Portfolio Optimization constraints Matrix/bvec explanation

Question

I recently got very interested in portfolio optimization and started playing around in R, to create a minimum variance portfolio,

library(quadprog)
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Answer 1

First step is to write down the mathematical model. That could look like:

The next part is to implement this in R's quadprog. That could look like:

• Adding comments to the code may help to understand it later
• Quadprog does not allow simple lower- and upper-bounds on the variables, so we need to convert these to >= inequalities.
• Notice that Quadprog minimizes 0.5*x'Qx. That has the same result as minimizing x'Qx.
• Shorting can be allowed by using other lower-bounds on x.
• Your data makes the model infeasible. I loosened the upper-bound on allocations from 0.5 to 0.8.