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What you will learn
- Explain why percentages with different starting values do not cancel out.
- Calculate the increase required to reach an earlier value.
- Distinguish a required mathematical change from a forecast.
From 100 to 80 and back again
An invented price falls from SEK 100 to SEK 80. The decline is 20 ÷ 100 × 100 = 20 percent. Reaching 100 again requires an increase of SEK 20 from the new base of SEK 80.
That increase is 20 ÷ 80 × 100 = 25 percent. The amount of SEK 20 is the same in both calculations, but the denominators differ. If 80 instead rises 20 percent, it becomes 96 rather than 100.
The formula for comparing two values
Required increase in percent = (earlier value ÷ current value − 1) × 100. For an earlier value of 100 and a current value of 80, the calculation is (100 ÷ 80 − 1) × 100 = 25 percent.
Current value must be greater than zero to use this formula. If something has lost all its value, there is no positive base from which to calculate an ordinary percentage recovery. The formula also does not say whether or when recovery is possible.
If the table does not fit, scroll it sideways.
| Decline | Value afterwards | Increase to reach 100 |
|---|---|---|
| 10 % | 90 | about 11.11 % |
| 20 % | 80 | 25 % |
| 25 % | 75 | about 33.33 % |
| 50 % | 50 | 100 % |
Multiply the change factors for two periods
Let SEK 1,000 first fall 20 percent and then rise 20 percent. The first step is 1,000 × 0.80 = SEK 800. The second is 800 × 1.20 = SEK 960. The total is SEK 40 below the starting value, a decline of 4 percent.
Check with 0.80 × 1.20 = 0.96. The factor 0.96 means that 96 percent of the original value remains. Adding −20 and +20 would lose the fact that the second change is calculated from SEK 800.
You can use the same calculation for a whole fictional portfolio value if you do not mix in deposits, withdrawals or other flows. When such flows exist, first clarify which value changes you are actually comparing.
A required increase is not a reason to expect that increase
Knowing that a rise of 25 percent is required tells you only how far the current value is from an earlier level. It says nothing about the company's activities, what a future buyer will pay or which outcome is likely.
Handelsbanken uses an example where a halving requires a doubling to reach the earlier value. This lesson explores the same relationship with its own amounts and several declines. Compare the calculations while keeping percentage mathematics separate from a real investment decision.
Finish an exercise with two sentences: what change is mathematically required, and what information would be needed to discuss the future? The formula alone cannot answer the second question.
Try it yourself
A fictional holding was worth SEK 2,400 and is now worth SEK 1,800. What percentage increase from SEK 1,800 would bring it back to SEK 2,400?
Show the solution and explanation
Approximately 33.33 percent.
The difference is SEK 600. 600 ÷ 1,800 × 100 is about 33.33 %. The earlier decline was 600 ÷ 2,400 × 100 = 25 %. The two calculations use different denominators.
Check your understanding
After a 50 percent fall, is a 50 percent rise enough to recover?
No. Falling from 100 to 50 and then rising 50 percent gives 75. Reaching 100 from 50 requires a 100 percent rise.
Is the required increase a forecast?
No. It is a calculation of the relationship between two values. It predicts neither a future price nor a date.
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
Start here: shares and portfolios
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.
