When to use entropy, mutual information, or variance in portfolio uncertainty analysis
Practical Guide
September 24, 2026
by Jaya Prakash Rao
Variance is intuitive, but has blind spots
Variance is the default measure of uncertainty for most analysts. It is simple, intuitive, and relies on assumptions about the distribution of returns. However, variance is blind to nonlinear dependencies and ignores the shape of the underlying distribution. When returns are not normally distributed, variance alone can mislead. This is common in Indian markets, where fat tails and asymmetry are not unusual. Variance works best for quick diagnostics but should not be the only tool in your kit.
Entropy captures total unpredictability
Entropy steps up when you want a full picture of unpredictability. Unlike variance, entropy measures uncertainty across the entire probability distribution, not just its spread. This is particularly valuable for portfolios with asymmetric risk profiles or when evaluating the value of diversification. For Indian portfolios with exposure to emerging sectors, entropy clarifies risk that variance can hide. The catch: you need robust probability estimates to get meaningful results.
Mutual information reveals hidden dependencies
Mutual information measures how much knowing the outcome of one asset reduces uncertainty about another. It detects relationships that both correlation and variance miss. In portfolios, this helps identify hidden links between assets. For instance, two Indian sector indices might have zero correlation but significant mutual information due to nonlinear co-movements. Use mutual information to refine diversification, but remember: interpretation requires care.