Portfolio Optimization with fPortfolio

fPortfolio contains a number of function to make portfolio optimization easier. I can compare the results I get from the functions in fPortfolio to the results from my function from the previous post. I don’t expect them to be exactly the same, but they should be broadly similar.

First, install and load the package:
install.packages(‘fPortfolio’)
library(‘fPortfolio’)

Next, you need to build a returns matrix for the securities you are interested in. You can create return vectors for the different tickers (using methods from an earlier post) and then combine them together using cbind(). The function I wrote in the previous post also returns a matrix of security returns, so you can just use that code as well.

This is the function for the tangency or (highest Sharpe ratio) portfolio:
tangencyPortfolio(as.timeSeries(matrix),constraints=’maxW[1:9]=0.2′)

Here I set the same constraints as in the function I wrote. maxW[1:9]=0.2 says that for securities from 1 to 9 (which is all of them) set the maximum weight for each of them as 20%.

The output from this function call is:

Title:
MV Tangency Portfolio
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints: maxW

Portfolio Weights:
NVDA.Adjusted     YHOO.Adjusted     GOOG.Adjusted    CAT.Adjusted   BNS.Adjusted
      0.0000                0.0000                 0.2000                0.0335         0.2000
POT.Adjusted       STO.Adjusted        MBT.Adjusted       SNE.Adjusted
      0.2000               0.1760                  0.1905               0.0000

Covariance Risk Budgets:
NVDA.Adjusted     YHOO.Adjusted    GOOG.Adjusted    CAT.Adjusted   BNS.Adjusted
      0.0000                0.0000                0.1301               0.0286           0.1409
POT.Adjusted       STO.Adjusted       MBT.Adjusted      SNE.Adjusted
     0.2407               0.1773                0.2823                0.0000 

Target Return and Risks:
  mean        mu        Cov      Sigma      CVaR       VaR
0.0006   0.0006  0.0161   0.0161   0.0398   0.0224

This obviously runs much faster, and gives greater and more readable information than the function I wrote. Oh well. It is interesting to see that the weights given for a couple of the securities are different. Not having read the code written by the authors of this function, I am more inclined to trust the results of the brute force function I wrote, however the difference is most likely due to different covariance estimation methods/procedures.

It is commonly known that portfolio weights in a Markowitz mean-variance optimization framework are very sensitive to the estimated means and covariances, and even differences in rounding can lead to fairly different weights. Also, technically, we are supposed to be using expected returns as input and not historical returns. Using historical returns assumes that the returns of each period are independent, come from the same distribution and sample the true distribution of the security. All of these assumptions can be very easily shown to be false.

In the next post, I will experiment with some of the graphs and plots we can make using fPortfolio.