Unformatted text preview: amework in
portfolio selection.
• While investors may prefer to use diﬀerent risk measures, the fundamental issue in investment science is to strike a balance between the
risk and the expected return within a twoobjective decision making
framework.
• Compared to the utility framework, it is easier for investors to appreciate the returnrisk framework and is more direct for investors to relate
themselves to the returnrisk framework, as risk is clearly quantiﬁed.
• Meanvariance formulation leads to a quadratic programming problem
which possesses a lot of computational advantages. 4
MeanSemivariance Model • Both Markowitz (1959) and Mao (1970) suggested to adopt the lower
semivariance
n E [(min{ n Ri xi ], 0})2 ] Ri xi − E [
i=1 i=1 as a risk measure for (downside) risk of the portfolio.
• If distribution is symmetrical, semivariance is proportional to variance.
• Although the meansemivariance model can be also transformed into
a convex quadratic programming problem, it is not widely used as the
variance. 5
MeanAbsolute Deviation Model • Konno and Yamazaki (1991) proposed to adopt the absolute deviation
as the risk of a portfolio:
n E [ n Rj xj − E [
j =1 Rj xj ]].
j =1 • Obviously, the absolute deviati...
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This note was uploaded on 01/05/2013 for the course SEEM 5820 taught by Professor Duanli during the Fall '11 term at CUHK.
 Fall '11
 DuanLI

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