Delta Hedging (Tutorial version)

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A trader in option market always looks for delta hedging for his/her portfolio. A delta hedging gives an opportunity to the trader to keep his/her trading position neutral from market movement.

What is Delta?
Delta is the ratio which measures change in price of the derivative with respect to the change in price of underlying asset  . So, if delta (∆) for an option is 0.5 then it implies for every one dollar change in the price for the underlying asset (whether it is an increase or decrease), there will be a change of 50 cents to the option price.

Characteristics of Delta

For a call option, delta moves between 0 and +1 while, for a put option it fluctuates between -1 and 0. Delta will be close to zero if the option (call or put) is ‘out of the money‘. When the call option is ‘in the money‘, delta will tick close to +1 while, for put option, it will be close to -1. Options, ‘at the money‘ will have delta around +0.50 for call, and -0.50 for put.

The mechanism behind delta

A trader tries to hedge his/her portfolio by establishing delta long or delta short position in accordance with the underlying assets. For example, a trader takes a call option of $10 which gives right to buy 100 shares of Apple Inc (trading at $ 430) with a delta at 0.70 (i.e. in the money). Suppose if the market price of shares are now at $450 then what will be the option price? Since, delta is 0.70 an increase in underlying price of $20 ($450-$430) will increase the call option price by 0.70*20= $1.40. So, the new call option price will be $10+$1.4=$11.4.

Thus, an increase of $20 in the Apple Inc share will increase the call option price to $1.40 or call option price for share of Apple Inc trading at $450 will be $11.40.

Delta Neutral Hedging

The objective of Delta Neutral Hedging is to remove price risk regardless of how the stock moves. According to the trading jargon, an option contract with 0.50 delta is referred as “50 deltas”. So, 100 deltas are related to 100 shares thus each share will have delta value equals to 1. To sum up, if you are long on 100 deltas then increase of $1 in stock price will give a gain of $100 and if it fall $1 then you will end up having loss of $100. If a position is long on 50 deltas then increase in price of stock for $1 will fetch you $50 and in case of decrease in stock price, a loss of $50.

So, if a trader buys 100 shares of a stocks to get his/her portfolio a delta neutral position, he/she has to buy 2 put contracts; at the money with a delta value of -50 per contract.

Thus, 100(delta value of 100 shares)- 100( 2 put contacts* 50 deltas)= 0 delta.

For example, if a trader held 100 shares of Apple Inc for $400 per share on 14 March 2013. On 14 May, when Apple Inc was trading at $430, the trader performed a delta neutral hedge against possible price change while being able to make profit. The trader bought 2 ‘contracts of July31 put’ to get the delta neutral hedge on his/her position.
100 (delta of 100 shares) – 100 (delta of 2 contracts of at the money put options of 50 deltas) = 0 delta

Now what will happen is if the stock moves up by $1, trader will make  $100 with shares, but loses $50 with each put, so $100 lost in the puts; overall no gain or loss in his position.  Although ideally it would not happen as the put option price would change with the change is stock price and since the position is long (i.e. long straddle) the trader will end up with some profits. So, if Apple rallies from $430 put option will expire being worthless and the trader will gain from increase in the price of stock by keeping his position alive in the market and the put option loss will be offset by the profits he/she would make.
There are many permutations and combinations among call and put option to get a delta neutral hedging. We will have more on the topic later.  Keep reading and learning.

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