I don’t get how they got the answer. Are we suppose to calculate the std then the sharpe to compare. I know it’s like the old portfolio multiple by correlation, but I have no idea what that means. Also how they got .9558

I took an education guess on this question. Since the Sharpe Ratios were relatively similar, I assumed that the option with -.75 correlation should be added. What the answer said to do was multiply the correlation (-.75) with the current stock’s Sharpe Ratio (.50) and then subtract the product from the fund’s Sharpe ratio. That is where they got the .958. Do this for the other two fund’s, highest result is chosen.

Can we rationalize that since p of short fund is negative thus the benefit of diversification is greatest?

Well it also depends on the asset’s Sharpe Ratio as well. When comparing one investment…Add asset if:

Investment Sharpe Ratio > Portfolio Sharpe Ratio X correlation with Investment

This is the first time I have seen it with multiple investment choices.

For the Aggressive FOF , the sharpe ratio is 1.00 which is greater than the portionfolio sharpe ratio * correlation which is 0.2875 , so still dont understand why the answer for this one is C?