Portfolio Selection Essay

4758 Words Aug 13th, 2012 20 Pages
American Finance Association

Portfolio Selection Author(s): Harry Markowitz Source: The Journal of Finance, Vol. 7, No. 1 (Mar., 1952), pp. 77-91 Published by: Blackwell Publishing for the American Finance Association Stable URL: http://www.jstor.org/stable/2975974 . Accessed: 23/06/2011 20:52
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If two or more securitieshave,the same value, then any of these or any combination of these is as good as any other. We can see this analytically:suppose there are N securities;let rBbe the anticipated return (howeverdecided upon) at time t per dollar invested in security i; let d be the rate at which the return on the Oh security at time t is discounted back to the present; let Xi be the rela0 O tive amount invested in security i. We exdude short sales, thus Xi for all i. Then the discounted anticipated return of the portfolio is oo N

R=3

E

di,t itX i=1 t=1

=

i=l

XiEdit

t=l

rit)

= returnof the ith security,therefore RX E di rit is the discounted t=1 R = YXiRi where Ri is independent of Xi. Since Xi 3 0 for all i and 2Xi = 1, R is a weighted average of RXwith the Xi as non-negative weights. To maximize R, we let Xi = 1 for i with maximum Ri. If several Raa, a = 1, ..., K are maximum then any allocation with
K

= E Xaa 1 a=1 maximizes R. In no case is a diversifiedportfolio preferredto all nondiversifiedportfolios. It will be convenient at this point to consider a static model. Instead of

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