If a delta-hedged position were risk-free, its gamma would be zero (page 209, CFA vol 5) - what does this mean ?
it means that in order for delta-hedge to be risk-free, gamma has to be zero (i.e., no gamma risk) and the position should be hedged continuously given that delta is constantly changing
ok, what it means is that when you delta hedge, you selling options based on delta, so if delta doesnt change when your position is fully hedge. Gamme is a change in delta so if delta doesnt change gamma is 0
Volkovv, by hedged continuously I assume you mean that at gamma = 0 (assuming gamma stays at 0) you don’t need to re-balance, since delta isn’t changing given changes in price.
So delta hedging works best for deep ITM or OTM options, where gamma is close to 0. It is riskiest ATM, where gamma is the largest. And continuous hedging means that every time the price changes by even a little, you’ll need to re-evaluate what delta is and adjust your hedge portfolio. If you wait even an instant, you’ll be down a bit (if you have negative gamma) or up a bit (if positive gamma). Realistically, you’re constrained by transaction costs and execution time, but these constraints muck up the “perfectness” of the hedge. So you’ll have to make some decisions about how often you are going to restructure your hedge and how big a move you need to observe before the benefits of adjusting the hedge outweigh the transaction costs.
To correct myself, if gamma is trully 0 and stays at 0 (which unlikely to be true in practice and can only happen for deep OTM and ITM options, especially when they are close to maturity, as bchadwick said), delta is not changing and you don’t need to rebalance. However, when gamma is not exactly 0 but close to it and assuming you can rebalance continuously (and ignoring transaction costs), then by doing so, you are maintaining close to a risk-free position (which of course is not risk-free due to transaction costs, bid-ask spread, slippage, etc.)