How is the tangency portfolio found analytically?

w* = Sigma^-1 * (mu - rf*1) / (1' * Sigma^-1 * (mu - rf*1)). The tangency weights are proportional to the product of the inverse covariance matrix and the excess return vector.

Why is the tangency portfolio sensitive to return estimates?

Small errors in expected returns are amplified by matrix inversion. A 0.1% change in expected return can shift portfolio weights by 10-50%. This is the estimation error problem that motivates Black-Litterman and robust optimization.

Maximum Sharpe Tangency Portfolio Calculator

Find the tangency portfolio that maximizes the Sharpe ratio. Solve max (mu-rf)'w / sqrt(w'Sigmaw) subject to w'1=1. The tangency is the single optimal risky portfolio in CAPM theory.

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$ 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. Find the tangency portfolio that maximizes the Sharpe ratio. Solve max (mu-rf)'w / sqrt(w'Sigmaw) subject to w'1=1. The tangency is the single optimal risky portfolio in CAPM theory. Use the max sharpe tangency result to inform your calculation.

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Frequently Asked Questions

How is the tangency portfolio found analytically?

Why is the tangency portfolio sensitive to return estimates?