Consider a portfolio (w^{mathrm{p}} otin mathrm{PF}). Show that, in the variance expected return plane, the line which

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Consider a portfolio \(w^{\mathrm{p}} otin \mathrm{PF}\). Show that, in the variance expected return plane, the line which connects the two points \(\left(\sigma^{2}\left(\tilde{r}_{w^{\mathrm{p}}}\right), \mathbb{E}\left[\tilde{r}_{w^{\mathrm{p}}}\right]\right)\) and \(\left(\sigma^{2}\left(\tilde{r}_{w^{\mathrm{MVP}}}\right), \mathbb{E}\left[\tilde{r}_{w^{\mathrm{MVP}}}\right]\right)\) intercepts the expected return axis at the level \(\mathbb{E}\left[\tilde{r}_{w^{\mathrm{q}}}\right]\), where \(w^{\mathrm{q}}\) is the portfolio such that \(\operatorname{Cov}\left(\tilde{r}_{w^{\mathrm{q}}}, \tilde{r}_{w^{\mathrm{p}}}\right)=0\) and with the minimum variance among all portfolios with zero correlation with \(w^{\mathrm{p}}\).

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