"If you hedge you will make a little bit of money if the stock goes in either direction". Thanks. Should I not make more if the stock goes up 5%, then down 5% as opposed to it just keeps going up.? I am talking of the case where I hedge.
Depends.....what vol did you use to calculate your delta? If you bought the straddle because you felt IV was cheap and you were proven right once it popped up 5%, then you have to form some opinion as to what the future vol might look like over the remainder of the option's life. If you think the big move was a one-off event and you'll likely be in a low-vol or slightly uptrending market, you would want to hedge at a lower vol. Lower vol means your (now ITM) calls show higher delta values, meaning you'll short more stock to get flat. This means that if you're wrong and vol continues to be high, you'll be sacrificing upside since you shorted more stock. But if you're right and vol remains low and the market continues creeping up or coming back, you will have locked in your profit better. The opposite case implies you need to hedge at a higher vol. Higher vol pulls ITM call delta values closer to 50, hence you're shorting less stock and leaving more upside in case 5% turns into 10%. If you're wrong and the vol collapses, then your hedge will not sufficiently hold up your P&L should the stock start coming back down. The point is your hedging regime has to take into account the expected realized vol over the remaining life of the option. In a whippy, mean-reverting market with high vol, your hedges will be smaller, meaning smaller scalps each time, but if you're right then you should have MORE scalps to make up for it since vol is higher. In a low-vol market, you will get less scalps so each one has to earn more for you hence a bigger delta hedge. Choosing what vol to hedge at and evaluating your expectations of what vol may do going forward is paramount to managing risk/reward expectations and getting the most out of your delta hedging. Trust me, if I've learned one thing it is that just blindly plugging IV into Black-Scholes and not taking the time to think about what your hedging strategy is truly implying will almost certainly result in failure. This stuff is hard. It truly is an art form.
Well you might if your gamma changes as spot moves. But that's a more Complicated answer. You would make the same regardless of the next direction if you hedged.