mp3bu

treynor = rp-rf/beta
sharpe = rp-rf / stddev

A has higher sharpe
A has lower treynor

sharpe A > Sharpe B could happen bcos
=============================
1. (RpA > RpB and StdDevA <= StdDevB ) -- A is more diversified.
OR
2. (RpA=RpB) and StdDevA < StdDevB ) -- A is more diversified
OR
3. If RpA < RpB then StdDev A must be << StdDev B -- again A is more diversified.

treynor A < Treynor B
================
1. RpA > RpB and BetaA > BetaB (more systematic risk for A)
or
2. RpA = RpB and Beta A > Beta B (more systematic risk for A)
or
3. RpA < RpB then beta A >> beta B ...

so higher systematic risk for A.
more diversified

there is a particular scenario where A could achieve lower return than B.
(Not sure about the 3rd part of the question).

CP