John is a typical mean$-$variance investor, currently invested $100\%$ in a diversified U$.$S$.$ equity portfolio with expected return of $12\mathrm{.}46\%$ and volatility of $15\mathrm{.}76\%.$ John is considering adding the fund ABC to his portfolio. ABC invests in U$.$S$.$ small$-$capitalization, high technology firms and has an expected of $14\mathrm{.}69\%$ and a volatility of $32\mathrm{.}5\%.$ John has determined its correlation with his current portfolio to be $0\mathrm{.}7274.$ He is also intrigued by the fund PRQ$,$ which invests in several emerging markets. The expected return on the fund is only $12\%$; it has $35\%$ volatility and a correlation of $0\mathrm{.}2$ with his portfolio. The correlation of the fund PRQ with the fund ABC is $0\mathrm{.}15.$ Assume that the risk$-$free rate is $5\%.$

If John is interested in improving the Sharpe ratio of his portfolio, will he invest a positive amount in one of the funds? Which one? Carefully explain your reasoning.