Feasible Set: The set of all possible portfolios formed by combining the risky assets with non-negative weights summing to one (no short selling). Each point represents a particular allocation across the three assets.
Efficient Frontier: The upper boundary of the feasible set. Portfolios on the efficient frontier offer the highest expected return for each level of risk (standard deviation). A rational investor would never hold an interior or lower-boundary portfolio because a frontier portfolio dominates it.
Tangency Portfolio (P*): The unique risky portfolio that maximizes the Sharpe ratio (E[rP] − rf) / σP. Graphically, it is the point where the Capital Allocation Line is tangent to the efficient frontier. All mean-variance investors hold the same tangency portfolio regardless of their risk preferences (Separation Property).
Capital Allocation Line (CAL): The straight line from the risk-free rate through the tangency portfolio. It represents all combinations of the risk-free asset and the tangency portfolio. Its slope is the maximum achievable Sharpe ratio.
Optimal Complete Portfolio (C*): Given the investor's risk aversion coefficient A, the optimal fraction invested in the tangency portfolio is y* = (E[rT] − rf) / (A · σ²T). The remainder (1 − y*) is invested in the risk-free asset. If y* > 1, the investor borrows at the risk-free rate (leveraged position). The complete portfolio lies on the CAL.