# Delta Hedging Strategies in Options Trading

Before discussing Delta, let’s look at figure 1 above to familiarize ourselves with the four risk dimensions of options:* Vega, Theta, Delta, and Gamma.*

** Delta** measures the sensitivity of an option price to changes in the price of its underlying asset and is the magnitude of the change in the option price caused by a one-unit change in the price of the underlying asset, i.e., a one-unit change in the price of the underlying asset is followed by a one-unit change in the price of the option contract. value is 0.65, this means that if the price of the underlying stock increases by $1 per share, all else being equal, its options will increase by $0.65 per share.）

Figure 2 above contains some hypothetical values for S&P 500 call options that are at, out, and in the money (in all these cases, we will be using long options). Call delta values to range from 0 to 1.0, while put delta values range from 0 to –1.0. As you can see, the at-the-money call option (strike price at 900) in the figure has a 0.5 delta, while the out-of-the-money (strike price at 950) call option has a 0.25 delta, and the in-the-money (strike at 850) has a delta value of 0.75. ）

As a transition into looking at position delta, let’s first look at how short and long positions change the picture somewhat. First, the negative and positive signs for values of delta mentioned above do not tell the full story. As indicated in figure3 above, if you are long a call or a put (that is, you purchased them to open these positions), then the put will be delta negative and the call delta positive. However, our actual position will determine the delta of the option as it appears in our portfolio. Note how the signs are reversed for short put and a short call.

If the delta sign in your portfolio is positive, the value of the position will increase if the underlying increases. Likewise, if you are short a call position, you will see that the sign is reversed. The short call now acquires a negative delta, which means that the short call position will lose value if the underlying rises. This concept leads us to position delta. Many of these intricacies involved in trading options are minimized or eliminated when trading synthetic options

Also, keep in mind that this simple example assumes no change in other variables. The following holds true about delta:

- Delta tends to increase as you get closer to expiration for near or at-the-money options.
- Delta is not a constant, a concept related to gamma (another risk measurement), which is a measure of the rate of change of delta given a move by the underlying.
- Delta is subject to change given changes in implied volatility.）
- Delta is a ratio — sometimes referred to as a hedge ratio — that compares the change in the price of an underlying asset with the change in the price of a derivative or option.
- For options traders, delta indicates how many options contracts are needed to hedge a long or short position in the underlying asset.)

Delta Hedging Strategies

The most basic type of delta hedging involves an investor who buys or sells options and then offsets the delta risk by buying or selling an equivalent amount of stock or ETF shares. Investors may want to offset their risk of move in the option or the underlying stock by using delta hedging strategies. More advanced options strategies seek to trade volatility through the use of delta-neutral trading strategies.

Offsetting Delta Risk

Assume that SPY, the ETF that tracks the S&P 500 index, is trading at $205 a share. An investor buys a call option with a strike price of $208. Assume the delta strength for that call option is 0.4. Each option is the equivalent of 100 shares of the underlying stock or ETF. The investor can sell 40 shares of SPY to offset the delta of the call option. If the price of SPY goes down, the investor is protected by the sold shares. The investor has a delta-neutral position that is not impacted by minor changes in the price of SPY.

The delta of the overall position shifts as the price of the underlying stock or ETF changes. If the investor wants to maintain the delta neutral position, he has to adjust the position regularly. The disadvantage of doing this is the commissions and costs that eventually impact the profitability of the strategy.

Delta position

If an S&P 500 call option has a delta of 0.5 (for a near or at-the-money option), a one-point move (which is worth $250) of the underlying futures contract would produce a 0.5 (or 50%) change (worth $125) in the price of the call option.

Therefore, a delta value of 0.5 tells you that for every $250 change in the value of the underlying futures, the option changes in value by about $125. If you were long for this call option and the S&P 500 futures move up by one point, your call option would gain approximately $125 in value, assuming no other variables change in the short run. We say “approximately” because as the underlying moves, delta will change as well

In other words, you need two long call options to hedge one short futures contract. (Two long call options x delta of 0.5 = position delta of 1.0 equals one short futures position). This means that a one-point rise in the S&P 500 futures (a loss of $250), which you are short, will be offset by a one-point (2 x $125 = $250) gain in the value of the two long call options. In this example, we would say that we are position delta neutral.

By changing the ratio of calls to several positions in the underlying, we can turn this position delta either positive or negative. For example, if we are bullish, we might add another long call, so we are now delta positive because our overall strategy is set to gain if the futures rise. We would have three long calls with a delta of 0.5 each, which means we have a net long position delta by 0.5.

On the other hand, if we are bearish, we could reduce our long calls to just one. This would give us a net short position delta. This means that we are net short of the futures by -0.5. Once you’re comfortable with these aforementioned concepts, you can take advantage of advanced strategies, such as position-delta neutral trading.