How to Calculate the Return Needed to Recover Your Investment: Why a 20% Loss Requires a 25% Gain
If your investment falls by 20%, you need to earn a 25% return on the remaining assets to recover your original investment. When KRW 1,000,000 falls to KRW 800,000, you must earn KRW 200,000 to get back to KRW 1,000,000. That amount represents 25% of the remaining KRW 800,000.
The loss percentage and the recovery return differ because they are calculated using different starting amounts.
This calculation applies when investments in stocks, ETFs, funds, cryptocurrencies, or other assets lose value because of price fluctuations. However, it assumes a simple return calculation with no fees, taxes, additional deposits, or withdrawals.
If KRW 1,000,000 Falls to KRW 800,000, How Much Would You Still Be Short After a 20% Gain?
If you invest KRW 1,000,000 and suffer a 20% loss, a subsequent 20% gain will not fully restore your original investment. A 20% increase from the remaining KRW 800,000 brings the balance to KRW 960,000, leaving you KRW 40,000 short of your starting amount.
The following is a hypothetical calculation, not an actual investment result.
The initial investment is KRW 1,000,000, excluding fees and taxes.
Step 1: A 20% Loss Occurs
KRW 1,000,000 × (1 − 0.20) = KRW 800,000
Step 2: A 20% Gain on the Remaining Balance
KRW 800,000 × 1.20 = KRW 960,000
Step 3: Calculate the Gain Required to Recover the Original Investment
(KRW 1,000,000 − KRW 800,000) ÷ KRW 800,000 × 100 = 25%
Therefore, the remaining KRW 800,000 must increase by 25% to return to exactly KRW 1,000,000.
KRW 800,000 × 1.25 = KRW 1,000,000
The key distinction is that the loss is calculated against KRW 1,000,000, while the recovery return is calculated against KRW 800,000.
Simply adding a 20% decline and a 20% increase and treating the result as 0% gives a misleading picture of how the investment's value actually changes.
What Formula Calculates the Return Needed to Recover Your Original Investment?
To calculate the return required to recover an investment after a loss, divide the loss percentage by the percentage of the investment that remains.
Required return to recover the original investment (%) = Loss percentage (%) ÷ (100 − Loss percentage (%)) × 100
If the loss is 20%, the calculation is as follows.
20 ÷ (100 − 20) × 100 = 25%
The same formula can be written as follows when the loss percentage is expressed as a decimal.
Recovery return=L1−L\text{Recovery return}=\frac{L}{1-L}Here, L represents the loss percentage expressed as a decimal. For a 20% loss, L is 0.20.
This formula is also presented in Exceljet's guide to calculating the return needed to recover an investment loss. The guide explains the mathematical relationship showing that larger losses require increasingly greater gains to return to the original investment value.
The required recovery return is the same regardless of the size of the original investment. Whether KRW 1,000,000 suffers a 20% loss or KRW 10,000,000 suffers a 20% loss, the remaining balance must rise by 25% to return to its original value.
How Much Return Is Needed When Losses Increase to 30%, 50%, or 70%?
As losses deepen, the gain required to recover the original investment grows much faster than the loss percentage itself. In particular, after a 50% loss, the remaining investment must double in value to recover the original amount.
The following table shows calculations based on an initial investment of KRW 1,000,000.
| Loss Percentage | Balance After Loss | Return Required to Recover Original Investment |
|---|---|---|
| 5% | KRW 950,000 | 5.26% |
| 10% | KRW 900,000 | 11.11% |
| 20% | KRW 800,000 | 25.00% |
| 30% | KRW 700,000 | 42.86% |
| 40% | KRW 600,000 | 66.67% |
| 50% | KRW 500,000 | 100.00% |
| 60% | KRW 400,000 | 150.00% |
| 70% | KRW 300,000 | 233.33% |
| 80% | KRW 200,000 | 400.00% |
| 90% | KRW 100,000 | 900.00% |
Calculated by the author. Recovery returns were rounded to two decimal places, with fees, taxes, additional deposits, and withdrawals excluded.
