Recovery is measured from what remains after a loss. A 50% rise does not offset a 50% fall: moving from 100 down to 50 takes a 100% gain from the lower value to return to 100. This describes a mathematical distance, not its probability or the time needed.
Equal cash differences do not imply equal percentage changes when the starting values differ.
BTKWIN.COM · EDUCATIONAL EXAMPLEWhy loss and recovery percentages differ
A percentage compares a change with a starting base. From 100 to 50, the difference is 50 against a base of 100, giving a 50% loss. Returning from 50 to 100 also involves a difference of 50, but the new base is 50, so the required gain is 100%.
A rise of only 50% after the fall takes the remaining 50 to 75. Multiply 100 × 0.5 × 1.5 to verify it. Multiplying growth and loss factors applies each movement to the value that actually precedes it; adding opposite percentages directly would hide the change in base.
The same principle applies to smaller changes. A 10% fall leaves 90 from an initial 100. A subsequent 10% rise makes it 99 before costs. Apply the actual sequence of returns and handle deposits or withdrawals separately rather than assuming two opposite percentages cancel.
The general formula and its limits
If a loss is written as a decimal d, the remaining fraction is 1 − d. The gain required to return is d ÷ (1 − d), then expressed as a percentage. With a 20% loss, d is 0.2, so 0.2 ÷ 0.8 gives 0.25, or 25%. With an 80% loss, 0.8 ÷ 0.2 gives 4, or 400%.
The model requires a positive remaining value and a comparison of the same economic amount without unaccounted cash flows, quantity changes or costs. Do not confuse the decimal 0.2 with the whole number 20 when applying the formula.
| Loss from the start | Remaining from 100 | Gain required |
|---|---|---|
| 10% | 90 | About 11.11% |
| 20% | 80 | 25% |
| 40% | 60 | About 66.67% |
| 50% | 50 | 100% |
| 75% | 25 | 300% |
| 90% | 10 | 900% |
At a 100% loss the denominator becomes zero. No finite percentage gain applied to a zero remaining value restores the original amount under this model. Products involving liabilities or negative balances may fall outside it altogether.
Successive losses do not simply add
Suppose an illustrative balance of 1,000 loses 20% and becomes 800, then loses 25% of what remains and becomes 600. The total loss is 40%, not 45%. Returning from 600 to 1,000 requires approximately 66.67%. The second loss was measured against 800 rather than the original 1,000.
In another path, two consecutive 50% losses leave one quarter of the starting value, not zero. A starting 1,000 becomes 500 and then 250. The remaining 250 needs a 300% gain to reach 1,000. A small remaining amount can still suffer another large percentage loss from its current level.
Write the factors for each period, such as 0.8 and 0.75 in the first example. Their product is 0.6; subtracting one gives an overall change of −40%. When checking a multi-period record, verify whether the reported returns already include costs so those charges are not deducted twice.
A price recovery may not restore the net account value
Imagine buying ten units at 100 for an asset value of 1,000 and paying a separate cash purchase fee of 2. Total entry cost is 1,002. If you sell all ten again at 100 with a hypothetical 0.2% selling fee, you receive 998. The price has returned, but proceeds remain 4 below the amount paid.
Under those assumptions, break-even sale price is 1,002 ÷ [10 × 0.998], approximately 100.4008. That assumes a proportional sale fee deducted from the proceeds and no other costs. Fees deducted in asset units or paid with a third asset require a reconstruction of the quantities and costs from the actual records.
Investor.gov explains why fees reduce investment returns. The numbers here are educational assumptions rather than a platform’s current prices. Use the profit-after-fees calculator only when its stated fee model fits the scenario.
A new deposit increases the balance, not the investment return
If an account starts with 1,000, falls to 600 and then receives a new deposit of 400, the displayed balance returns to 1,000 without investment gains recovering the loss. Total money contributed is now 1,400, assuming no withdrawals. The larger balance is real, but calling it performance recovery would hide the new funding.
Keep external cash flows and investment outcomes in separate columns. In this simplified example, a value of 1,000 minus contributions of 1,400 leaves a cash loss of 400. Turning a history with differently timed cash flows into a rate of return requires a stated method; do not automatically divide by the latest balance.
Withdrawals require the same distinction. A balance falling because cash was transferred to a bank is not automatically a market loss. Record the date, amount and currency of each external flow. Two applications may handle incoming transfers or their acquisition cost differently, even when the asset quantities agree.
Additional purchases change the holding being measured
Suppose ten units were bought at 100 and another ten at 50. Total cost before fees is 1,500 for twenty units, giving an average purchase price of 75. At a current price of 50, the holding is worth 1,000 and has a loss of 500.
The combined holding needs a 50% price rise from 50 to 75 to reach its raw purchase cost. The first purchase on its own needs 100% to return from 50 to its entry of 100. Those figures describe different quantities and amounts committed. The lower average does not erase the outstanding loss.
Adding money is not automatically suitable because it changes an average. It also increases quantity and the amount exposed. When comparing before and after, show the extra funding and the new units. The average-cost calculator describes a purchase-only model; it does not recommend averaging down.
Asset recovery and portfolio recovery are different
If half of a hypothetical 1,000 portfolio is in an asset that loses 50% while the other half stays unchanged, the portfolio falls 25%. Its parts become 250 and 500, totalling 750. The portfolio as a whole needs about 33.33% growth to return to 1,000, but that does not by itself specify the move needed from one constituent.
Rebalancing, sales, different quote currencies and liabilities can change what is being measured. Do not use one coin’s price recovery to claim recovery of an account holding other assets or cash. Value each component in a consistent currency and at a consistent time, and record the actual quantities and external flows.
To check a simple calculation without flows, divide the target value by the current value and subtract one. Reverse-check by multiplying the current amount by one plus that result. Keep precision until the final display; rounding differences are not genuine gains or costs. The calculation measures distance to a defined reference point, not a promise of recovery.
Continue reading
English content and examples reviewed: 27 October 2026. Read the Arabic edition.
