Your mutual fund falls 20% one year and rises 20% the next. Most people assume they are back at zero. They are not: you have lost 4% of your money, and the deeper the first fall, the bigger the climb you need just to break even.
Why the two percentages do not cancel out
A percentage change is always measured against the value you start from. The fall is calculated on your original amount, but the rise is calculated on the smaller amount that is left after the fall. So the rise is a percentage of a smaller number, and it brings back less money than the fall took away.
This property is known as the non-symmetrical reversibility of percentages: a percentage increase needs a different percentage decrease to return to the original value, and the other way round. A simple shop example shows it. A price that goes up 25%, from $100 to $125, has to come down 20%, not 25%, to get back to $100.
The real numbers on a 1 lakh investment
Say you invest ₹1,00,000.
- Year 1, the value falls 20%: ₹1,00,000 × 0.80 = ₹80,000
- Year 2, the value rises 20%: ₹80,000 × 1.20 = ₹96,000
The two percentages look like they average out to zero, but you are ₹4,000 short. The rule behind it is simple: a rise and a fall of the same size always leave you down by that percentage multiplied by itself. For 20%, that is 0.20 × 0.20 = 0.04, so a 4% loss. For 10%, it is 1%. The order makes no difference either: rising 20% first and then falling 20% also leaves you at ₹96,000.
How much you need to gain to recover a loss
To find the gain that fully repairs a loss, divide 1 by what is left of your money, then subtract 1. After a 20% fall, 80% is left: 1 ÷ 0.80 = 1.25, so you need a 25% gain, not 20%.
| Loss | Left of ₹1,00,000 | Gain needed to get back |
|---|---|---|
| 10% | ₹90,000 | 11.1% |
| 20% | ₹80,000 | 25% |
| 25% | ₹75,000 | 33.3% |
| 30% | ₹70,000 | 42.9% |
| 50% | ₹50,000 | 100% |
| 75% | ₹25,000 | 300% |
| 90% | ₹10,000 | 900% |
Small losses are easy to repair. Large ones are not: a 50% loss needs a 100% gain, which means your money has to double just to return to where it was. This is why investors watch the maximum drawdown of a fund, its worst fall from a peak to a low since it started. The biggest fall is usually the one that takes the longest to recover from.
The average return trap
The same effect hides inside average returns. Imagine four years of returns: +50%, −20%, +30% and −40%. Add them up and divide by four, and you get a tidy average of +5% a year. Now follow the actual money:
- ₹1,00,000 × 1.50 = ₹1,50,000
- ₹1,50,000 × 0.80 = ₹1,20,000
- ₹1,20,000 × 1.30 = ₹1,56,000
- ₹1,56,000 × 0.60 = ₹93,600
Despite a “5% average”, you finish with ₹6,400 less than you put in, a real loss of 6.4%, or a loss of about 1.64% a year once compounding is taken into account. That per-year figure is called the geometric average, and it is the one that matches your actual money. It is almost always lower than the simple average, and the gap grows the more the returns jump up and down.
Common mistakes to avoid
- Adding percentages together. A fall and a rise must be multiplied, not added. The same trap catches shoppers with stacked discounts.
- Trusting an average return on its own. Returns are often published as averages. To see what really happened to the money, compound the yearly returns one after the other, or use the CAGR from the starting and ending values.
- Thinking “it only needs to go back up the same amount”. After a 30% fall, a 30% rise is not enough. Check the table: you need almost 43%.
The takeaway: protecting your money from large falls matters as much as chasing big gains, because every rupee lost has to be earned back from a smaller base. If you want to see how steady growth adds up instead, the rule of 72 shows how long your money takes to double.