The key point in the table is that even when the loss percentage doubles from 20% to 40%, the return needed to recover rises much more sharply, from 25% to approximately 66.67%.
A 50% loss requires a 100% gain to recover, while a 80% loss requires a 400% gain.
This is because larger losses leave a smaller asset base.
Furthermore, if the loss reaches 100% and the asset value falls to KRW 0, no finite percentage gain applied to the remaining assets can restore the original investment.
Why Can't You Simply Add Losses and Gains When Calculating Compound Returns?
Investment returns over multiple periods must be calculated by multiplying the return factors for each period, rather than simply adding the percentages.
For example, if an investment loses 20% in the first year and gains 20% in the following year, its cumulative return is not 0% but -4%.
(1−0.20)×(1+0.20)−1=−0.04(1-0.20)\times(1+0.20)-1=-0.04
In other words, the cumulative return is -4%.
Investor.gov, the investor education website of the U.S. Securities and Exchange Commission (SEC), explains how compounding works by including previously earned returns in the calculation base for subsequent periods.
The same multiplication principle applies to investment gains and losses: the asset value at the end of one period becomes the basis for calculating the return in the next.
Consider a hypothetical example in which an initial investment of KRW 1,000,000 changes as follows.
| Period | Return During the Period | Asset Value at Period End |
|---|---|---|
| Initial investment | - | KRW 1,000,000 |
| Year 1 | -20% | KRW 800,000 |
| Year 2 | +10% | KRW 880,000 |
| Year 3 | +10% | KRW 968,000 |
Simply adding the returns over 3 years gives 0%.
However, the actual calculation shows that the ending value is KRW 32,000 less than the initial investment of KRW 1,000,000.
The cumulative return is calculated as follows.
0.8×1.1×1.1−1=−0.0320.8\times1.1\times1.1-1=-0.032
Therefore, the cumulative return over 3 years is -3.2%.
This example demonstrates that compounding does not always work in an investor's favor.
How Many Years Would It Take to Recover a 20% Loss With Annual Returns of 5%?
Assuming an investment loses 20% and then earns a compound return of exactly 5% every year, it would first exceed its original value in year 5.
This result is based on an initial investment of KRW 1,000,000 declining to KRW 800,000.
| Recovery Period | Asset Value After Annual Compounding at 5% |
|---|---|
| Starting point | KRW 800,000 |
| Year 1 | KRW 840,000 |
| Year 2 | KRW 882,000 |
| Year 3 | KRW 926,100 |
| Year 4 | KRW 972,405 |
| Year 5 | Approximately KRW 1,021,025 |
Author's calculations. The assumptions are that a constant return of 5% is earned every year, all returns are reinvested, and there are no additional deposits, withdrawals, or costs.
By year 4, the investment still has not recovered its principal, but by year 5, its value exceeds KRW 1,000,000.
The required recovery period can also be calculated using the following formula.
n=ln(1.25)ln(1.05)n=\frac{\ln(1.25)}{\ln(1.05)}
The calculated result is approximately 4.57 years.
This represents the theoretical point at which the investment reaches its original value when an annual compound growth rate of 5% is applied over a continuous range of time periods. If returns are actually credited only once at the end of each year, the investment exceeds its original principal in year 5.
However, this calculation is strictly a hypothetical scenario.
Actual annual returns on stocks or ETFs are not constant. This does not mean an investment will earn 5% every year or recover its principal within 5 years.
Does Lowering Your Average Purchase Price Through Additional Buying Mean You've Recovered Your Losses?
Lowering your average purchase price by buying additional shares does not automatically eliminate an existing unrealized loss. When you invest additional funds, your gains and losses are recalculated based on the new total amount invested and the revised average purchase price.
As a hypothetical example, suppose you purchase 10 shares at KRW 100,000 per share.
