The Hansen ratio in mean--variance portfolio theory

2020/07/31 by Aleš Černý, Černý, Aleš · 1 citation
Economics, Econometrics and Finance · #60G51 #91B02 #91B16 #91G10 #FOS: Economics and business #General Economics (econ.GN) #General Finance (q-fin.GN) #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #econ.GN #msc:60G51 #msc:91B02 #msc:91B16 #msc:91G10 #q-fin.EC #q-fin.GN #q-fin.MF #q-fin.PM

paper · pdf · doi:10.48550/arxiv.2007.15980

11 pages

arxiv created 2020/07/31 · arxiv updated 2020/08/05

Abstract

It is shown that the ratio between the mean and the L²-norm leads to a particularly parsimonious description of the mean-variance efficient frontier and the dual pricing kernel restrictions known as the Hansen-Jagannathan (HJ) bounds. Because this ratio has not appeared in economic theory previously, it seems appropriate to name it the Hansen ratio. The initial treatment of the mean-variance theory via the Hansen ratio is extended in two directions, to monotone mean-variance preferences and to arbitrary Hilbert space setting. A multiperiod example with IID returns is also discussed.

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