Coefficient of Correlation (r) 📉🔗
In the previous chapter, we learned about Covariance. While Covariance tells us the direction of movement, it is very hard to read because its value depends on the units of the stock prices. The Coefficient of Correlation (r) solves this by "normalizing" the relationship into a scale from -1.0 to +1.0.
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1. Meaning of Correlation Coefficient
The Correlation Coefficient measures both the strength and the direction of the linear relationship between two securities.
- It is a unit-less number.
- It is the most important input for building a diversified portfolio.
2. Calculation of Correlation (r)
Correlation is calculated by dividing the Covariance of two stocks by the product of their individual standard deviations.
Formula:
r_ab = Cov(A, B) / (Sa * Sb)
Where:
- Cov(A, B): Covariance between Stock A and Stock B.
- Sa: Standard Deviation of Stock A.
- Sb: Standard Deviation of Stock B.
3. Interpreting the Values (The Scale)
The value of r always falls between -1.0 and +1.0.
| Value of r | Meaning | Impact on Portfolio Risk |
|---|---|---|
| +1.0 | Perfect Positive Correlation. | No risk reduction at all. |
| +0.5 | Moderate Positive Correlation. | Some risk reduction. |
| 0.0 | No Correlation (Independence). | Significant risk reduction. |
| -0.5 | Moderate Negative Correlation. | Very high risk reduction. |
| -1.0 | Perfect Negative Correlation. | Risk can be reduced to Zero. |
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In the real world, most stocks in the same market have a correlation between +0.4 and +0.7. This means while they move together, there is still plenty of room for risk reduction through diversification.
4. Why Correlation is the Manager's Best Friend
A portfolio manager's job is not just to find "good" stocks, but to find stocks that have Low Correlation with each other.
- Example: Combining a Bank stock and an IT stock is better than combining two Bank stocks because they are less correlated.
- Example: Combining Stocks and Gold is even better because they often have zero or negative correlation.
Summary
- Correlation (r) is a standardized version of Covariance.
- It ranges from -1.0 to +1.0.
- The lower the correlation, the better the diversification.
- It is used to calculate the final Portfolio Risk.
Quiz Time! 🎯
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