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Efficient Frontier

The set of portfolios offering the highest return for each level of risk.

The efficient frontier is a curve in risk-return space representing portfolios that are 'mean-variance optimal'. Each point on the frontier offers the maximum expected return for its level of volatility (risk). Portfolios below the frontier are suboptimal because you could achieve higher return for the same risk or lower risk for the same return.

Formula
maxw  E[rp]s.t.σpσtarget\max_{w} \; E[r_p] \quad \text{s.t.} \quad \sigma_p \leq \sigma_{\text{target}}