Just to confirm, are there THREE or TWO possibilities of optimal portfolios? My confusion stems from whether #2 and #3 below are the same or different? Assumptions: - required return is between corner portfolio X and corner portfolio Y - corner portfolio Y has the highest Sharpe Ratio 1) Optimal portfolio is between Corner Portfolio X and Corner Portfolio Y (when no borrowing and no shorting allowed) 2) Optimal portfolio is between Corner Portfolio Y (highest Sharpe Ratio) & INVEST IN Risk Free Asset (i.e. LONG Risk Free Asset) (when borrowing is allowed) 3) Optimal portfolio is between Corner Portfolio Y (highest Sharpe Ratio) & LEND Risk Free Asset (i.e. SHORT Risk Free Asset) (when shorting is allowed)
2 & 3 are the same - you are combining the risk free asset (either short or long) to achieve the required return.
CFAI 2005 AM has another scenario in Question 3 B - in this one they combine the tangency portfolio with the risk free asset to arrive at the required return (ie. no lending or borrowing). I gather that if the return requirment is below the E® of the tangency portfolio (the one with the highest Sharpe), you need only that portfolio + the risk free asset.
Aimee and Newsuper - Thanks for your replies! QUESTION A) So in otherwords, there are only two possible answers in corner portfolio questions, which are: 1) Optimal portfolio is between Corner Portfolio X and Corner Portfolio Y (when no borrowing and no shorting allowed) 2) Optimal portfolio is between Corner Portfolio Y (highest Sharpe Ratio) & INVEST IN Risk Free Asset (i.e. LONG Risk Free Asset) or LEND Risk Free Asset (i.e. SHORT Risk Free Asset) (when no restrictions) QUESTION B) How do you know when to Long the risk free asset instead of Short the risk free asset???
Rate of return higher than PF with highest sharpe> short RFR, to short and invest in PF Rate of return lower than PF with highest sharpe, long RFR, to compliment highest shape PF. I have to say I haven’t done the 2005 exam yet (but I do have it in front of me) but there is some language about the sharpe ratio being the dominant factor in asset allocation for the directors, which maybe was supposed to be the clue?
Merci allepourpecher. Je le comprends maintenant! Mon question etait une question generale, c’est pas une question de 2005.
pas problem mon ami
bidder Wrote: ------------------------------------------------------- > Aimee and Newsuper - Thanks for your replies! > > QUESTION A) > So in otherwords, there are only two possible > answers in corner portfolio questions, which are: > > 1) Optimal portfolio is between Corner Portfolio X > and Corner Portfolio Y > (when no borrowing and no shorting allowed) > > 2) Optimal portfolio is between Corner Portfolio Y > (highest Sharpe Ratio) & INVEST IN Risk Free Asset > (i.e. LONG Risk Free Asset) or LEND Risk Free > Asset (i.e. SHORT Risk Free Asset) > (when no restrictions) > > QUESTION B) > How do you know when to Long the risk free asset > instead of Short the risk free asset??? Just solve for the weights of the Portfolio Y and Rf. Say the portfolio Y weight = 1.3; therefore the Rf will be (1-1.3 = -.3). This says you borrow @ Rf and lever up Port Y. If it was say .7 & .3 than you’d lend Rf.
Sponge_Bob_CFA: So to clarify… If Rf was -ve, then Short Rf = Borrow Rf. If Rf was +ve, then Leverage = Long Rf = Lend Rf. Correct?