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Odean said, “I traded too actively, traded too speculatively and clung to my losses…. I violated all the advice I now give"

I don't understand "clung to my losses" in this sentence.

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In this particular example, it means he held onto stock that falling in price for too long in hopes of the price rebounding instead of just selling his shares and investing in something better.

This is related to something called the "sunk cost fallacy". This is a condition where you refuse to do something because to do it is to admit failure. For example, in sports, you'll see teams hang on to a terrible player instead of just releasing him because they've already paid millions in salary already.

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It probably means that he refused to admit that he had failed.

CLING TO STH | meaning in the Cambridge English Dictionary:

cling to sth

to refuse to stop believing or hoping for something:

She clings to the hope that her husband will come back to her.

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