# O The optimization problem in Mean Variance Portfolio

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O The optimization problem in Mean Variance Portfolio Optimization (MVO)
entails either finding the portfolio w that has the highest expected return
for a given level of risk as measured by portfolio variance or finding the
portfolio w that has the smallest risk that achieves a target return as
shown below:
min o?
P,w
= w'Ew s.t.
w'u = 1 = target return
Hp,w
w'1
%3D
%3D
%3D
= 1
i. Using matrix algebra, work out the optimal portfolio w that has the
smallest risk that achieves the target return
ii. Explain why most optimization schemes follow the approach in (i)
above (i.e. finding the portfolio w that has the smallest risk that
achieves a target return as opposed to finding the portfolio w that
has the highest expected return for a given level of risk)
[8 marks]
[4 marks]