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This paper demonstrates that options trading does not have a uniform impact on the volatility of underlying stocks. Although uninformed traders are able to hedge the risk of underlying stocks by maintaining opposite positions in the options market, informed traders hold outright options positions to capitalize on their information. This hedging behavior tends to reduce noise in the stock market, whereas the speculating behavior tends to generate noise in the stock market. As a result, stocks that were originally volatile, i.e., traded primarily by uninformed traders, will be stabilized by the introduction of options. Conversely, stocks that were more stable become destabilized by options trading.