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 trade-off factor (i.e. risk
aversion factor) that corresponds to the investor’s chosen trade-off 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 risk-return trade-off 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 long-only
portfolio the portfolio weight is zero, i.e. constrained by the long-only
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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Other Portfolio optimisation functions
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Computation units used
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