Talk:Portfolios and linear programming 1

Of note is that we could invest less than 100% and get a larger maximal z:

Optimal Solution: z = 17.9169; x1 = 0, x2 = 0, x3 = 0, x4 = 0, x5 = 0, x6 = 0.15, x7 = 0, x8 = 0, x9 = 0, x10 = 0, x11 = 0, x12 = 0, x13 = 0.15, x14 = 0, x5 = 0, x16 = 0, x17 = 0, x18 = 0, x19 = 0, x20 = 0.15, x21 = 0, x22 = 0, x23 = 0, x24 = 0.15, x25 = 0, x26 = 0.15, x27 = 0, x28 = 0.145212, x29 = 0, x30 = 0, x31 = 0, x32 = 0, x33 = 0, x34 = 0, x35 = 0, x36 = 0

Thats interesting, maybe we could add that as a note to our optimal solution. I wonder why it's the case, it seems natural that having more money to invest would raise our return on the portfolio. Why would having unused resources raise our return?

We were limited by our risk constraint. This in combination with the requirement to invest 100% of our money made us invest in a couple ETFs with low volatilities and very low returns (like $x_{33}$ (ZCS)). Without the requirement to invest 100% of our money we could invest purely in ETFs with higher rates of return and still satisfy our risk constraint.

Oh ok, that makes sense, thanks a lot.