What you need to make to recover your losses

What you need to make to recover your losses

https://myinvestingnotes.blogspot.com/2010/03/what-you-need-to-make-to-recover-your.html

What you need to make to recover your losses
Cost    Loss    Price   Return
price   (%)     After   required (%)
                loss (%)
$100    5       95      5.3
$100    10      90      11.1
$100    20      80      25
$100    50      50      100
$100    70      30      233
$100    90      10      900
SOURCE: FAIRFAX

This is a classic and crucial concept in investing and finance, often called the "percentage gain to recover a loss" or the "asymmetry of gains and losses."

Let's break down the table, the underlying math, and its profound implications.

Understanding the Table

The table illustrates a simple but non-intuitive truth: The percentage gain needed to recover from a loss is always greater than the percentage lost.

• Cost Price: Your initial investment ($100 in all examples).

• Loss (%): The percentage your investment falls from the cost price.

• Price After Loss: The new, lower value of your investment. (Calculated as: Cost Price × (1 - Loss%))

• Return Required (%): The percentage gain needed on the reduced capital to get back to the original $100.

The Key Mathematical Principle

The reason for the asymmetry is that the base (100%) changes after the loss.

• When you lose 10% on $100, you lose $10. You now have $90.

• To get from $90 back to $100, you need a gain of $10.

• However, that $10 gain is now calculated as a percentage of your new base of $90.

• Formula: Required Gain % = (Loss %) / (1 - Loss %)

  • For a 50% loss: Required Gain = 0.50 / (1 - 0.50) = 0.50 / 0.50 = 1.00 = 100%

This is why the "Return required" column escalates so dramatically.

Critical Discussion and Comments

1. The Exponential Curve of Pain: The relationship is not linear; it's exponential. As losses deepen, the recovery requirement skyrockets. A 50% loss needs a 100% gain (doubling your money). A 70% loss needs a 233% gain. A 90% loss is nearly impossible to recover from (needing a 900% gain).

2. Primary Investment Implication: Risk Management is Paramount. This is the single most important lesson for any investor or trader. Preventing large, permanent losses is more critical than chasing large gains. A portfolio that avoids catastrophic drawdowns has a significant mathematical advantage over one that suffers large losses and then tries to fight back.

3. The Psychological Toll: Beyond the math, large losses create immense psychological pressure. Investors may become fearful, abandon their strategy, or take excessive risks in a desperate attempt to recover, often leading to further losses.

4. The "Wait to Get Back to Even" Fallacy: Many investors hold a losing asset, thinking, "I'll sell when it gets back to my purchase price." This table shows why that can be a poor strategy. The time and opportunity cost of waiting for a 100% gain (after a 50% loss) could be enormous, as that capital could be deployed more effectively elsewhere.

5. Application to Different Scenarios:

   • Trading/Volatile Assets: For assets like cryptocurrencies or speculative stocks, a 20-30% drop is common. The table reminds traders that a 25-43% rebound is needed just to break even, which is not a trivial move.

   • Bear Markets: In a market downturn where a portfolio drops 30%, it requires a ~43% subsequent gain to recover. This explains why bull markets often need to be longer and stronger to fully repair bear market damage.

   • Company Performance: A company whose profit falls 50% must see profits double (increase 100%) just to return to the original level.

6. The Source ("SOURCE: FAIRFAX"): This table or variations of it are a staple in financial education materials from firms like Fairfax and others. It's used to visually shock clients and advisors into respecting the power of compounding losses and to justify a conservative, capital-preservation approach to investing.

Conclusion

This simple table encapsulates one of the most fundamental rules of wealth building: It's easier to preserve capital than to recover lost capital.

The takeaway is not to avoid risk entirely, but to:

• Use position sizing to ensure no single loss can be catastrophic.

• Employ stop-losses or hedging strategies to limit drawdowns.

• Have a balanced and diversified portfolio to avoid overexposure to a single crashing asset.

• Understand that recovering from even a moderate loss requires a disproportionate and challenging gain.

In investing, the math of recovery is brutally unforgiving, making the prevention of large losses the most important strategic objective.