# Corner Portfolios - confused

If given just a table with a list of portfolios (with their expected return %, standard deviations and underlying security weights…you’re not given portfolio correlations with one another), how can you tell: a) which portfolios lie on the efficient frontier? b) which portfolios are corner portfolios?? Please help! Thanks

All CPs lie on EF, but the one you chose is the one with Max(Sharpe ratio), when borrowing is permitted.

LaGrandeFinale Wrote: ------------------------------------------------------- > All CPs lie on EF, but the one you chose is the > one with Max(Sharpe ratio), when borrowing is > permitted. LaGrandeFinale, did you mean when borrowing is not permitted. I thought that was the idea of the portfolio weights either being zero or greater than zero.

Corner portfolios are usually lined up on the frontier by their Sharp Ratios (Sharpe ratio is essentially your frontier’s slope)… so you would always want to combine the ones that are the closest to each other, and in combination they are equal or better than the required return…

no, he’s right. When borrowing and lending is allowed, you pick the portfolio with highest sharpe and combine with risk-free asset. When borrowing is not allowed, you need to pick the 2 corner portfolios that encompass the required return you need.

If you are given two portfolios with the same risk… but one has a higher return, then the portfolio with the higher return is the most efficient one; hence, it lies on the efficient frontier and is considered a corner portfolio… Now, if the portfolios’ returns are the same, but one has a lower risk the the rest, then the portfolio with the lowest risk will lie on your efficient frontier; hence, this is one of the corner portfolios… I hope this helps…

i hope the whole test is on corner portfolios. every question. just one after the other. that’d make me happy. it is one of the few things i can do well on this test.

if no shorting allowed, highest sharpe ratio is the market portfolio! If shorting is allowed then the highest portfolio would be above market portfolio

Cheers for the above but still not 100% clear to me. Maybe if I give an example ye can explain: A B C D E F Security 1 weight 100 80 60 40 20 0 Security 2 weight 0 20 40 60 80 100 expected return 8% 9% 10% 11% 12% 13% standard deviation 14% 13.2% 13.9% 15.8% 18.6% 22% which are corner portfolios? which are the EF?

portfolio A is not a corner portfolio because given that his risk is 14%, his return should be greater than portfolio B and C… Strategy: Line up SD on X-axis… Your vertical axis is portfolio returns… Now start plotting the graph (don’t forget to label the dots) and see if you can connect the line that lies the highest to the left…

Yes, shorting is restricted Kurmanal - I read in Schweser that a corner portfolio is when a portfolio weight goes positive to zero, or from zero to positive => therefore, i would have expected portfolio A (and portfolio F) to be a corner portfolio, no?? What about the other portfolios, B,C,D & E?

dec1892 Wrote: ------------------------------------------------------- > Yes, shorting is restricted > > Kurmanal - I read in Schweser that a corner > portfolio is when a portfolio weight goes positive > to zero, or from zero to positive => therefore, i > would have expected portfolio A (and portfolio F) > to be a corner portfolio, no?? > > What about the other portfolios, B,C,D & E? All the mentioned portfolios lie on the efficient frontier, except for A. However, if there is another portfolio G that has a return of 11% but with only 13.5% standard deviation, only portfolio B, E, F, and G will lie on the efficient frontier… A, C, and D will fall off the line… Why try to invest in a portfolio that is inefficient…

LaGrandeFinale said above though that all corner portfolios lie on the EF? Is this true?However, Kunmanal, you’re saying A is a corner portfolio but is not on the EF? Sorry for all the questions, would just like to get this straight in my head before next saturday

what kurmanal is saying is correct. You know what the efficient frontier looks like so as long as the risk-adjusted returns keep going higher with each added risk, your STILL on the efficient frontier. Once your risk adjusted return drops with increased risk, then it is no longer on the efficient frontier.

dec1892 Wrote: ------------------------------------------------------- > LaGrandeFinale said above though that all corner > portfolios lie on the EF? Is this true?However, > Kunmanal, you’re saying A is a corner portfolio > but is not on the EF? > > Sorry for all the questions, would just like to > get this straight in my head before next saturday I did not say that portfolio A is a corner portfolio (I actually stated otherwise)… it is simply an inefficient portfolio… LGF is correct saying that Efficient Frontier consists of corner portfolios… I don’t think we are in disagreement here…

Sorry Kurmanal, misread your earlier post - CFA study is playing mind games on me! So if A is not a corner portfolio, what is Schweser on about so when it says a corner portfolio is when a portfolio whose weight goes from positive to zero, or from zero to positive? By this definition, I would have expected A to be a corner portfolio

dec1892 Wrote: ------------------------------------------------------- > Sorry Kurmanal, misread your earlier post - CFA > study is playing mind games on me! > > So if A is not a corner portfolio, what is > Schweser on about so when it says a corner > portfolio is when a portfolio whose weight goes > from positive to zero, or from zero to positive? > By this definition, I would have expected A to be > a corner portfolio Don’t have schweser so can’t be 100% BUT I think its saying “Assuming the portfolio is on the efficient frontier” when an asset class goes from zero to non-zero or from non-zero to zero in a portfolio’s asset allocation, it can be a corner portfolio… but only if that portfolio satisfies the return requirements for the portfolio you’re trying to create. If this isn’t correct someone let me know… otherwise i’m in a bit of trouble

When shorting is allowed, the efficient frontier is smooth; introduce a shorting restriction and the curve turns choppy/with points along it as “corner portfolios”. If borrowing is NOT allowed (i.e. no leverage) you would select the two corner ports that bookend your desired return and solve for the two weights. Remember these weights you calculate are the same you use to determine the resulting standard deviation of the combination. If borrowing is allowed, you take the corner port with highest Sharpe ratio and combine it with Rf and do the same weight calculations. So if it says weigh of 1.3 to the highest sharpe corner port you are borrowing 30% of Rf. Remember these weights you calculate are the same you use to determine the resulting standard deviation of the combination. In both cases when you are calculating the standard deviation from the combo you are not taking into account their correlation, so risk is likely over stated.

CF_AHHHHHHHHH Wrote: ------------------------------------------------------- > dec1892 Wrote: > -------------------------------------------------- > ----- > > Sorry Kurmanal, misread your earlier post - CFA > > study is playing mind games on me! > > > > So if A is not a corner portfolio, what is > > Schweser on about so when it says a corner > > portfolio is when a portfolio whose weight goes > > from positive to zero, or from zero to > positive? > > By this definition, I would have expected A to > be > > a corner portfolio > > > Don’t have schweser so can’t be 100% BUT > > I think its saying “Assuming the portfolio is on > the efficient frontier” when an asset class goes > from zero to non-zero or from non-zero to zero in > a portfolio’s asset allocation, it can be a corner > portfolio… but only if that portfolio satisfies > the return requirements for the portfolio you’re > trying to create. > > > If this isn’t correct someone let me know… > otherwise i’m in a bit of trouble -correct!