ISSN:
1467-9965
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Mathematics
,
Economics
Notes:
We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let xi= (xi, xi2,…, xim)t denote the performance of the stock market on day i, where xii is the factor by which the jth stock increases on day i. Let bi= (bi1 bi2, bim)t, b;ij≫ 0, bij= 1, denote the proportion bij of wealth invested in the j th stock on day i. Then Sn= IIin= bitxi is the factor by which wealth is increased in n trading days. Consider as a goal the wealth Sn*= maxb IIin=1 btxi that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that Sn * exceeds the best stock, the Dow Jones average, and the value line index at time n. In fact, Sn* usually exceeds these quantities by an exponential factor. Let x1, x2, be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence of portfolios 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu1" location="equation/MAFI_1_mu1.gif"/〉 db yields wealth 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu2" location="equation/MAFI_1_mu2.gif"/〉 such that 〈inlineGraphic alt="inline image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu3" location="equation/MAFI_1_mu3.gif"/〉, for every bounded sequence x1, x2…, and, under mild conditions, achieve〈displayedItem type="mathematics" xml:id="mu4" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:09601627:MAFI1:MAFI_1_mu4"/〉where J, is an (m - 1) x (m - I) sensitivity matrix. Thus this portfolio strategy has the same exponential rate of growth as the apparently unachievable S*n.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1467-9965.1991.tb00002.x
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