TY - JOUR
T1 - Master funds in portfolio analysis with general deviation measures
AU - Rockafellar, R. Tyrrell
AU - Uryasev, Stan
AU - Zabarankin, Michael
PY - 2006/2
Y1 - 2006/2
N2 - Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. They lead nonetheless to generalized one-fund theorems in which a more customized version of portfolio optimization is the aim, rather than the idea that a single "master fund" might arise from market equilibrium and serve the interests of all investors. The results that are obtained cover discrete distributions along with continuous distributions. They are applicable therefore to portfolios involving derivatives, which create jumps in distribution functions at specific gain or loss values, well as to financial models involving finitely many scenarios. Furthermore, they deal rigorously with issues that come up at that level of generality, but have not received adequate attention, including possible lack of differentiability to th deviation expression with respect to the portfolio weights, and the potential nonuniqueness of optimal weights.
AB - Generalized measures of deviation are considered as substitutes for standard deviation in a framework like that of classical portfolio theory for coping with the uncertainty inherent in achieving rates of return beyond the risk-free rate. Such measures, derived for example from conditional value-at-risk and its variants, can reflect the different attitudes of different classes of investors. They lead nonetheless to generalized one-fund theorems in which a more customized version of portfolio optimization is the aim, rather than the idea that a single "master fund" might arise from market equilibrium and serve the interests of all investors. The results that are obtained cover discrete distributions along with continuous distributions. They are applicable therefore to portfolios involving derivatives, which create jumps in distribution functions at specific gain or loss values, well as to financial models involving finitely many scenarios. Furthermore, they deal rigorously with issues that come up at that level of generality, but have not received adequate attention, including possible lack of differentiability to th deviation expression with respect to the portfolio weights, and the potential nonuniqueness of optimal weights.
KW - Basic fund
KW - Conditional value-at-risk
KW - Convex analysis
KW - Deviation measures
KW - Efficient frontier
KW - Master fund
KW - One-fund theorem
KW - Portfolio optimization
KW - Risk measures
KW - Value-at-risk
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U2 - 10.1016/j.jbankfin.2005.04.004
DO - 10.1016/j.jbankfin.2005.04.004
M3 - Article
AN - SCOPUS:32944471861
SN - 0378-4266
VL - 30
SP - 743
EP - 778
JO - Journal of Banking and Finance
JF - Journal of Banking and Finance
IS - 2
ER -