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    Matrices and scalars for inverse covariance

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    I am unclear as to how some scalars have been calculated. I know what the two vectors and the inverse covariance variance matrix are but please could you clarify the operations required to compute into a single number? There is also a set of data on page two that needs computing along with a general explanation of how to do it. If you are a Matlab or a Mathematica user then such a script would be helpful for me along with general explanations.

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    Solution Preview

    Explanations are in the attached files

    Correlation structure

    Covariance matrix

    • b)


    Subject to


    Where we have replaced

    o This optimisation is essentially saying that we are trying to select what weight to apply to assets in a portfolio given two constraints. Firstly that we are constrained to invest a predetermined percentage of wealth into the portfolio, in this case all wealth. Secondly that we are constrained to achieve a predetermined return, in this case 10%.

    o Solve optimisation using the Lagrange method

    We formalise our constraints with the

    1 is an n-element unit vector. The sum of all weights must be 1 as our wealth must be entirely invested in n assets
    The asset return and standard deviation vectors are given as ...

    Solution Summary

    This provides examples of working with correlation structure and covariance matrix to calculate scalars.