To understand how delta neutral trading works, we first need to grasp what the options delta is. The delta is one of the ‘greeks’ involved in regular option pricing modules and simply put, is an indication of the amount by which an option price is expected to move in proportion to a price movement in the underlying stock, commodity etc. It is usually expressed as a number to 4 decimal points.

Call options always have a positive delta, which may vary from virtually zero to as high as 1.0. Put options always have a negative delta with the same parameters as calls. At-the-money call and put options theoretically have a delta of 0.5 and -0.5 respectively. The further in-the-money an option goes, the greater the delta, up to a maximum of 1.0.

So let’s imagine we were looking at some options with a strike (exercise) price of \$100 and then compared this to various prices at which the underlying stock might trade. We notice the following:

\$85 share price – ‘out of the money’ CALL options have a delta of 0.0148
\$85 share price – ‘in the money’ PUT options have a delta of -0.9852
The total of the above two deltas equals 1.0000
If we held both positions, they would be delta neutral.

So the value of a put option contract with a strike price of \$100 would increase at almost a 1:1 ratio with the underlying, should the share price continue to fall below \$85. The way-out-of-the-money \$100 call option however, would hardly move at all. So the delta is a measure of the SENSITIVITY of option prices to the price movements in the underlying.

### Delta Neutral Trading in Action

#### 1. Hedging Your Share Portfolio

Let’s say we own 200 shares currently trading at \$110. We want to hedge our shares against future loss, but also in such a way that we can profit from a rise in share price as well.

We observe the options delta for ATM \$110 put options is -0.4200 and they cost \$0.91 each. We also note from the list of options, that should the share price rise to \$112, our put options will decrease in value to \$0.28 each with a delta of -0.16.

The delta of the shares themselves will of course, be 1.0000

• Our 200 shares have a total delta of 2.0000 (2 x 1.0000)
• We need to purchase 5 put option contracts at a delta of -0.42 to give us a total delta of -2.10 (5 x -0.42)
• Our overall position delta is therefore -0.10 (2.0000 – 2.1000)

#### The Share Price Increases

Should the share price now increase to \$112, our put options will decrease in value to \$0.28 and our loss will be \$3.15 per contract, or \$315 total.

Our gain on shares however, will be \$400 (200 x \$2)
So our overall net profit will be \$0.85 (4.00 – 3.15) per share.

The Share Price Falls

If the share price now falls to \$108, our put options will increase in value to \$2.14 with a delta of -0.73 and realize a profit of \$6.15 per contract, or \$615 total.

Our loss on shares however, will be \$400 (200 x \$2)
So our overall net profit will be \$2.15 (6.15 – 4.00) per share.

The above scenarios work on the assumption that the underlying price movements will be in the short term and do not take into account the time decay factor in option pricing. Nevertheless, all the information you need for delta neutral trading can be obtained from looking at the option chains data on any reputable broker site.

Once you understand how delta neutral trading works, why limit yourself to hedging shares? Instead of risking \$22,000 on 200 shares at \$110, why not set up the same position for a fraction of the cost using futures contracts or CFDs instead of buying the shares themselves? Futures and CFDs always have a 1.0000 delta with the underlying, so you can receive the same outcomes and put your funds to better use elsewhere.

### 2. Delta Neutral Trading With Options

The straddle is the classic and most widely known delta neutral option trading strategy. A straddle is defined by the purchase of an equal number of at-the-money call and put options with the same expiry date. Since ATM options have a delta of around 0.5000 and since calls are positive and put deltas are always negative, the one will balance out the other to make the overall position ‘delta neutral’.

Strangles on the other hand, involve OTM options whose deltas will be much less than 0.5 or -0.5. But again, depending on the price of the underlying financial instrument in relation to the option strike prices when you buy, the respective OTM deltas should practically neutralise each other.

For more extensive information about option straddles and strangles, click on the links to take you to the relevant pages (each will open with a new tab).

Excellent profits can be made from delta neutral trading using options alone, but you must take other other ‘greeks’ particularly theta (time decay) into account when choosing your positions.