In investments, we all wish we had a crystal ball. Many people need to plan their lives around how much their investments will grow. So, in order to calculate the answer, many financial advisors, insurance salespeople and budget gurus use a simple investment growth calculator such as the one below. It takes an annual percentage return and applies it to your investments year after year.
Unfortunately, these calculators are will give you the wrong answer. Why?
They Often Don’t Factor in Inflation
Inflation is a phenomenon that causes money to be worth less with the passage of time. Pretend you want to retire in 25 years and you want to have all the things a million dollars can buy you in the year 2016. In 25 years, things will cost a lot more because of inflation. (For related reading, see: Can You Stomach the Perfect Investment?)
Let’s say inflation will average 3.4% over the next 25 years. Let’s also say you manage to grow your investments to one million dollars by 2040. Unfortunately, you will find that your million dollars in 2041 can only buy as much as $420,000 bought in 2016 thanks to that 3.4%.
You would actually have to save $2,307,000 by 2041 if you wanted to have all the things a million dollars would have bought you in 2016. Unfortunately, even if you try to subtract 3.4% from your returns to account for inflation, you can’t fix these calculators. That is because…
The Entire Premise Is Flawed
This kind of calculator shows a fundamental misunderstanding of mathematics. In such a calculator, highly variable compounding factors (e.g. investment returns, inflation) are averaged and applied linearly (every single year).
For instance, pretend you start with $100,000 and you have an average investment return of 25% over two years. This sort of calculator will indicate you have $156,000 in your investment account. In actuality, you might only have $100,000. How can that be? See the second year scenario below for an example:
Year one: In 2016, you start investing with $100,000. Your investments decline 50% over the course of the year. You now have $50,000.
Year two: At the beginning of 2017, you have $50,000. Over the course of the year, your investments go up 100%, meaning they double. You are back where you started at $100,000. (For related reading, see: Why You Should Diversify and Rebalance.)
Now, you had two years of returns: -50% and +100%. To find the average, add those numbers together (-50%+100%=50%) and divide that 50% by two (50%/2=25%). As you can see, you have an average yearly return of 25% and nothing to show for it. The calculator is clearly flawed, yet many continue to use it. So, how should it be done?
Monte Carlo: A More Accurate Solution
Calculators can use many approaches, but one common method involves the Monte Carlo simulation. Monte Carlo is a mathematical modeling tool that takes historical data and randomizes that data to generate yearly investment returns. For instance, under a Monte Carlo calculator you might have a -5% return in year one and a 15% return in year two. If you want to know how much money you will have in 20 years, a calculator utilizing Monte Carlo will generate those random numbers for 20 years, ending with one final value.
However, it goes even further. If you used a calculator to generate one set of 20 annual returns and called it a day, you might have gotten very unlucky a couple of years. Maybe you had two years in a row where the stock market declined by 40%. It isn’t likely, but if you just ran the numbers once, very lucky or unlucky scenarios could give you an inaccurate result.
A Monte Carlo simulation runs the numbers thousands or tens of thousands of times. In this way, the calculator can provide a good estimate of what your return will be over time. It may sound more complicated, but it is much more accurate. When it comes to planning for financial goals, accuracy matters. (For related reading, see: 8 Common Biases That Impact Investment Decisions.)