions about how much to allocate towards each asset class in order to optimize returns.

What are the use cases of the Monte Carlo simulation?

Monte Carlo methods can be used to assess risks and in general make accurate long-term predictions. Some examples are:

• Business:  a marketing manager wants to know if it makes sense to increase the advertising budget for an online baking class. A Monte Carlo simulation with variables such as subscription rate, advertising cost, registration percentage and customer retention would help foreseeing the impact of the changes on these factors to indicate whether the decision is profitable.
• Finance: predicting the stock prices and investment strategies using a Monte Carlo simulation to  consider market factors that could cause drastic changes in the value of the investment.
• Online video games: simulate the results and ensure a fair gaming experience by simulating the behavior or the characters.
• Engineering: simulate the likely failure rate of a product based on existing variables such as estimate the life of an engine when it works in various conditions.

How to build a custom portfolio using Monte Carlo simulation

When running a Monte Carlo simulation, it’s important to set up the parameters accurately. Think of it as a "what if" game for your investments. What if the economy takes a dip? What if interest rates go up? What if there's a major market disruption? This includes determining the asset allocation of each portfolio, as well as the expected rate of return and associated risks. Additionally, investors should consider their investment goals and time horizon when setting up their parameters.

Let's take an hypothetical example to illustrate better the steps needed to create a Monte Carlo model. We'll take a user called Bob. Bob wants to use the Monte Carlo method to do some retirement planning.

1. Let's assume Bob wants to know the size of the portfolio he would need at retirement to support his desired retirement lifestyle. He factors into the model things like reinvestment rates, inflation rates, asset class returns, tax rates, and even possible lifespans. The result is a distribution of portfolio sizes with the probabilities of supporting Bob's desired spending needs.
2. Bob next uses the Monte Carlo simulation to determine the expected value and distribution of a portfolio at his retirement date. The simulation allows Bob to take a multi-period view and factor in interdependency between market performance over time (the portfolio value and asset allocation at every period depend on the returns and volatility in the preceding period).
3. Bob uses various 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.
4. Bob's spending rates and lifespan can be factored in to determine the probability that the client will run out of funds before his death.

The result is a set of scenarios with different asset allocations. Bob can then pick the most appropriate depending on the risk tolerance he has.

Conclusions

What we just showed for Bob can also be done to help investors diversify their portfolios. By modeling different scenarios, an investor can see how their portfolio might perform under various market conditions. For example, a Monte Carlo simulation might show that investing in a mix of stocks, bonds, and real estate could lead to more stable long-term returns across a wide variety of market conditions, reducing the overall risk of the portfolio.

When it comes to tools, there are many options available. Many platforms provide users with the ability to run their own Monte Carlo simulations, while some offer pre-made models that they can use as a starting point. If you want something super easy, a good option is the Monte Carlo Simulation tool. If on the other hand you are tech-savvy, good options are Okama which is based on Python, or even a spreadsheet like Excel or Google Sheet can do the trick.