[R-SIG-Finance] chart.EfficientFrontier in PortfolioAnalytics Package

[Brian G. Peterson]

On Sat, 2022-02-12 at 19:39 +0100, Enrico Schumann wrote:
> On Sat, 12 Feb 2022, Pankaj K Agarwal via R-SIG-Finance writes:
> 
> > Dear AllWhen an efficient frontier is plotted using
> > chart.EfficientFrontier, the frontier shows a blue dot
> > labelled as Optimal which is different from tangency
> > portfolio at some given value of rf. 
> > To my understanding, the tangency portfolio should be THE Optimal
> > portfolio. Can someone help what i may be missing here? Thanks in
> > advance.
> > Regards,Pankaj K Agarwal
> > +91-98397-11444http://in.linkedin.com/in/pankajkagarwal/
> >         [[alternative HTML version deleted]]
> > 
> 
> You will have a better chance of receiving an answer
> if you provide a small reproducible example.
> (Also, please post in plain text, not HTML.)

Thanks Enrico.  I agree that a minimal reproducible example would be
necessary here.

Note that chart.EfficientFrontier works with *any* set of objectives
and constraints that PortfolioAnalytics supports.  

The classic closed form of the tangency portfolio doesn't support
weight constraints, for example (though there are versions which do).

As another example, the minimum variance portfolio which you may have
asked for will not equal the Max Sharpe Ratio portfolio. The tangency
portfolio is only "optimal" in the classic Markowitz mean-variance
convex portfolio context if you have asked for the max Sharpe ratio
portfolio from an unconstrained optimization.  

More complex objectives and constraints may create an 'optimal'
portfolio that does not lie on the efficient frontier.  For another
example, the Equal Risk Contribution (ERC) portfolio lies on a line
between the minimum variance portfolio and the equal weight portfolio.

Also, chart.EfficientFrontier will plot the tangent line only on the
two axes that make up the vertical and horizontal axes of the chart...
your objective set may have many more dimensions in a multi-objective
portfolio, and a three dimensional or n-dimensional surface may be a
better representation.  

You might also want to take a look at what the online version of Eric
Zivot's "Introduction to Computational Finance and Financial
Econometrics with R" has to say about the tangency portfolio:

https://bookdown.org/compfinezbook/introcompfinr/Efficient-portfolios-of.html


We really do need a minimal reproducible example though to look at
specifically what is going on in this case.

Regards,

Brian

-- 
Brian G. Peterson
ph: +1.773.459.4973
im: bgpbraverock