2-corner portfolio? equivalent, therefore, directly

RobertA

Looking for confirmation.  
The text says that using 2-corner portfolio analysis is mathematically equivalent to the more cumbersome MVO formulas for determining portfolio standard deviation (assuming correlations = 1).  It then says that the actual corner portfolios do in fact consider correlation and the results are therefore pretty accurate but will ultimately result in more conservative estimates than if actual correlation were directly factored in (ie not 1).
1.)   So how are we assuming correlations of 1 but the actual CPs include specific correlation - how are we not therefore capturing the correct correlation but instead assuming Corr =1 ?   
2.)   Can someone provide a simple example of how borrowing on short sale leverages up return - tyring to think through it and my mind is dead at the moment.
Many thanks everyone!

onelife1

If you actually read the CFAI text, it’s much clearer.
On p 236, the text says you can use the standard formula to calculate the exact stdev with the covariance table given.
Or you can take a short cut to approximate this stdev by a linear combination of 2 adjacent corner portfolios.
In the particular example given, the EF bows out to the left implying that a linear approximation will over-estimate the exact stdev which, in effect,  reflect a less-than-one positive correlation between 2 CPs.
You could draw a  diagram to visualise this. Think like convexity adjustment to bond duration.

SeanWest

BBUI, But if the 2CPs reflect actual, less than 1 correlations and we are using those 2 CPs in our calculation, then how are we overstating the standard deviation at all?  Don’t they inherently include the actual diversification benefits (ie actual correlation)?
Mr. Leverage, thanks again.  Your examples were very helpful!

former

What is important is the shape of the curve connecting the 2 CPs, it’s not straight. We are using the 2 CPs to deduce a point lying on that curve. Linear extrapolation only give an estimate not the exact stddev. Like I said before, we can use the weights and covariance matrix to calculate the exact value but it’s unyieldy, not going to be asked on the exam. You can do it easily with excel though.
just draw a chart, x axis is stddev, y is return. Draw a horizontal line at the level of return required, it will cut the actual curve at a lower x than that of the straight line connecting 2 CPs.