Portfolio theory as you know it leans on assumptions—normal distributions, independent returns, stable correlations. But the market laughs at those neat models. Information theory, specifically entropy and mutual information, strips away some illusions. It quantifies uncertainty, not just variability. For technical professionals, the challenge is integrating these tools with standard methods. My advice: start by overlaying entropy calculations on your usual risk metrics. Compare, contrast, and look for gaps. You’ll find that information measures can alert you to risks masked by traditional statistics.

The big pitfall is estimation error. Entropy and mutual information are powerful, but only as good as your underlying probability estimates. Garbage in, garbage out. Also, there’s a temptation to overinterpret these measures. Just because mutual information finds a dependency doesn’t mean it’s economically significant. Always sanity-check with other methods. My biggest recommendation: treat these measures as one lens among several.

Case in point: Indian fixed income markets. Covariances alone miss nonlinear dependencies across tenors and credit qualities. By calculating mutual information, we uncovered relationships between short-term and long-term bond yields missed by correlation. It changed our hedging approach. A real lesson: when data grows complex, information theory helps—but never replaces contextual judgment.

You have to be humble with these tools. They provide sharp diagnostics, but markets will always surprise you. Treat information-theoretic metrics as early warning systems, not oracles. Combine them with scenario analysis and judgment. And always remember: results may vary. That keeps your analysis honest and useful.