The return$/$risk profile of the Pervival investments portfolio is an investment of $10$ million in long$-$term bonds. The expected return on the portfolio is $9\%$ with a standard deviation of $10\%.$

An investment manager recommends, as a risk reduction strategy, replacing the portfolio with an SP$500$ certificate and risk$-$free treasury bonds. The index has an expected return of $14\%$ and a standard deviation of $16\%,$ while treasury bonds earn $6\%$ and are risk$-$free.

Could this combination generate a better risk$-$return profile than the current investment in bonds?