### Global Minimum Variance Weights

Derivation of the global minimum variance equation for long/short
portfolio weights. Here the only constraint is that the weights must
sum to 1.

multiplying both sizes by **1' **(substituting
into
)

substituting
into
we
get

### Tangency Portfolio

Weights for T, the tangency portfolio (where
)
is the portfolio excess return
:

Mean return of T:

Volatility of T:

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