How did Markowitz define risk?

Markowitz defined risk as the volatility of returns—specifically measured by variance or standard deviation. In simple terms, a riskier investment is one whose returns bounce around more unpredictably. If two investments have the same expected return, the one with lower volatility is considered less risky in the Markowitz framework. But here's where it gets interesting. Markowitz's key insight was recognizing that portfolio risk isn't just the sum of individual asset risks. It depends critically on how assets move relative to each other—their correlations or covariances. By combining assets that don't move in lockstep, investors can reduce overall portfolio volatility below what you'd expect from simply averaging individual risks. This covariance insight was revolutionary. It provided the mathematical foundation for why diversification works—not just holding many things, but holding the right combination of things that behave differently under various market conditions.