On page 231 (Volume 6), the CFA book states: “However, the Sharpe ratio should be used only for the investor’s global portfolio. A portfolio whose objective is to be invested in foreign assets to diversify risk of the domestic assets cannot be evaluated separately from the total portfolio”. Doesn’t the first statement contradict the second?
Here, what I think they are trying to say is that we cannot use the sharpe ratio to evaluate the risk adjusted performance separately from the total global portfolio. They are saying the foreign portfolio should be evaluated by its contribution of the risk of the global portfolio. This is because when its included with the global portfolio, its risk gets diversified away. So we can use treynor/jensen measures instead of sharpe.
When a portfolio is diversified and there is no unsystematic risk then we could use Treynor (which uses beta as the risk measure), but for portfolios with systematic risk we should use Sharpe as its a measure of total risk (systematic + unsystematic).