Efficient Frontier

The exam loves the “minimum-variance frontier vs. efficient frontier” distinction: the full minimum-variance curve includes a lower inefficient half, and only the portion above and to the right of the global minimum-variance portfolio (GMVP) counts as efficient. A classic stem gives a portfolio and asks if it’s efficient — the tell is whether another portfolio offers an equal expected return at lower risk (or higher return at equal risk). Watch the investor-choice step: the optimal portfolio is where the investor’s indifference curve is tangent to the frontier, so a more risk-averse investor lands further down-and-left.

Don’t confuse the frontier with the Sharpe ratio, which ranks portfolios by risk-adjusted return. The trap: students assume the GMVP is “best,” but it only minimizes variance — it needs no expected-return inputs and is generally not the Sharpe-optimal (tangency) point. Note both the frontier’s x-axis and the Sharpe ratio use total risk (standard deviation) — not beta (that’s Treynor). Memory hook: “efficient = northwest” — every efficient portfolio sits up-and-left, dominating everything to its southeast.