Consider a risky portfolio $($P$)$ comprised of two assets: A bond fund $($B$)$ and a stock fund $($S$).$ According to portfolio theory, the variance of such portfolio will depend on the weight of each asset in the portfolio, the standard deviation of each asset in the portfolio, and the correlation between these two assets as given by the formula:

${}_{}^2=(w_B*{}_B{)}^2+(w_S*{}_S{)}^2+2*(w_B*{}_B)*(w_S*{}_S)*{}_{B,S}$

Based on this formula, the minimum variance portfolio will have the following weight $W_B$ in the bond fund:

$w_B=\frac{{}_S^2-{}_B*{}_S*{}_{B,S}}{{}_S^2+{}_B^2-2*{}_B*{}_S*{}_{B,S}}$

Therefore, when bond fund $(B)$ and the stock fund $(S)$ are perfectly correlated $($i$.$e$.$ correlation $=1),$ the weight in the stock fund $(S)$ the minimum variance portfolio will be:

$\frac{{}_S}{{}_S+{}_B}$

$\frac{{}_B}{{}_S+{}_E}$

$\frac{{}_S}{{}_B-{}_S}$

$\frac{{}_B}{{}_B-{}_S}$