The initial investment is KRW 1,000,000.
If the stock price falls to KRW 80,000, the market value of the shares held becomes KRW 800,000, resulting in an unrealized loss of KRW 200,000.
If you then purchase an additional 10 shares at KRW 80,000 per share, the figures change as follows.
Original investment: KRW 1,000,000
Additional investment: KRW 800,000
Total investment: KRW 1,800,000
Total shares held: 20 shares
New average purchase price: KRW 90,000
Immediately after the additional purchase, the market value of the shares held is KRW 1,600,000.
The unrealized loss remains KRW 200,000, but the loss percentage changes to approximately 11.11% when calculated against the total investment of KRW 1,800,000.
If the stock price rises to the new average purchase price of KRW 90,000, the total investment is recovered based on market value alone.
The required increase from the current price of KRW 80,000 to KRW 90,000 is 12.5%.
Therefore, after the additional purchase, the required price increase falls from the original 25% to 12.5%.
However, the total amount invested has increased from KRW 1,000,000 to KRW 1,800,000.
A lower average purchase price does not necessarily mean lower investment risk. If the stock price falls further after the additional purchase, the larger number of shares held could lead to a greater unrealized loss in absolute terms.
What to Check When Applying the 25% Principal Recovery Return to a Real Investment Account
The calculation showing that a 20% loss requires a 25% gain represents a nominal recovery return based solely on changes in investment value. In an actual account, the amount required to recover the original principal may differ depending on transaction costs, taxes, exchange rates, distributions, and additional deposits or withdrawals.
In particular, it is important to distinguish between the following measures.
Recovery Based on Market Value
This occurs when the market value of the assets held returns to their original purchase cost. Transaction costs are not included.
Recovery Based on Realized Profit or Loss
This measure considers the amount actually received after selling the investment. If selling commissions or applicable taxes are incurred, the realized profit or loss may differ even when the market value reaches the original purchase cost.
Recovery Based on the Entire Account
If additional deposits, withdrawals, dividends, distributions, or foreign exchange gains and losses have occurred, it is difficult to assess the overall investment performance of the account using only the price increase of a single holding.
For example, if an initial investment of KRW 1,000,000 falls to KRW 800,000 and you then deposit an additional KRW 200,000, the account balance could return to KRW 1,000,000.
However, this does not mean the investment loss has been recovered. The account balance increased because new funds were added from outside the investment.
Therefore, when evaluating actual investment performance, deposits and withdrawals must be calculated separately from investment gains and losses.
How to Calculate the Return Needed to Recover Your Principal in Your Current Account
You can calculate the required percentage increase by checking your original investment amount and the current market value of your holdings.
For a simple investment scenario with no additional deposits, withdrawals, or costs, use the following formula.
Required increase (%) = (Original investment ÷ Current market value − 1) × 100
For example, if the original investment was KRW 5,000,000 and its current market value is KRW 3,750,000, the calculation is as follows.
(KRW 5,000,000 ÷ KRW 3,750,000 − 1) × 100 = approximately 33.33%
Because the current market value is 25% lower than the original investment, the remaining amount must increase by approximately 33.33% to return to the original investment value.
Conversely, if the current market value is KRW 4,000,000, the required increase is 25%.
After completing the calculation, you should consider more than just the target return. It is also important to assess whether there are sound reasons to continue holding the assets and how much additional loss you can afford to absorb.
Although the return required to recover your principal can be calculated, this formula alone cannot tell you whether the market will rise by that amount or when a recovery might occur.
The loss percentage is the amount lost divided by the original investment, while the recovery return is the amount needed to regain the loss divided by the remaining investment value.
This difference in the calculation base is precisely why a 20% loss requires a 25% gain.
※ This article is provided for informational purposes to help readers understand market movements and does not constitute an investment recommendation for any particular security or asset. All investment decisions and their consequences remain the responsibility of the individual investor.