-50% Then +50% Is Not Back to Even, and Why It Feels Like It Is
TL;DR
- An arithmetic average can feel reassuring, but considering compounding, -50% followed by +50% does not restore original capital.
- Understanding geometric mean (compounding) lets you accurately gauge the gain needed to recover losses.
A relatable scenario: the illusion when checking your account
After a steep drop that halves an account, it is easy to assume that an equal percentage rebound returns you to even. When people say "-50% then +50%" it sounds like a wash, but calculating the actual balance shows otherwise. This simple experience is a common psychological trap for investors.
Two averages for returns: arithmetic vs geometric
The arithmetic mean simply adds period returns and divides by the number of periods, which is handy for small, non-compounding comparisons. Investing, however, is driven by compounding, where capital multiplies over time. The geometric mean captures that. For example, starting capital 100 falls -50% to 50, then rises +50% to 75. Arithmetic calculation gives (-50% + 50%)/2 = 0%, yet the actual balance falls short of the original capital.
Why we fall for this illusion: psychological factors
People intuitively fail to grasp the asymmetry of percentage changes. The gain required to recover from a loss is always larger than the loss percentage, but this is easy to overlook. Habitual comparison of simple averages and the desire to quickly dismiss losses also contribute. Emotional bias after losses makes optimistic figures more readily accepted.
Practical detection and checklist
- Calculate based on balance: do not rely solely on percent changes, write down actual amounts and compute. The example table makes it intuitive.
| Step | Change | Balance example (principal 100) |
|---|---|---|
| 1 | Start | 100 |
| 2 | -50% | 50 |
| 3 | +50% | 75 |
- Apply geometric mean: multiply period returns to reflect compounding when calculating average returns over multiple periods.
- Compute recovery gain needed: remember that the required rise to recover from a loss is not the same as the loss percentage. Use a calculator or Excel if the math is tedious.
- Avoid emotion-driven decisions: instead of quickly changing positions or overbetting after a loss, verify the situation with numbers. You can use My Stocks Radar to check profit and loss numerically.
Summary: trust the numbers and control emotions
The arithmetic mean is easy to understand and commonly used, but the geometric mean delivers more practical information for investing. Emotions react first when losses occur, but conditions for recovery should be judged by numbers. Check latest specifics like taxes and fees with your broker or relevant institutions.
This article is for informational purposes and not investment advice.
관련 테마의 대표 기업을 확인하고, 내 관심 종목은 뉴스·시그널·시장 맥락으로 이어서 볼 수 있습니다.
종목명을 입력하면 재무, 뉴스, 시장 데이터를 정보 제공용 점검 리포트로 정리합니다.
관심 테마로 저장하면 마이페이지에서 다시 볼 수 있고, 강한 움직임이 생길 때 주간 테마 시그널과 연결해 확인할 수 있습니다.
