An undivsersified fund is under consideration for addition to a broadly diversified investment portfolio. The most appropriate appraisal measure would be the Treynor ratio.
The Grinblatt-Titman performance measure uses a benchmark return based on a portfolio's own past holdings.
A skilled passive manager will have effective trade execution so performance does not differ much from an index.
An m2 alpha greater than zero would indicate that, on a risk-adjusted basis, the manager outperformed the benchmark.
Because information gathering is costly, investors will gather information until the costs of doing so are equal to its benefits, i.e. , until the net returns from active investing are equal to that of passive investing.
If an asset has asymmetric returns, downside risk measures that focus on losses would be appropriate.
Given two investments with the same returns, most investors will choose the one with less risk.