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A position that is not hedged. That is, the holder of a naked position has taken no step to reduce the risk inherent to the position. For example, if one buys 100 shares of AT&T, one is exposed to the risk that AT&T will decline in price. If one takes no action to prevent this (by buying put options or short selling AT&T, for instance), one holds a naked position in AT&T. Avoiding naked positions and hedging as much risk as possible is a substantial concern for many institutional investors.
A security position, either long or short, that is not hedged. For example, an investor short 500 shares of IBM with no other position in IBM stock (such as ownership of calls) has a naked position in that security. Because a naked position subjects the investor to large potential gains or losses, it is an aggressive investment position.