Average investment returns: compounding and recovering a loss

An average of yearly percentages does not necessarily describe how an investment balance grew. Each year's return applies to the amount left by the previous year, so the path through gains and losses matters to the final sum.

This guide explains the arithmetic using fictional figures. It does not predict returns or identify an investment likely to recover a loss.

Follow the pounds through the calculation

Start with £10,000. A 20% rise takes it to £12,000. A subsequent 20% fall removes £2,400, leaving £9,600.

The simple arithmetic average of plus 20% and minus 20% is zero. The actual two-year result is a 4% loss. The percentages did not cancel because they applied to different balances.

The same two returns in reverse order also leave £9,600 when there are no contributions or withdrawals. Once cash flows enter the example, their timing can change the outcome; that is a separate issue from this basic compounding calculation.

Understand an annualised return

An annualised compound return is the constant yearly rate that would connect the starting and ending values over the period, under the relevant assumptions. For £10,000 becoming £9,600 over two years with no external cash flows, it is approximately minus 2.020% a year.

It does not mean the investment actually fell by that amount in each year. It is a way of expressing the combined result, not a description of a smooth experience.

Academic work published by CFA Institute on arithmetic and geometric averages also distinguishes historical averages from forecasting. A neat historical compound rate should not be treated as a dependable future growth assumption.

Why recovering a loss needs a larger percentage gain

A fall reduces the base from which recovery starts. After a 25% loss, £10,000 becomes £7,500. Returning to £10,000 requires a £2,500 gain, which is one-third of £7,500: approximately 33.333%.

After a 50% loss, the remaining £5,000 needs a 100% gain to recover the original £10,000. These are mathematical relationships, not forecasts that a recovery will occur.

The general calculation is the original value divided by the remaining value, minus one. It is useful for understanding scale, but it should not become a target that encourages taking extra risk merely to get back to a previous balance.

Add costs and withdrawals carefully

Suppose an account falls from £10,000 to £8,000, then £1,000 is withdrawn. The investment balance is now £7,000. A later rise to £8,400 represents a 20% gain on the remaining investment.

The withdrawal was money received by the investor, not another investment loss. Keep it in the cash-flow record when assessing the overall experience. Equally, a new contribution can restore the displayed balance without repairing the investment return.

Charges should be included consistently. Do not subtract a fund cost a second time if the reported return already includes it, or compare a return before advice charges with one after all charges without identifying the difference.

Separate recovery from the financial goal

The original purchase price may be emotionally significant, but the plan concerns future spending and resources. Ask whether the investment still fits the time horizon and risk capacity, rather than assuming it must be retained until a particular number reappears.

If money is needed soon, a hypothetical long-term recovery may not solve the timing problem. If the goal is distant, reacting to every short-term fluctuation can create other costs and risks. The appropriate response depends on the whole plan, not the arithmetic alone.

An adviser can compare options using the same assumptions and explain the consequences of keeping, reducing or changing an investment without promising a recovery.

Questions for the next performance review

Ask whether each percentage is arithmetic, cumulative or annualised; whether external cash flows are included; and whether the figures are before or after all relevant charges. Request an explanation in pounds alongside the percentage.

For a projection, ask which assumptions generate the result and how the plan behaves under less favourable returns. A smooth line is useful for calculation, but it is not evidence that markets will follow it.

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