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 significantly—say, by 20% in the first year—only 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 Stock’s Journey: A 20% Gain Followed by a 25% Drop

Let’s 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 – 30 = 90

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?

Key Insights

Calculating the Net Percentage Change

Despite a strong first-year performance, the stock ends up valued lower—90, compared to the original 100.

To find the net percentage change:
Net change = Final price – Initial price = 90 – 100 = –10
Percentage change = (Net change / Initial price) × 100
= (–10 / 100) × 100 = –10%

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ight) = rac{1}{3} imes rac{1}{4} = rac{1}{12} $. Thus, the probability of at least one positive is $ 1 - rac{1}{12} = rac{11}{12} $. Final answer: $oxed{\dfrac{11}{12}}$.Question: Define $M(u) = u - rac{u^2}{2}$ for all real numbers $u$. If $a_1 = 1$ and $a_{n+1} = M(a_n)$ for $n \geq 1$, find $a_3$.
Solution: Start with $a_1 = 1$. Compute $a_2 = M(a_1) = 1 - rac{1^2}{2} = rac{1}{2}$. Next, compute $a_3 = M(a_2) = rac{1}{2} - rac{( rac{1}{2})^2}{2} = rac{1}{2} - rac{1}{8} = rac{3}{8}$. Thus, the value of $a_3$ is $oxed{\dfrac{3}{8}}$.
Question: Let $x, y, z$ be positive real numbers such that $2x + 3y + 4z = 12$. Find the minimum value of $x^2 + y^2 + z^2$.

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Final Thoughts

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 × 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 changes—simple arithmetic addition doesn’t 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.