# Portfolio Hedging under Uncertain Correlations

I have a portfolio ($w_0=1$) and two hedging assets ($w_1,w_2$) and a co-variance matrix for the three $\Sigma$. However the co-variance $\Sigma$ is only an estimate.

• For fairly well behaved assets (close to normal), what is a good way to understand the uncertainty in co-variance matrix using historical data?
• Using the two assets, how do I lower my portfolio volatility $\sigma_0$ to a target amount $\sigma_T$ with the most certainty?

References would be greatly appreciated.