Tangent p/f is the corner p/f with the highest sharpe ratio. If the required return happens to be greater than the tangent p/f return, there are two options: 1. If leverage is allowed, then you can still do a wt avg calcs with Risk free rate (Rf) & tangent p/f. The negative wt on Rf is the amount that needs to be borrowed. 2. If leverage is not allowed. I have seen two versions: (A) You look for the next avail tangent p/f - i.e. look for a corner p/f (with highest sharpe ratio) with a return greater than or equal to the required return. Then do a wt avg calcs with Rf. (B) You forget about Rf or tangent p/f. Just look for two corner p/f around the required return and do a wt avg calcs on this. Can someone clarify which of the two options is valid? - BN If you need illustration, look at Schweser SS#7 (pg 162-164).

in that example, they use Rf & tangent in section 2 because “assuming no constraint against leverage” They use 2 corner portfolios in section 3 because is a “situation where margin is not allowed” In my opinion, we won´t face examples as 2(A) as you describe above. If leverage is not allowed, just use 2 corner portfolios. They only situation where (I guess) you would use Rf and the tangent portfolio is one where the tangent portfolio has a higer return and volatility than what you are looking for, so instead of leveraging (negative weight for Rf) you invest a small weight (w) at the Rf (lend) and (1-w) in the tangent portfolio

Go for 2B. Reason NOT being that “we won’t face this”, as suggested by hala_madrid. 2B is actually more efficient than 2A. Think about the straight line joing the 2 CPs in 2B, and the straight line joining CP in 2A and Rf. The latter (ie, line for 2A) is always below the former. - sticky

Just building on what Sticky had to say, if you have a choice of picking between these two options to meet the required return: 1. Wt avg of two corner p/f 2. Wt avg between Rf & tangent p/f You could make both work (option 2 with or without leverage). How do you decide which one to pick? - BN

if you can do anything, I guess 2 is more efficient, as sticky said. actually you would be using the tangent portfolio which is the more efficient

hala_madrid Wrote: ------------------------------------------------------- > if you can do anything, I guess 2 is more > efficient, as sticky said. actually you would be > using the tangent portfolio which is the more > efficient Just to make things more complicated, actually I didn’t say 2 I only said it should be 1, IF NO LEVERAGE IS REQUIRED AND REQ RETURN > MKT PORT (HIGHEST SHARPE) RETURN. Having said that, provided the “whatever” context from BN, I agree with your choice of 2. - sticky