I have calculated my optimal portfolio weights following the mean-variance framework where I go $w_1$ in the risky asset and $1-w_1$ in the risk free rate.
I get the following result: $w_1$ = 1.5, 1-$w_1$ = -0.5
My question is, how can I interpret this? Obviously I need to short the risk-free rate and go long in the risky asset. However, if I have 100 dollars to use for my portfolio, how do I allocate this amount in practice?
Moreover, it should follow that I go long with 150 dollars and short 50, but the question is, where does this money come from? How is it possible that I get money when I go short?
One option would be to standardize the sum of the weights. Hence this is not possible as then you never will invest in the risk-free rate.