Initially, you had ONLY invested in a Vanguard Small-Cap [VSC] Mutual Fund (aside from risk free securities). VSC is a mutual fund consisting entirely of stocks that gave you an expected return of 14% with a volatility of 20%. At present, the risk free rate of interest is 3.09%.

Your financial advisor suggested you to invest in JPMorgan Mid Cap Growth [JPMCG] fund that has an expected return of 20% with a volatility of 60% and a correlation of 0.56 with VSCM fund. Following your financial advisors advice you made an investment of 60% in VSCM and 40% in JPMCG.

After talking with your risk analyst professor, you decided to reduce the investment in JPMCG. Now, you have a portfolio with an investment of 72% in VSCM and 28% in JPMCG. From the above 3 portfolios, which gives you the best expected return and the least volatility.

Then, find the Sharpe ratio for each of the three portfolios and finally, what portfolio weight in JPMCG fund maximizes the Sharpe ratio?