You've asked a variation of (1) a couple of times before and I tried to link you this thread:
https://quant.stackexchange.com/ques...ined-portfolio
I'm on my phone so can't type very well, but you can get the 2x2 variance-covariance matrix from:
"before AAPL was added, we had 3 vital portfolio theory stats 1) correlation between AAPL and SPY (that didn't include AAPL), 2) AAPL volatility, 3) SPY volatility"
Lets calls these:
a - volatility SPY
b - volatility AAPL
c - correlation between SPY and AAPL
If you are measuring volatility in terms of standard deviations:
Cov(a, b) = [ [ a^2, abc], [abc, b^2] ]
If you are measuring volatility in terms of variance:
Cov(a, b) = [ [ a, sqrt(ab)*c], [sqrt(ab)*c, b] ]
So from that thread I linked:
Quote:
You can obtain the covariance between 2 portfolios by multiplying the row vector, containing the weights of portfolio A with the variance-covariance matrix of the assets and then multiplying with the column vector, containing the weights of assets in portfolio B.
Cov = [0.9, 0.1] * Cov(a, b) * [0, 1]^T
Var = [0.9, 0.1] * Cov(a, b) * [0.9, 0.1]^T
Corr = Cov / sqrt(Var)*b
(or Corr = Cov / sqrt(Var*b) if b is variance)
Juk