Noise Math Example 2

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Example 2

medium
Stock prices show daily fluctuations. Stock A has daily changes: {+2%,−1%,+3%,−2%,+1%}\{+2\%, -1\%, +3\%, -2\%, +1\%\}. Stock B changes: {+0.1%,−0.1%,+0.1%,0%,+0.1%}\{+0.1\%, -0.1\%, +0.1\%, 0\%, +0.1\%\}. Identify which has more noise and what that means for investors.

Solution

  1. 1
    Stock A daily change mean: (2−1+3−2+1)/5=0.6%(2-1+3-2+1)/5 = 0.6\%; range: 5%, SD reflects high volatility
  2. 2
    Stock B daily change mean: (0.1−0.1+0.1+0+0.1)/5=0.04%(0.1-0.1+0.1+0+0.1)/5 = 0.04\%; range: 0.2%, very small fluctuations
  3. 3
    Stock A has more noise (daily fluctuations of ±2-3%); Stock B is more stable
  4. 4
    Investor implication: Stock A is harder to predict day-to-day (higher risk); trend signal is harder to detect amid noise; Stock B's trend is clearer

Answer

Stock A has more noise (higher daily volatility); the underlying trend is harder to see amid fluctuations.
Financial noise refers to random day-to-day price movements that obscure the underlying trend. High noise makes it harder to detect true signals (e.g., a genuine price trend) and increases investment risk.

About Noise

Noise is random variation in data that is not explained by the underlying pattern or model — the unpredictable fluctuations around the true signal.

Learn more about Noise →

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