Passing by reference : This means that if we do in python
fred = squareArray
and then fred[1,1] = 0
Python does not make a copy of squareArray, rather its just passed as a reference, hence by changing fred[1,1], squareArray also gets changed.
Whereas if we want to pass by value something like
fred = squareArray.copy() should be done.
the general formula for the variance of returns for a portfolio is:
σ²(port) = ΣΣw(i)w(j)σ(i)σ(j)ρ(i,j)
where the first sum is taken over all is, and the second over all js. Thus, for a 5-asset portfolio, the formula would be:
σ²(port) = w1²σ1² + w2²σ2² + w3²σ3² + w3²σ3² + w5²σ5²
+ 2w1w2σ1σ2ρ(1,2) + 2w1w3σ1σ3ρ(1,3) + 2w1w4σ1σ4ρ(1,4) + 2w1w5σ1σ5ρ(1,5)
+ 2w2w3σ2σ3ρ(2,3) + 2w2w4σ2σ4ρ(2,4) + 2w2w5σ2σ5ρ(2,5)
+ 2w3w4σ3σ4ρ(3,4) + 2w3w5σ3σ5ρ(3,5)
ρ is covariance