Educational material from 
What you will learn
- Subtract percentages to get a difference in percentage points.
- Divide the difference by the starting proportion for relative percentage change.
- Distinguish a changed portfolio weight from an investment return.
A proportion describes how much of a whole is included
In our fictional portfolio, a holding is worth SEK 2,000 out of a SEK 10,000 total. Its proportion is 2,000 ÷ 10,000 = 20 percent. Think of it as 20 out of 100 equal parts of this particular whole. SEK denotes Swedish kronor.
At the next comparison, the proportion is 25 percent. Begin with the question you want to answer: how many steps has the percentage moved, or how large is the increase relative to the old percentage? Name the measure before calculating to make the answer clear.
Five percentage points and 25 percent describe the same change
The difference in percentage points is 25 − 20 = 5. The relative percentage change is (25 − 20) ÷ 20 × 100 = 25. The denominator in the second calculation is the starting proportion, 20. That is why the two numbers differ.
Write the full sentence: the proportion rose from 20 to 25 percent, an increase of 5 percentage points. If you also state a 25 percent relative increase, say what it is relative to. That helps the reader reconstruct the calculation.
If the table does not fit, scroll it sideways.
| From → to | Difference | Relative change |
|---|---|---|
| 20 % → 25 % | +5 percentage points | +25 % |
| 40 % → 30 % | −10 percentage points | −25 % |
| 10 % → 20 % | +10 percentage points | +100 % |
An increased weight does not automatically mean a gain
Now suppose the holding is still worth SEK 2,000 but other parts fall, reducing the total to SEK 8,000. Its weight is 2,000 ÷ 8,000 = 25 percent. It rose from 20 to 25 percent without the holding itself gaining value.
The holding's value change in this scenario is zero. Its weight change is 5 percentage points. The whole portfolio's value change is −20 percent. Three correct measures describe three different things; do not report the higher weight as the share's return.
Check the base and direction
Moving back from 25 to 20 percent is −5 percentage points, but −20 percent relative to 25. The relative decrease is not the same size as the earlier increase because the starting value is now different. Subtraction and division still answer the same two questions.
With a starting proportion of zero, you can describe the move from 0 to 5 percent as 5 percentage points. You cannot use the usual relative formula because it would divide by zero. State the start and end instead of inventing a percentage increase.
- Write both the old and new proportions.
- Use percentage points for a direct difference.
- State the starting proportion for a relative change.
- Separate a change of proportion from a change of monetary value.
Try it yourself
An invented proportion moves from 30 to 36 percent. What is the change in percentage points and in percent relative to the starting proportion?
Show the solution and explanation
+6 percentage points and +20 percent relative to the starting proportion.
36 − 30 = 6 percentage points. Divide 6 by the starting proportion of 30, then multiply by 100: 6 ÷ 30 × 100 = 20 percent.
Check your understanding
Is a move from 10 to 20 percent an increase of 10 percent?
It is 10 percentage points. Relative to the starting proportion of 10, the increase is 100 percent because the proportion doubles.
Can a weight rise while the holding value stays unchanged?
Yes. If other parts fall, the total is smaller, so the same holding value becomes a larger proportion.
Practise with virtual money
Try what you just learned in a practice portfolio with virtual money. You don't deposit any real money.
How the practice portfolio worksKeep learning and practising
More lessons on this topic
Prices, company events and currency
- Share price and market cap: why price does not show company size
- What is a stock split? Calculate shares, price and ownership
- Calculate return including dividends: a simple example
- Currency effects on stock returns: calculate price and exchange rate
- Read a stock chart: time period, starting point and price basis
Sources and examples
The sources support the factual explanations. Calculations and exercises were created for this lesson. Amounts and price changes are invented unless stated otherwise.
This material is educational and does not recommend securities to buy. A simulated result does not guarantee a future result.
