'How do I get individual betas of components of portfolio if I have the correlation matrix
lets assume I have a portfolio of 7 stocks and the correlation matrix is shown below.
AAPL AMZN GE GOOG MSFT TSLA WMT
AAPL 1.000000 0.375099 0.284080 0.433243 0.493551 0.295611 0.236871
AMZN 0.375099 1.000000 0.207204 0.592426 0.486348 0.337323 0.146736
GE 0.284080 0.207204 1.000000 0.314619 0.345414 0.221990 0.220034
GOOG 0.433243 0.592426 0.314619 1.000000 0.599558 0.330133 0.216136
MSFT 0.493551 0.486348 0.345414 0.599558 1.000000 0.299540 0.257328
TSLA 0.295611 0.337323 0.221990 0.330133 0.299540 1.000000 0.164783
WMT 0.236871 0.146736 0.220034 0.216136 0.257328 0.164783 1.000000
standard deviations of each in the list
std = [0.22,0.29,0.20,0.23,0.22,.39,.19]
is there a way to calculation Beta of individual stocks to the total portfolio using just the given information? I am assuming that I dont have any timeseries or anything to run regression etc.
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