In this problem, the required return (6.29%) is above the tangent portfolio’s return (5.03%). The solution does the allocation based on the corner portfolios. However, as the problem does not mention that leverage is not allowed, wouldn’t it be better to do the allocation by borrowing at the risk-free rate and investing in the tangent portfolio? Or do we always need to assume that leverage is never allowed? Thanks.
If the two portfolios includes teh Tangent portfolio then use those 2 portfolios…but I did see on I think a CFAI test where if the Tangent portfolio is NOT one of the 2 portfolios then use the Tangent + Risk free asset to get the required return… I think this was on the 2005 test.
it was in CFAI and schweser too, if long only constraint you cannot borow to extend your portfolio to be on CML, so you have to take 2 closest corner portfolios, if you return is below tangent you can use Rfr and Tangent to get better risk/return combination then by just taking portfolio on efficient frontier
If the required return is less than the return on the tangent portfolio, it is clear that we should use the tangent portfolio, and combine it with the risk-free rate to reduce the risk but keep the same Sharpe ratio. If the required return is more than the return on the tangent portfolio and leverage is not allowed, it is also clear that we should use the corner portfolios. So I agree with you, comp_sci_kid. But if the required return is more than the return on the tangent portfolio and leverage is allowed, borrowing and using the tangent portfolio is superior to using the corner portfolios. Whether one of the corner portfolios is the tangent portfolio or not will not change this, though when one of the corner portfolios is the tangent portfolio, the difference between the two approaches tend to be small. So I still do not understand why the solution to Problem 9 goes with the corner portfolios when something out there is better, and not against any constraint.
Just do as CFAI tells you to. If one of the Corner Portfolios is teh Tangent then use the Tangent and the Other Corner portfolio. If it doesnt include the Tangent, then use the Tangent plus Risk-Free rate.
OK, I just hope CFAI sticks to that. What frustrates me is that for some topics, they are really picky about details and for others, they are approximate, so I never know how accurate we must be. I wonder how much leaway they give for essay questions on that stuff.
Well, if we’re not sure what to do - solve for both solutions (tangent +Rf and corner portolios) and then compare Sharper Ratio.
The world may never know…Except for JoeyD.
Borrowing is not allowed when you have corner portfolios. Corner portfoljos only arise when you have a constraint against short selling (or possible other constraints, not sure)
You can still be allowed to borrow at Rf, but not short. Corner portfolios arise when there is maximum limit on weight of securities too.
The constraint is against shorts…you can have corners with borrowing, i think
ws, I think you had this all figured out. There were 4 different scenarios that were there. Can you please note them down for us? I am not able to find the earlier thread.
bigwilly, if you can borrow i dont see why you cant combine borrowing with tangent portfolio then. The whole idea is that you cant have leveraged positions?
I guess you have a point…that if you can leverage than you should just leverage up the Tangent portfolio… But if you can’t leverage than use tangenet and other corner. 
The key to remember that tangent portfolio has ALWAYS the highest sharpe ratio. Why? Sharpe ratio is the slope of the line
here is our discussion on corner portfolios http://www.analystforum.com/phorums/read.php?13,671062,page=1 CareerChange Wrote: ------------------------------------------------------- > ws, I think you had this all figured out. There > were 4 different scenarios that were there. Can > you please note them down for us? > I am not able to find the earlier thread.
Is this the final verdict ? - Re: Corner Portfolios Posted by: ws (IP Logged) [hide posts from this user] Date: March 13, 2008 11:44PM There are lot way to do this: Sharp port means higest sharp rate portfolio in the following text. Total 4 different situatios: 1. If your required rate is LOWER than your Sharp port. and short IS allowed. Combine your sharp port. with risk-free asset. (ie. 70% sharp port. 30% risk-free asset) 2. If your required rate is LOWER than your sharp port and short is NOT allowed. Combine your sharp port. with risk-free asset. (ie 70% sharp port. 30% risk-free asset) 3. If your required rate is HIGHER than your Sharp port. and short IS allowed. Combine your sharp port. with risk-free asset. (ie. 130% in Sharp port and -30% in risk free…totally made up numbers) 4. If your required rate is HIGHER than your Sharp port. and short is NOT allowed. Combine your corner port. However, the resultant port. won’t be as efficient as other because it is not combined with a highest sharp port. therefore it is not on CAL.
I agree with that.
I dont totally agree… Because all the examples I have seen say, you should combine the Tangent portfolio with the Adjacent corner portfolio if the return requirement falls with in the range of the two corners. If it doesn’t then you would use the Tangent and Risk Free. I have only seen one instance when you had to use the Rf and Tangent and that was on one of teh CFAI exams… I haven’t reviewed this yet, but my gut tells me so
I have a read of this question and agree with frenchriviera. The solution to doesn’t sound right to me. Since there is no policy against the use of leverage, I think the best SAA is corner 4 (highest sharpe) leveraged with Rf. Any idea?