Why is a volatility trading strategy considered to be a non-directional strategy?

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The objective in a volatility trading strategy is that regardless of how the price of the underlying stock price changes, the mispriced convertible bond's value will outperform the value of the short position in the underlying stock's value. Hence, this convertible bond strategy is
a non-directional strategy. That is, the performance of the strategy is based purely on the volatility of the underlying stock price not the direction in which the stock price moves. Effectively, this strategy is a bet on the volatility of the underlying stock and hence the name given to this type of convertible bond arbitrage strategy, volatility trading. As with most option trading strategies, the position of a strategy must be changed as the price of the underlying changes. Hence, in implementing this strategy, the transaction cost associated with the shorting of the stocks must be taken into account. There are risks associated with this strategy, and they can be quantified using other measures taken from option theory.

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