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Unformatted text preview: on is an L1 metric version of the variance approach.
• Mean-absolute deviation model leads to a linear programming formulation. 6
Roy’s Safety-First Principle
• Although many of us might only recognize the contribution of Markowitz
(1952) to the modern portfolio theory, Markowitz (1999) himself wrote:
“On the basis of Markowitz (1952), I am often called the father of
modern portfolio theory (MPT), but Roy (1952) can claim an equal
share of this honor.”
• Roy (1952) claims that most ﬁrms are primarily concerned with avoiding trapping into a possible disaster. Mathematically, safety-ﬁrst investors derive their optimal portfolio from solving the following optimization problem:
n min P( Ri xi ≤ D )
n s. t. E ( Ri xi ) ≥ µ,
where D is a threshold below which the portfolio return is considered
to be a disaster and µ is pre-given return level.
• While Markowitz (1952) concerns about the variability of a portfolio,
Roy (1952) is rather interested in avoiding extreme losses through
minimizing the disaster probability.
• Contrary to the Markowitz’s mean-variance measure that concentrates
on the ﬁrst- and second-order central moments, Roy’s safety-ﬁrst principle concerns more about the ext...
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- Fall '11