Let's assume you manage an SP 500 index fund and are ONLY willing to consider additional strategies that increase expected return without increasing...

Let's assume you manage an S&P 500 index fund and are ONLY willing to consider additional strategies that increase expected return without increasing overall portfolio risk. A hedge fund manager proposes you allocate 25% of your assets to her fund which has the following characteristics:

Beta to the S&P 500 = 0.4

Volatility = 9%

Expected Alpha = 4%

Correlation to with the S&P = .40

Taxes are not a consideration. Would you make the investment or not? Please describe why or why not and back up answer with calculations. Additionally, what would the alpha on the hedge fund have to be for you to change your decision?