How to Read Percentage Change Without Getting Fooled

Percentages are the most common way numbers are used to mislead — usually without anyone intending to. Four ideas cover nearly all of it.

1. Percentage change is not symmetrical

A 50% fall followed by a 50% rise does not return you to the start:

• 100 → falls 50% → 50
• 50 → rises 50% → 75

Each percentage applies to a different base. To recover from a fall of *p* you need a rise of p ÷ (1 − p):

This is why a portfolio down 50% needs to double, and why "recovered half its losses" usually means much less than half.

2. Percent and percentage point are different

An interest rate rising from 4% to 6% has increased by:

• 2 percentage points
• 50 percent

Both correct, wildly different in feel. Whenever a report says a rate "rose 50%", check whether it means points — the difference is frequently the entire story.

3. Reversing a percentage means dividing

A jacket costs £96 after 20% off. The original was not £96 × 1.20 = £115.20.

The £96 is 80% of the original:

original = 96 ÷ 0.80 = £120

Check: 20% of 120 is 24, and 120 − 24 = 96. ✓

The same applies to tax: to strip 20% VAT from £120, divide by 1.20 to get £100. Multiplying by 0.80 gives £96, which is wrong. This is the most common percentage error in ordinary financial life.

4. Successive percentages multiply

Three 10% rises are not 30%:

1.10 × 1.10 × 1.10 = 1.331 → 33.1%

And a 20% rise followed by a 20% fall is not zero:

1.20 × 0.80 = 0.96 → a 4% loss

Order does not matter; the loss appears either way. Over many periods this compounding effect becomes larger than the individual changes.

Averaging percentages

The average of percentage changes is usually not the overall change. Returns of +50% then −50% average to 0% but leave you down 25%. The correct measure is the geometric mean: multiply the growth factors and take the nth root.

Quick mental methods

• 10% — shift the decimal one place
• 5% — half of 10%
• 15% — 10% plus half again
• Swap trick — a% of b = b% of a. 8% of 25 is awkward; 25% of 8 is

obviously 2.

Check anything consequential with the percentage calculator.