ReverseQuadraticPortfolioOptimiser
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Function Description
Returns a vector containing the ‘implied alphas’ for a given
set of active positions, i.e. the return assumptions that need to be held for a
portfolio to be optimal (ignoring constraints), given active positions,
standard deviations, a correlation matrix and a tradeoff factor (i.e. risk
aversion factor) that corresponds to the investor’s chosen tradeoff between
return and risk. It is assumed that the investor has a quadratic utility
function of the following form, where is a
vector of returns, is a covariance
matrix and is a
vector of active weights (i.e. , where is
a vector of portfolio weights with elements
and is the
corresponding vector of benchmark weights):
Please bear in mind that if a given set of returns, ,
is optimal in this context then so is the set of returns defined by for
any constant (scalar, i.e. asset class independent) values of and
. This
function adopts the convention that or
equivalently , i.e.
that and that scales
in line with the riskreturn tradeoff factor, i.e. .
Please also bear in mind that if the active position within
a live portfolio is at the limit of a constraint (e.g. for a longonly
portfolio the portfolio weight is zero, i.e. constrained by the longonly
constraint) then it is not possible to calculate accurately the implied alpha
for that position, since we do not then know (merely from the portfolio
weights) how positive or negative is the view that the manager is assigning to
that position.
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Interactively run function

Interactive instructions

Example calculation

Output type / Parameter details

Illustrative spreadsheet

Other Portfolio optimisation functions

Computation units used
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