Consecutive percentage returns act on changing capital. With no cash flows, combine them by multiplication, not addition. This explains why +10% followed by −10% leaves a loss and why a fixed monthly-rate example is a mathematical scenario, not an income forecast.

What is compounding and where does a 79.6 percent return come from?

Assume €10,000, exactly +5% each month for 12 months, no withdrawals and no additional costs. The result is 10,000 × 1.0512 = €17,958.56, about +79.59%. The assumption produces the answer; it does not show that the return is attainable.

For a different fixed-base model, earn and withdraw €500 each month. The account stays at €10,000 and separate withdrawals total €6,000. Combined funds are €16,000; the brokerage balance itself is not €16,000.

Why does compounding cut both ways during account drawdowns?

Assume −5% in each of the same 12 periods. Then 10,000 × 0.9512 = €5,403.60, a 45.96% decline. The percentage is fixed, but each loss is measured from a smaller base.

After a 20% loss, an 8,000 balance needs a 2,000 gain, or 25%, to regain 10,000. After a 50% loss it needs 100%. These are recovery identities, not probabilities or targets. After total loss, applying a positive rate to zero cannot restore the funds.

Changing bases also explain what it takes to return to the starting amount. After a hypothetical 20 percent loss, a 20 percent gain is insufficient: 8,000 × 1.20 = 9,600 PLN. The missing 2,000 PLN must now be measured against 8,000 PLN.

Worked example

Recovery uses the smaller base

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Recovery uses the smaller baseA 20 percent loss from 10,000 leaves 8,000; returning to the start requires a 25 percent gain. A 50 percent loss leaves 5,000, which must double to return to 10,000.Starting reference: 10,000 PLNAfter a 20% loss: 8,000 PLNShortfall: 2,000 PLN2,000 / 8,000 = 25% required gainAfter a 50% loss: 5,000 PLNShortfall: 5,000 PLN5,000 / 5,000 = 100% required gainRecovery gain = loss / (1 − loss)

Model assumptions. No deposits, withdrawals or additional fees; the loss applies to the whole starting capital. The formula L / (1 − L) applies for 0 ≤ L < 1, with L expressed as a fraction. It says nothing about the probability or time required for recovery.

The missing cash amount is a different percentage of the capital left. This is an arithmetic identity, not a forecast or strategy target.

The derivation is straightforward: after a loss L, capital left is K × (1 − L), and the shortfall is K × L. Dividing gives L / (1 − L), so starting capital cancels out. At a total loss, the denominator is zero; a positive return on zero cannot restore funds. This calculation does not justify increasing volume after a loss.

What does the formula tell you about realistic returns?

It tells you the consequence of supplied inputs. Choosing +5% monthly or any lower number does not make it an expected result. A historical account-loss percentage likewise cannot establish your monthly return distribution or a ceiling for all possible strategies.

How do returns combine across a longer horizon?

Without external flows, ending capital is K0 × (1 + r1) × (1 + r2) × … . For a constant rate r over n periods, this becomes K0 × (1 + r)n. Monthly r needs a count of months; annual r needs years.

The rule of 72 approximates doubling time as 72 divided by a positive annual rate expressed in percent. At an assumed 7%, it gives about 10.3 years; the exact constant-rate calculation is ln(2) ÷ ln(1.07) ≈ 10.24. This approximation does not prove that steady returns beat every variable path.

How does active currency trading compare to broad index ETFs?

Compare the same dates, currency, cash flows, costs and return definition. A price index, a total-return index and a client’s after-tax fund result are different. The model €10,000 × 1.0730 ≈ €76,123 is arithmetic under an assigned 7% annual rate; it is not evidence that an index will deliver that rate or involve no stress.

What are realistic return expectations versus get-rich-quick promises?

Taxes, fees and withdrawals affect the amount available to reinvest. Their treatment depends on the actual product and jurisdiction. Define what “net” includes rather than subtracting a charge already included in reported returns. Trading profit withdrawn to a personal account is not automatically a corporate dividend.

A deposit is an external cash flow, not a gain. Dividing annual profit by starting capital is adequate only for a compatible no-flow calculation. A history with contributions and withdrawals needs a method that accounts for their timing; GIPS distinguishes time-weighted and money-weighted measurement.

What to do this week to put compounding into practice?

  1. Reproduce +10% and −10% on €10,000: 10,000 × 1.10 × 0.90 = €9,900.
  2. Change the rates to +2%/−2% and +20%/−20%: the results are €9,996 and €9,600. Equal arithmetic averages need not give equal compound returns.
  3. Separate deposits and withdrawals from returns, and document charges already included.
  4. Test adverse inputs as well as positive ones. A drawdown limit is a plan, not a guaranteed exit price.

Related materials: realistic trader goals, trading as a business, time horizons and risk management.