The price of a stock increased by 20% in the first year and decreased by 25% in the second year. What is the net percentage change? - Parker Core Knowledge
Understanding the Net Percentage Change: When Stock Price Rises 20% Then Drops 25%
Understanding the Net Percentage Change: When Stock Price Rises 20% Then Drops 25%
Investors often track stock performance through percentage gains and losses across multiple years. A common scenario is when a stock rises significantlyโsay, by 20% in the first yearโonly to fall sharply, such as 25% in the second year. But how does that translate to the overall change? What is the net percentage change after these two consecutive movements? This article breaks down the math and explains why stock performance over two years does not merely add up linearly.
Understanding the Context
The Stockโs Journey: A 20% Gain Followed by a 25% Drop
Letโs use a concrete example to clarify. Assume the initial stock price is 100 units.
Year 1: +20% Increase
A 20% gain means the stock rises by:
20% of 100 = 20
New price = 100 + 20 = 120
Year 2: -25% Decrease
Now, a 25% drop applies to the new price of 120:
25% of 120 = 30
New price = 120 โ 30 = 90
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Key Insights
Calculating the Net Percentage Change
Despite a strong first-year performance, the stock ends up valued lowerโ90, compared to the original 100.
To find the net percentage change:
Net change = Final price โ Initial price = 90 โ 100 = โ10
Percentage change = (Net change / Initial price) ร 100
= (โ10 / 100) ร 100 = โ10%
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Why the Result is Less Than the Sum of Both Changes
Although the stock gained 20% and then lost 25%, the final value is lower than the starting price. This counterintuitive result stems from compounding effects. Multiplicative changes affect successive levels, not absolute values:
- Gain: Multiply by 1.20
- Loss: Multiply by 0.75
- Combined: 1.20 ร 0.75 = 0.90, or a 10% overall decline
Key Takeaway
When a stock increases by 20% in Year 1 and decreases by 25% in Year 2, the net effect is a 10% decrease from the original price. This highlights the importance of compounding and order in percentage changesโsimple arithmetic addition doesnโt apply.
Final Thoughts
Investors should always look beyond headline gains or losses and examine percentage changes using multiplicative rules. Understanding the net percentage change helps make informed decisions and sets realistic expectations about long-term performance.
