2-Asset Efficient Frontier
Plot the efficient frontier, minimum variance portfolio, and tangency portfolio for any two assets: adjust return, volatility, and correlation.
How It Works
The 2-Asset Efficient Frontier tool plots all possible portfolios you can create by combining two assets in varying proportions. For each weight combination from 0% to 100% in Asset A, the tool computes the portfolio's expected return and risk (standard deviation), then plots them on a risk-return chart.
The resulting curve is the efficient frontier. The tool also identifies two key portfolios: the minimum variance portfolio (lowest possible risk) and the tangency portfolio (highest possible Sharpe ratio). Adjust the six inputs: each asset's return and volatility, their correlation, and the risk-free rate: to see how the frontier and optimal portfolios change in real time.
The Formulas
rₚ = wₐ × rₐ + (1 − wₐ) × rᵇ σₚ² = wₐ²σₐ² + (1−wₐ)²σᵇ² + 2ρσₐσᵇwₐ(1−wₐ) wₘᵢₙ = (σᵇ² − ρσₐσᵇ) / (σₐ² + σᵇ² − 2ρσₐσᵇ) Max Sharpe = w that maximizes (rₚ − rᶒ) / σₚ
FAQ
What is the efficient frontier?
The efficient frontier shows the set of portfolios that offer the highest expected return for a given level of risk. Each point on the curve is a different combination of Asset A and Asset B. Portfolios below the frontier are suboptimal because you could achieve a higher return for the same risk or lower risk for the same return.
What is the minimum variance portfolio?
The minimum variance portfolio is the combination of two assets that produces the lowest possible portfolio volatility. Its weight depends on the two assets' volatilities and their correlation. Mathematically, it is found by setting the derivative of portfolio variance with respect to weight to zero.
What is the tangency portfolio?
The tangency portfolio is the point on the efficient frontier that maximizes the Sharpe ratio: excess return per unit of risk. It is also called the optimal risky portfolio. When combined with the risk-free asset, the tangency portfolio gives you the Capital Market Line (CML), which dominates all other frontier portfolios.
How does correlation affect the frontier?
Correlation measures how two assets move together, ranging from -1 (perfectly opposite) to +1 (perfectly together). Lower correlation produces more diversification benefit: the frontier bulges more to the left. At correlation = -1, you can achieve zero portfolio risk with the right weights.
Which portfolio should I choose?
You can test different values by adjusting the sliders. Try high return/high vol for A vs low return/low vol for B. Vary the correlation to see how the frontier shape changes. The tangency dot moves based on the risk-free rate: a higher risk-free rate pushes you toward lower-risk assets.
Related Tools
Also try: Sharpe/Sortino Ratio, Max Drawdown Calc, Portfolio Temperature: more tools for assessing risk-adjusted returns and portfolio construction.