Trojan Investment LLC that has recently launched a new fund called Trojan Explorer. Although the fund has been quite volatility (with a monthly return volatility of 16%), the fund has had an average return of 3% per month. In contrast, the average monthly return of the S&P 500 has been around 0.8% with a monthly volatility of 4%. Assume the risk-free rate is 0.2% per month. For this problem, take the S&P 500 to represent the market.

Find a portfolio of the risk-free asset and the Trojan Explorer fund that ha s the same volatility as the S&P 500. What is the weights of the portfolio? What is the expected return of the portfolio?
Suppose that the correlation between the Trojan Explorer fund and the S&P 500 is 0.50. Find the beta of the fund.
According to the CAPM (using the S&P500 as the market), what should the expected return of the fund be? What is the alpha of the fund?