Mean absolute deviation model leads to a linear

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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 ) i=1 n s. t. E ( Ri xi ) ≥ µ, i=1 7 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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