What is the tangency portfolio?

The tangency portfolio maximizes the Sharpe ratio — it's where the Capital Market Line (CML) is tangent to the efficient frontier. All investors should hold a combination of cash and the tangency portfolio.

Why does the efficient frontier curve upward?

As you move up the frontier, you can achieve higher returns only by accepting more volatility. The curve's shape reflects diminishing diversification benefits as portfolios become more concentrated.

Efficient Frontier Calculator

Plot the mean-variance efficient frontier for a portfolio of assets. Calculate the tangency portfolio (maximum Sharpe), minimum variance portfolio, and efficient frontier curve given expected returns and covariance matrix inputs.

Principal ($)

Annual Rate (%)

Years

Compounding / Year

$ Finance Disclaimer: These calculators are for educational and illustrative purposes only. Results do not constitute financial advice. Consult a licensed financial advisor before making investment or borrowing decisions.

How to Use

Enter the values for the scenario you are assessing. Plot the mean-variance efficient frontier for a portfolio of assets. Calculate the tangency portfolio (maximum Sharpe), minimum variance portfolio, and efficient frontier curve given expected returns and covariance matrix inputs. Use the efficient frontier result to inform your calculation.

Efficient Frontier Calculator

How to Use

Frequently Asked Questions

What is the tangency portfolio?

Why does the efficient frontier curve upward?