In finance, delta neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged when small changes occur in the value of the underlying security (having zero delta).
Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.
A related term, delta hedging, is the process of setting or keeping a portfolio as close to delta-neutral as possible.
In practice, maintaining a zero delta is very complex because there are risks associated with re-hedging on large movements in the underlying stock's price, and research indicates portfolios tend to have lower cash flows if re-hedged too frequently.
[1] Delta hedging may be accomplished by trading underlying securities of the portfolio.
Delta measures the sensitivity of the value of an option to changes in the price of the underlying stock assuming all other variables remain unchanged.
of the option's fair value with respect to the spot price of the underlying security.
This method can also be used when the underlier is difficult to trade, for instance when an underlying stock is hard to borrow and therefore cannot be sold short.
: For any small change in the underlier, we can ignore the second-order term and use the quantity
to determine how much of the underlier to buy or sell to create a hedged portfolio.