JoshuaZ comments on Harry Potter and the Methods of Rationality discussion thread, part 26, chapter 97 - Less Wrong Discussion
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One can use time-turners so you know what the market will do in advance (making sure that for any given stock you trade in small enough quantities that it won't substantially alter the asking price to avoid messing with time issues).
If magic isn't limited by speed of light issues then one can send trading signals faster (already attempts are made to put computer systems as close as possible to get a jump on slower traders. How much this actually matters is unclear.)
One could apparate to and assassinate people who are in specific corporations or governments, being able to anticipate resulting economic problems and short-sell accordingly.
These are only the most obvious sorts of things, deliberately restricting to those that don't add value to the system.