Retired cards (September 2026)

The set of portfolios that maximize expected return for each level of variance (or minimize variance for each level of expected return). In (σ, μ) space it forms an upward-sloping hyperbola; only the upper branch is efficient.

Without a risk-free asset, every mean–variance efficient portfolio is a linear combination of any two distinct efficient portfolios. Investors differ only in the mix, not in the underlying risky funds held.

E[Rₚ] = Rf + ((E[Rₘ] − Rf)/σₘ) · σₚ. The CML connects the risk-free asset to the market (tangency) portfolio; its slope is the market Sharpe ratio.

Bootstrap returns from estimated (μ, Σ), recompute the efficient frontier on each resample, then average the resulting weight vectors at each risk level. Produces smoother, more diversified portfolios that are less sensitive to input noise.

∂V/∂t + ½ σ² S² ∂²V/∂S² + r S ∂V/∂S − r V = 0, with payoff V(T, S) = h(S).

For a derivative with payoff h(Sₜ) at T in a complete arbitrage-free market: Vₜ = 𝔼^ℚ[ e^(−∫ₜᵀ rₛ ds) h(S_T) | ℱₜ ].