TD - Real world assets, the covariance matrix and the market price of risk

The covariance matrix σi
, must be positive definite as assets cannot have
arbitrary covariances. For example, it is evidently impossible to have 3 risky
assets where all the covariances are −1 as 3 assets cannot all move independently in opposite directions to each other.
Now consider the portfolio Π = λ1S1 + λ2S2 + λ3S3 where the λi sum to 1
(but need not be between 0 and 1).
We have