YieldClarity

Forecasting and uncertainty

Expected path vs Monte Carlo: two ways to forecast FI

Most financial independence tools give you one of two kinds of forecast: a single projection using a steady return, or a simulation that tries thousands of uneven ones. This guide explains how they differ and how to read them together.

By Yield ClarityPublished 3 min read

Key takeaways

  • An expected path shows what happens if every year delivers your assumed return.
  • Monte Carlo shows the range of outcomes when returns vary around that assumption.
  • Use the expected path to understand your inputs; use Monte Carlo to understand uncertainty.
  • Neither is a prediction. Both describe the consequences of your assumptions.

The expected path

An expected path projects your wealth forward one month at a time using a steady return, your contributions and your inflation assumption. The FI date is the first month in which your wealth reaches the target.

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The illustrative plan's expected path reaches £1,050,000 in June 2035.

Because every input is fixed, the result is easy to follow and to change. Save more and the date moves earlier; assume a lower return and it moves later. That makes it a good tool for understanding which inputs matter most.

Its weakness is that real returns never arrive smoothly. A steady projection cannot show how a run of bad years would affect you.

Monte Carlo simulation

A Monte Carlo simulation runs the same plan many times. Each run, or path, draws a different sequence of returns that varies around your assumption. Some paths do better than the expected path and some worse.

Instead of one date, you get a range: the share of paths that reach FI by a chosen date, the dates by which most of them get there, and the spread of portfolio values over time. Our Monte Carlo guide explains how to read these results.

Side by side

How the two methods compare

  • Returns

    Expected path
    The same return every month
    Monte Carlo
    Returns that vary from month to month

  • Result

    Expected path
    One estimated FI date
    Monte Carlo
    A probability, a likely window and a range of values

  • Best for

    Expected path
    Seeing how inputs affect the date
    Monte Carlo
    Seeing how uncertain that date is

  • Shows sequence risk

    Expected path
    No
    Monte Carlo
    Yes

  • Easy to check by hand

    Expected path
    Yes
    Monte Carlo
    No

One plan, both views

One estimated date from the expected path, and the likely window from Monte Carlo, for the same plan.

The two views agree on the centre but tell different stories. The expected path says June 2035. Monte Carlo says that date is close to the middle of the outcomes, and that a delay of two years or more is entirely plausible.

Which to use when

Matching the question to the method

  • When might I reach FI if things go roughly to plan?

    Start with
    Expected path

  • How much earlier would saving more get me there?

    Start with
    Expected path, or a scenario

  • How likely am I to reach FI by a particular date?

    Start with
    Monte Carlo

  • How wide is the range of possible FI dates?

    Start with
    Monte Carlo

  • Could a bad start to retirement run my money down?

    Start with
    Monte Carlo sustainability

Comparisons are usually more reliable than absolute numbers. Whether a change moves your probability by ten points tells you more than whether the probability is 48% or 52%.

What neither can tell you

  • Both depend on your return, inflation and spending assumptions. Long-run returns have differed widely between countries and periods (Pfau, 2010), and inflation has often moved away from the 2% target.
  • Neither knows about future changes to tax, pension rules or your circumstances.
  • Simulations use simplified models of markets, which tend to understate extreme events.

The methodology explains exactly how Yield Clarity calculates the expected path and Monte Carlo results, including the assumptions each one makes.

Sources

  1. Methodology: how Yield Clarity calculates your plan. Yield Clarity. How the product implements the ideas in this guide.
  2. An International Perspective on Safe Withdrawal Rates. Wade D. Pfau, Journal of Financial Planning, December 2010. Historical research across 17 countries.
  3. Inflation and the 2% target. Bank of England.

This guide is general information, not financial advice. Figures for the illustrative plan are examples, not market data.

Related guides

See both views of your plan

Start with an expected path for free, then explore the range of outcomes with Monte Carlo.

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