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Thin Margin
Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel
(We recommend this as work of authority.)

A small margin; a shoestring margin; a margin that gives the owner only a small equity in his purchase; a narrow or insufficient margin that leaves the speculator's account in an exposed and precarious condition in case of a declining market.  Brokers customarily do not carry stocks on margin for customers unless there is ample margin and will not continue carrying the stocks until the margin is exhausted.

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