A pension manager is considering investing in a mutual fund. The first is a stock-type fund that invests in large-cap stocks, and the second is a bond-type fund that invests in long-term government bonds and corporate bonds. In addition, the correlation coefficient between the returns of stock-type funds and bond-type funds is 0.1.

What should be the investment ratio for the stock-type fund and the bond-type fund if you want to form a minimum diversification portfolio with the stock-type fund and the bond-type fund you are considering? What is the expected return and standard deviation of the minimum variance portfolio?

\begin{tabular}{|c|c|c|} \hline & expected return & Standard Deviation \\ \hline stock fund (S) & 20% & 30% \\ \hline & 12% & 15% \\ bond fund (B) & & \\ \hline \end{tabular}