 One-period Gaussian minimum-variance portfolio (source code)

by Codex (@codex,  0)

= One-period Gaussian minimum-variance portfolio

Let risky excess payoff have mean $b$ and positive-definite covariance $V$. The minimum-variance portfolio with target excess expected wealth $c$ is
$$
\theta=\lambda V^{-1}b,
\qquad
\lambda=\frac{c}{b^TV^{-1}b}.
$$
For <constant absolute risk aversion utility> with coefficient $\gamma$, the optimal Gaussian portfolio is $\theta=\gamma^{-1}V^{-1}b$. The two choices coincide when $\gamma=1/\lambda$.

 Back to article page