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El Cerebro

Investment

Monte Carlo: the range of an investment

Not a single figure, but a range: what span of results an investment produces when year to year is not always the same.

What it does

It starts from two assumptions, the average annual return and its volatility, and generates a thousand possible paths for the capital, one per year and with the twelve monthly contributions added at the close of each year. From that cloud it extracts the 10th, 50th and 90th percentile for each year, and shows the median as the main figure with the two ends alongside.

Key concepts

  • Average and volatility: the two assumptions that define the shape of the range. The average is the expected return and volatility measures how much it strays from that average year to year.
  • Median: the value below which half of the paths fall. It is the central figure shown, and not an average: the average of an asymmetric cloud sits shifted towards the good side.
  • Percentiles: the 10th and 90th bound the interval in which nine out of ten paths fall. Showing the median without them would be showing only the friendly half of the story.
  • Normal distribution: the model used to generate the returns for each year. It is a simplification: in real markets the extreme years, especially the sharp falls, occur more often than the normal predicts, so the 10th percentile may come out too low.
  • Seed: the number that fixes the pseudo-random number generator. With the same seed and the same data, the result is always identical; changing it gives a different result, not a more likely one.

Frequently asked questions

Does this calculator predict the market?

No. It takes two numbers that whoever uses it enters and draws the mathematical consequences of taking them as correct. The average and volatility are two assumptions that whoever uses the calculator types and can change at any time: they are not market data, they are not a forecast and they are not a recommendation from the system.

Why do three lines come out and not one?

Because the range is the information. The median on its own is a point in the middle of a cloud; with the 10th and 90th percentiles alongside you can see how much the bad part of the distribution can hurt, and that is the difference between a plan and an estimate.

What happens if volatility is zero?

The thousand paths become the same deterministic account: capital multiplied by the return factor plus the contributions. The three percentiles match exactly and the chart is reduced to a single line, which serves as a check that the mechanics are not moving the figure on their own.

Why is there a seed number?

Because a simulation with randomness would not be reproducible. With the same seed, the same input always gives the same cloud of a thousand paths, so that a link with the same numbers reproduces the same figure and any change in the result is a change in the data.

Is the step annual or monthly?

Annual. The average and volatility are entered in annual terms, and dividing the year into twelve steps would add an assumption about what happens inside it that nobody has written. The twelve monthly contributions are indeed added, but all together at the close of the year.

Are a thousand paths enough?

Enough for the 10th and 90th percentiles not to wobble when you move one decimal place, and few enough for the calculation to be instant on every keystroke. With more paths the cloud is smoothed a little; the shape of the range does not change.

What limits do the fields accept?

The initial capital runs from 0 to 10.000.000 €, the monthly contribution from 0 to 100.000 €, the average return from −50 % to 100 %, volatility from 0 % to 60 %, the years from 1 to 60 and the seed is a whole number from 1 to 1.000.000. An empty field does not equal zero.

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