## Delta Hedging Introduction

What is the meaning of risk in the stock markets? 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 the direction of the market. Delta Hedging is accomplished by establishing a **delta** equivalent long or short position in the underlying reference against a long or short position in the option (more here).

Delta hedging is important for option a trader who uses complex option positions. If an option trader is planning to make profit from the time decay 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 ranges 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 the *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*have a delta close to zero (they hardly move).*Deep in the money (ITM) call options*have a delta close to +1 (they moves almost as much as the underlying’s price).*Deep in the money put options*have a delta close to -1 (they moves almost as much as the underlying’s price, but in the opposite direction).*At the money (ATM) options*have a delta about 0.50 for call and for put -0.50.

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

- Trader holds a
*call option*slightly*in the money*with a**delta**of 0.60 and*market price*of 18. This call option gives you the right to buy 250 shares in ABC company for Rs. 200 (the strike price). Let’s say ABC company stock is now trading at 220 (the underlying market price). What will happen if the stock price increases to 225? - The
**option’s delta**(0.60) tells us that when the underlying stock goes up by 1 rupee, the option’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 option’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 positions by summing up the 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

The *total delta* of this position is:

- 2 x 0.60 (2 contracts of long calls)
- 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 – 0.35 – 0.30 =
*0.55* - A trader can expect your portfolio’s market value to increase by 0.55 paisa for every 1 Rupee of the underlying stock’s price increase. He can use delta hedging to adjust the total delta of his total portfolio.

## Delta Hedging Example: Long straddle position

Let’s say trader has **opened a long straddle position** 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 are *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 money *call option* has a delta of roughly 0.50 (if stock price goes up Rs.1, the call option’s price goes up by 0.50 paisa), while an *at the money put option* has a delta of roughly -0.50 (if stock price goes up by Rs.1, the put option’s price goes down by 0.50 paisa). If trader holds both options simultaneously, the total delta of position is the sum of the two deltas, which in this case equals **zero**.

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

If ABC Company’s **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 option’s delta moves closer to zero and it is now somewhere between -0.50 and zero.

We again calculate the **total long straddle delta** 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 option’s delta is 0.70, the put option’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 closer 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. The **long straddle becomes directional**, but in this case it is **bearish** (the total delta is negative). The further the stock falls, the more negative the straddle’s delta gets, and in an extreme case long straddle can behave almost like a short stock position.

## Delta Hedging Summary

It’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.