## Delta Hedging Introduction

What is the meaning of risk in the stock markets? The risk is basically defined as loss of trading capital. This means losing money in trading. Option trading always termed as risky mainly because of the nature of stock and index options as they are highly leveraged and option trading risks can lead to huge losses if managed not properly. So that is the reason why hedging comes into the picture and why delta hedging is a good tool for option traders to minimize their risk.

## What is Hedging?

Hedging is the practice of taking a position in one market to offset and balance against the risk adopted by assuming a position in a contrary or other market or investment. Delta hedging is a form of hedging.

## What is Delta?

The ratio comparing the change in the price of the underlying asset to the corresponding change in the price of derivatives, sometimes it is referred as the "hedge ratio." For example, an option with a delta of 0.5 will move half a rupee for every one rupee movement in the underlying stock. Which means, stock options with a higher delta will increase/decrease in value more with the same move on the underlying stock versus stock options with a lower delta value. Delta hedging involves working with the calculated delta of options.

## What is Delta Hedging?

The process of reducing the exposure of an option to theÂ directionÂ of the market. Delta Hedging isÂ accomplishedÂ by establishing a **delta** equivalentÂ long or short positionÂ in the underlying reference against a long or short position in the option.

Delta hedging is important for option a trader who uses complexÂ option positions. If an option trader is planning to make profit from the time decayÂ of his short-term stock options, then that option trader needs to make sure that the overall delta value of his position is near to zero so that changes in the underlying stock price do not affect the overall value of his position.

## Option Delta Value Range

Delta of call options can reach values between 0 and +1. Delta or put options range from -1 to 0. The value depends mainly on the moneyness of the particular option (in the money vs. out of the money). Delta hedging involves various deltas to get a picture of risk.

### Delta and Moneyness of options<

Just by looking at theÂ *delta*, you can tell if the option is in the money, out of the money, or at the money.

*Far out of the money (OTM) options*Â have a delta close to zero (they hardly move).*Deep in the money (ITM) call options*Â have a delta close to +1 (they moves almost as much as the underlyingâ€™s price).*Deep in the money put options*Â have a delta close to -1 (they moves almost as much as the underlyingâ€™s price, but in the opposite direction).*At the money (ATM) options*Â have a delta about 0.50 for call and for putÂ -0.50.

## How the option price moves based on changes in the stock price

- A trader holds aÂ
*call option*Â slightlyÂ*in the money*Â with aÂ**delta**Â of 0.60 andÂ*market price*Â of 18. This call option gives you the right to buy 250 shares in ABC company for Rs. 200 (the strike price). Letâ€™s say ABC company stock is now trading at 220 (the underlying market price). What will happen if the stock price increases to 225? - TheÂ
**optionâ€™s delta**Â (0.60) tells us that when the underlying stock goes up by 1 rupee, the optionâ€™s market price will go up approximately by 0.60 paise. In the example, the stock goes up by 5 Rs. What will be the increase in the optionâ€™s market price? - 5 rupees times the delta, or 5 x 0.60 = 3. You can expect this option to go up by 3 Rupees. If ABC Company stock goes to 225, the call option will be worth approximately 18 + 3 = 21.

## Calculating your Portfolio's Delta

We can easily calculate the total delta of the positionsÂ by summing up theÂ deltas of individual options. This is the first step towards delta hedging. For example, a portfolio with the following options:

- 2 ITM Long calls with a delta of 0.60
- 1 OTM Short call with a delta of 0.35
- 1 OTM Long put with a delta of -0.30

TheÂ *total delta* of this positionÂ is:

- 2 x 0.60 (2 contracts of long calls)
- Â 0.35 (subtract because option is short)
- -0.30 (add because option is long, but the delta is negative because it is a put)
- = 1.20 â€“ 0.35 â€“ 0.30 =Â
*0.55* - A trader can expect your portfolioâ€™s market value to increase by 0.55 paisa for every 1 Rupee of theÂ underlying stockâ€™s priceÂ increase. He can use delta hedging to adjust the total delta of his total portfolio.

## Delta Hedging Example: Long straddle position

Letâ€™s say a trader hasÂ **opened a long straddle position**Â by buying a call and a put option on ABC company, both options with strike price of 250. If ABC company is trading at 250 at the time, both these options areÂ *at the money*. This is when a long straddle position can be bought for the lowest price and when it makes the most sense to open it. Let's look at different scenarios and how delta hedging plays into it.

## Long straddle delta at the money is zero

An at the moneyÂ *call option*Â has a delta of roughly 0.50 (if stock price goes up Rs.1, the call optionâ€™s price goes up by 0.50 paisa), while anÂ *at the money put option*Â has a delta of roughly -0.50 (if stock price goes up by Rs.1, the put optionâ€™s price goes down by 0.50 paisa). If trader holds both options simultaneously, theÂ total delta of positionÂ is the sum of the two deltas, which in this case equalsÂ **zero**.

### Stock goes up from the strike price: delta turns positive

If ABC Company'sÂ **stock price goes up**, the call option trader hold as part of the straddle is now in the money and its delta increases to somewhere between 0.50 and 1.00. The put option is out of the money (if the stock ended up higher than the strike price, the put option would be worthless at expiration). The put optionâ€™s delta moves closer to zero and it is now somewhere between -0.50 and zero.

We again calculate theÂ **total long straddle delta**Â by summing up the two deltas (a larger positive number for the call and a smaller negative number for the put). You get a positive number. For example, the call optionâ€™s delta is 0.70, the put optionâ€™s delta is -0.30, and the total long straddle delta is 0.40. As a result of the underlying stock price going up, the **long straddle position has become directional**. It has a positive delta and its value and your profit increases as the stock price goes up.

### Stock goes down from the strike price: delta turns negative

On the other hand, if ABC company's stock goes down from the strike, the call option is out of the money and its delta is close to zero, while the put option is in the money and its delta is closer to -1.00. The overall delta of the long straddle position is now negative. TheÂ **long straddle becomes directional**, but in this case, it isÂ **bearish**Â (the total delta is negative). The further the stock falls, the more negative the straddleâ€™s delta gets, and in an extreme case long straddle can behave almost like a short stock position.

## Delta Hedging Summary

Itâ€™s true that option trading is risky and a trader can lose all his money if he is not managing his option positions carefully. Delta hedging allows traders to view their portfolio from another perspective and manage their risk. Using this and other various tools can help the trader manage his risk effectively during highly volatile markets.