Do we have any rule for deciding when to use weighted average of returns of corner portfolios for the efficient portfolio or use weighted average of the highest SR portfolio and Rf?
I am not sure if this is the question but for non-constraint portfolio use borrowing at RF and invest 100 % into Highest Sharpe portfolio. Thus Return is weighted average of both (eg. 120 % in Sharpe portfolio + (-20 %) borrowings at RF). For constrained portfolio (leverage not accepted) use weighted average of adjanced portfolios on Efficient frontier (eg. 80 % of corner portfolio 4 and 20 % of corner portfolio 3).
The non-constraint (leveraged) strategy is more powerful strategy.
If borrowing and lending at the risk free rate is allowed then use the portfolio with the highest sharpe ratio and combine that with the risk free rate to get to your required rate of return. If the question clearly says no borrowing and lending allowed use the weighted average. There is an example in CBOK where nothing is mentioned about borrowing and lending there they have used the portfolio with the highest sharpe ratio and combined with the rf.
If borrowing and lending at the risk free rate is allowed then use the portfolio with the highest sharpe ratio and combine that with the risk free rate to get to your required rate of return. If the question clearly says no borrowing and lending allowed use the weighted average. There is an example in CBOK where nothing is mentioned about borrowing and lending there they have used the portfolio with the highest sharpe ratio and combined with the rf.