If your fund performs better then another fund per the treynor method but underperforms per the sharpe measure, which fund is better diversified?
good question 
i’ve made mistake on this one, and i kinda dig the explanation but i didnt have a chance to work through the formual to prove it mathematically. In general you should think that if std is the same but fund A has better treyoner then B that means A takes more unsystematic risk then B
Really hard to make an absolute statement. You have to be presented with beta and std to make a relative statement. In general, if a fund does well in treynor and poorly in sharpe, you can say it has “MORE” unsystematic risk==>Less diverisifed.
If alpha and Treynor measurements are better than Sharpe and M-squared measurements, the manager likely took on a significant amount of non-systematic risk. Since beta measures systematic risk and alpha and Treynor use beta, the non-systematic risk isn’t factored into their values. The high degree of non-systematic risk means that the manager is less diversified.
alright thanks guys makes sense now.