Risk and Return
You cannot have higher expected return without accepting more risk — that trade-off is the deepest law in investing, and quantifying it precisely is the achievement that launched modern finance. The surprising twist is that risk is not simply additive: combine imperfectly related assets and some risk cancels out for free. Diversification is the closest thing finance has to a free lunch, and portfolio theory is the math of exploiting it.
Higher expected return requires more risk — and the surprising twist is that diversification reduces risk for free when assets are imperfectly correlated. Volatility, covariance, the efficient frontier, systematic vs. idiosyncratic risk, and how CAPM prices risk through beta. (Educational, not financial advice.)