Assume that you want to purchase a straddle on a given stock because of some anticipated news that you expect will move its price significantly. You create a neutral straddle 6 days before the expected news by buying puts and going long the stock. But before the news comes out, the stock rises slightly, and this changes the deltas of the puts and therefore the delta of the overall position. The table below gives an illustration.
Your position is no longer neutral, but slightly bullish: if the underlying stock goes up by $1 the total value of the position will increase by $100 but if the underlying falls by $1, then the total value of the position will decrease by $100. If your goal is to remain neutral an adjustment needs to be made. The total delta could be adjusted by trading either puts (purchasing additional puts) or the underlying shares (by selling some of the ones held). There is a strong argument for trading the shares in making any adjustments. First, shares have higher deltas than options, so fewer shares need to be traded. And second, transaction costs tend to be lower on stocks than on options so this will minimize our transaction fees.
The adjustment that needs to be made in the above example is very straightforward: sell 100 shares of stocks to bring the total deltas back to zero.
What if 4 days after the initial straddle is purchased (and after the above adjustment was made 2 days later) the stock reverts back to its original level? The straddle would have to be re-adjusted, this time by purchasing 100 shares of stock. This results in a profit on the stock transaction, a direct result of the underlying’s volatility.
The question now arises of how often one should rebalance the puts and the stock so that the total deltas add up to zero. There are 2 schools of thought here: rebalance at fixed time intervals (such as the end of each trading day), or rebalance whenever the total deltas reach a set level such as +100 deltas or -100 deltas. Neither is intrinsically better than the other, so you may want to “paper trade” these to find which one better fits your trading style.