efficient frontier- why is this so simple and why is this so hard?

CFA General
#1

Very simple (Even high school students can follow)

http://economistatlarge.com/portfolio-theory/efficient-frontier

Very difficult (Use mmult, TRANSPOSE) http://faculty.washington.edu/ezivot/econ424/Efficient%20Portfolios%20in%20Excel%20Using%20the%20Solver%20and%20Matrix%20Algebra.pdf

Will there be a different in result?

#2

I had a quick glance for you.

Using the MMULT and TRANSPOSE fomulas simplies for the process of calculating portfolio variance as you do not need to build the covariance table outlined in the ‘simple’ method.

The outputs should be exactly the same assuming the inputs are the same.

Also, if you are looking to generate the efficient frontier using VBA, the second method usually is better.

#3

Also, you need some knowledge of matrix multiplication to understand the formulas in the second method, hence it may look a bit more confusing.

#4

Thanks jimmy for telling me they are the same. Sound great to me as I will dare try learn it

#5

I realise for the simpler approach, it cannot generate the inefficient part of frontier

#6

If you have more than two or three assets, you pretty much have to do MMULT to do the optimization.

#7

Why did you say that? The simple efficient frontier method has 6 stocks to work with

#8

Go ahead and write out the risk equation for 10 assets. The number of terms increases (approximately) with the square of the number of assets. The matrix formulation keeps the terms organized for you so you can work with (almost) any number of assets.

Edit: OK, I went back and looked at how the “simple” method did the sum. That’s a clever way to get the number in excel, and it isn’t too hard to scale up if needed. However, the matrix format is just a lot more flexible… once you know it in excel, you can do the same thing in R or Matlab or a number of other contexts that you might need.