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Interactive Risk (Covariance) 🤝📉

When you combine two stocks, the total risk isn't just the sum of their individual risks. There is a third type of risk called Interactive Risk. This risk exists because stocks have a relationship with each other. The mathematical tool used to measure this interactive risk is Covariance.

1. Meaning of Covariance

Covariance measures the degree to which two variables (returns of two stocks) move together.

  • Positive Covariance: When Stock A earns more than its average, Stock B also tends to earn more than its average.
  • Negative Covariance: When Stock A earns more than its average, Stock B tends to earn less than its average.
  • Zero Covariance: The movement of Stock A tells you nothing about the movement of Stock B.

2. Calculation of Covariance

Covariance is the average of the products of the deviations of two stocks from their respective means.

Formula:

Cov(A,B) = Σ [ Pi * (Ra - E(Ra)) * (Rb - E(Rb)) ]

Where:

  • Pi: Probability of scenario i.
  • (Ra - E(Ra)): Deviation of Stock A from its expected return.
  • (Rb - E(Rb)): Deviation of Stock B from its expected return.

3. Covariance and Portfolio Risk

In the portfolio variance formula (which we saw in Chapter 21), Covariance represents the "interaction" term.

Portfolio Variance = (Wa^2 * Sa^2) + (Wb^2 * Sb^2) + 2(Wa * Wb * Cov_ab)

[!TIP] Correlation vs. Covariance: Covariance tells you the direction of the relationship, but its value is hard to interpret (e.g., a Covariance of 45.3 doesn't tell you much). Correlation is simply a "standardized" version of Covariance that always stays between -1 and +1.

4. Why it Matters for Diversification

The goal of a portfolio manager is to find pairs of stocks with Negative Covariance.

  • If Stock A has a bad year, Stock B has a good year.
  • The bad outcome of A is "covered" by the good outcome of B.
  • The total portfolio value remains stable.

Summary

  • Covariance measures the joint variability of two stocks.
  • It is the foundation for calculating Correlation.
  • Negative Covariance is the "holy grail" of risk reduction.
  • It is a key input for the Markowitz Model.

Quiz Time! 🎯

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