Late trading is trading executed after the standard local national exchanges have closed. This is distinct from after-hours trading, as they have in context specific meanings, the former may be illegal while the latter is legal.
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Mutual funds
In the mutual fund context, late trading involves placing orders for mutual fund shares after the close of the stock market, 4:00 p.m for the New York Stock Exchange, but still getting that day's closing price, rather than the next day's opening price. The price of mutual funds is usually set only once per day, so intraday prices are not applicable.
Controversy
In the United States this practice is illegal under SEC rules but many mutual fund managers appear to have allowed exceptions for certain hedge funds and other favored investors who were able to obtain that day's price, notwithstanding that their orders were received after-hours.