In a standard delta (neutral) hedge you buy or sell the appropriate number of options so that the gain/loss on the underlying position is exactly offset by the loss/gain on the option position.
However, if you anticipate a particular direction of movement for the underlying price, you can adjust the number of options so that if prices move as you expect you’ll earn a profit, instead of exactly hedging and getting zero profit.
Suppose that you own 10,000 shares of stock, and the delta on a particular call option is 0.4. For a delta neutral hedge you’d sell 10,000 ÷ 0.4 = 25,000 call options; if the price of the stock changes up or down, the price change on the calls will come very close to offsetting the price change of the stock, leaving the portfolio value nearly unchanged.
If you had a strong feeling that the stock price were going to increase, you could sell fewer than 25,000 calls; if the price does, indeed, rise, you’ll make a profit, as the gain on the stock will be more than the loss on the calls. Of course, if the price falls, you’ll have a loss.
If you had a strong feeling that the stock price were going to decrease, you could sell more than 25,000 calls; if the price falls, you’ll make a profit, as the loss on the stock will be less than the gain on the calls. Of course, if the price rises, you’ll have a loss.