# Delta Neutrality

Delta neutral refers to a portfolio of underlying assets, where the value of the portfolio is unaffected by small changes in the value of the underlying assets.

Such a portfolio is created by taking positions in options such that the positive and negative deltas of various positions will offset each other thereby creating a portfolio whose value is insensitive to changes in the prices.

It is an important concept for institutional traders who establish large positions using various option strategies such as straddles, strangles, and ratio spreads.

We will take an example of a strangle to explain how delta neutrality can be achieved.

### A Strangle Example

A stock currently trades at $50. The annual volatility of the stock is estimated to be 20%. The risk-free rate is 5%. An options trader decides to write six-month strangles using$45 puts and \$55 calls.

As a quick refresher, a strangle involves taking position in both a call and put with different strike prices but with the same maturity and underlying asset. This option strategy is profitable only if there are large movements in the price of the underlying asset.

The two options will have different deltas, so the trader will not write an equal number of puts and calls.

How many puts and calls should the trader use?

The delta for the call option is 0.3344

The delta for the put option is -0.1603

The ratio of the two deltas is -0.1603/0.3344 = -0.48. This means that delta neutrality is achieved by writing 0.48 calls for each put.

One approximate delta neutral combination is to write 25 puts and 12 calls.

Delta neutrality is useful for strategies in which a trader is neutral about the future dynamics for the market. So, the trader doesn’t assume either a bullish or a bearish position.