#### Going Forward in Delta Neutral

By: Steve Smith

Ever since bursting to new highs in mid-July the broad indices have been mostly stuck in neutral. This has forced option traders of all stripes, even those who like to place directional trades, to look at a way of hedging off both time decay and an adverse price moves, in case the market or specific stock suddenly wakes from the doldrums.

One of my favored tactics is to take a ‘delta neutral’ approach, establishing a position through a combination of strikes (it could be both puts and calls) in which the overall value is not greatly impacted by a short-term and relatively small price move.

Before we get any further a quick review of delta is probably in order. As discussed in this article delta is used to describe the expected change in an options’ price for every $1 move in the price of the underlying stock. Delta can range from 0.00 to 1.00, with calls being expressed as a positive number and puts as a negative. The rule of thumb is that an at-the-money option has a delta of 0.50.

It is very important to understand delta is not fixed. It is a function of the underlying stock price and the time remaining until expiration. As an option moves further into-the-money and time decays, the delta increases at an accelerated rate. Conversely, as an option moves further out-of-the-money and has more time remaining, delta decreases at a slower rate.

The second part is crucial in understanding ‘delta neutral’ is, in practice, only a short-term tool. The concept of “delta neutral” is an intriguing one – especially to traders who have had a hard time predicting the market or to those who don’t believe the market can be predicted (random walkers).

The concept is even sometimes “sold” to novice investors as a sort of “can’t-lose” trading method, even though that isn’t true at all. While the idea of having a position that can make money without predicting the direction of the underlying stock seems attractive, in practice the strategy is difficult, if not impossible, to apply – at least in terms of keeping a position delta neutral.

A delta neutral position may be constructed out of any number of options and the underlying – from as few as 2 options as in this example:

Example: XYZ: 48

Buy 1 July 50 call & Sell 2 July 60 calls

July 50 call delta: 0.50 / July 60 call delta: 0.25

Delta neutral position: Since the ratio of the deltas is 2.0-to-1 (50 divided by 25), then the indicated spread is delta neutral

Or more complex positions, such as market makers might hold. No matter how many options are in one’s position, the position delta can be computed by multiplying the quantity of each option held by the delta of that option and summing over all the options held. That sum will generally not be zero, but it is a simple matter to neutralize the position by taking an offsetting position in the underlying stock. Here is more a complicated example, showing this concept:

Example: Suppose the following prices exist:

XYZ: 48

July 60 call delta: 0.25

Oct 55 call delta: 0.40

July 50 call delta: 0.50

And further suppose that this is a position that you hold:

Long 20 July 60 calls

Long 30 Oct 55 calls

Short 10 July 50 calls

The position delta of your holding can be computed by multiplying the quantity of each option in your position by its delta (and then multiplying by 100, assuming the option is for 100 shares of stock). This computation is also sometimes called the “equivalent stock position (ESP)” because it shows how many shares of stock are equivalent to the given option position:

Hence the total “exposure” of all these options combined is equivalent to being long 1200 shares of XYZ. To neutralize this position – i.e., to make it “delta neutral,” one could simply short 1200 shares of XYZ while still keeping the option holdings the same.

When a delta neutral position is established, the position has no delta – that is, it does not profit (on the very short term) if the underlying moves up or down. That’s all “delta neutral” really means. It does not mean, for example, that the position will profit no matter which way the stock moves. This simple statement may come as a big surprise to more novice traders who thought that delta neutral was more of a “lock” in terms of profits.

This misconception usually arises from a concept introduced in the first papers written about the Black- Scholes model by its authors, Fisher Black and Myron Scholes. They concluded that, if one bought or sold “mispriced” options and hedged them in a delta neutral manner, arbitrage-like profits would be made because of the mispricing. This concept is true, of course, but only in a theoretical sense. It is impossible to keep a position delta neutral at all times, especially when one considers the commission costs and bid-asked spread costs involved with “constantly” adjusting a position.

**Manage Through Price and Time**

So, why bother with delta neutral at all, in the real world? It has some merit because it allows one to establish a position in which the trader truly doesn’t care which way the stock moves, but then – as the trade develops and the stock begins to move – the trader must take actions based on the price of the underlying stock in order to make money.

The concept of delta neutral is a short-term one. As stated above, it really only means that the position will neither profit nor lose from stock price movements – but only over the very short term and for very small stock price movements. As soon as time passes or as soon as the stock moves far enough or if volatility changes – any or all of these things – the deltas will change, and the position will no longer be delta neutral.

In fact, what may be delta neutral might not even correspond with one’s own longer-term concepts of what delta neutral means. Let’s use a straddle purchase to demonstrate what I’m talking about here.

If we buy a delta neutral straddle, we can compute the upside and downside breakeven points. Since the straddle is neutral to begin with, one would think that the probabilities of reaching the breakeven points would be equal. In other words, what’s the point of being delta neutral if the position has a longer-term bias – if there is a greater chance of reaching one breakeven point than the other?

The point is, once again, that delta neutrality is really only descriptive of short-term movements by the underlying. To attempt to apply it to longer-term projections or to expect a delta neutral position to “magically” be capable of producing profits would be wrong.