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Standard Deviation: The Total Risk Measure 📊📏

In the previous chapter, we discussed Variance. While Variance is mathematically sound, it has one major flaw: its units are "squared" (e.g., 25% squared). How do you compare a 10% return with a 25% squared risk? You can't. To solve this, we take the square root of Variance to get the Standard Deviation (sigma).

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Important

Total Risk: Standard Deviation captures both Systematic and Unsystematic risk combined.

2. Formula for Standard Deviation

The formula is simply the square root of the Variance:

SD (σ) = √Variance
SD (σ) = √[ Σ [ Pi * (Ri - E(R))^2 ] ]

Where:

  • sigma = Standard Deviation
  • Pi = Probability of outcome i
  • Ri = Possible return i
  • E(R) = Expected return

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4. Interpretation in a Normal Distribution

If returns follow a Normal Distribution (Bell Curve):

  1. 68% of the time, the actual return will be within 1 sigma of the mean.
  2. 95% of the time, it will be within 2 sigma.
  3. 99% of the time, it will be within 3 sigma.
Tip

In our example above (E(R)=7%, sigma=11.87%), we can say with 68% confidence that the return will be between -4.87% (7 - 11.87) and +18.87% (7 + 11.87).

Summary

  • Standard Deviation is the square root of Variance.
  • It measures Total Risk (both unavoidable market risk and company-specific risk).
  • It is expressed in Percentage, allowing direct comparison with returns.
  • The "Sharpe Ratio," which we will learn later, uses sigma to evaluate how much return you get "per unit of risk."

Quiz Time! 🎯

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