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.

Delta_Hedging_India_VIX

India VIX is an indicator of market expectation of volatility in the near term

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

  1. 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?
  2. 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?
  3. 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.

Puneet Maheshwari

Puneet Maheshwari

Puneet holds a MBA (Finance) degree. He has worked with various options traders and helped them build customized strategies through the use of automated trading. In his free time he enjoys playing cricket, billiards, and cooking.

  • Anant Sawant.

    Puneetji .Really Excellent.

    • Puneet Maheshwari

      Thanks!

  • Manish seth

    Excellent simple Option trading details by Mr.Puneet.

    Regular 100% Option trader would like to know more about Deriviatives.

    • Puneet Maheshwari

      Hi Manish,

      Thanks for liking the post. On my next blog I will be writing more on Derivatives.

  • Pardeep Kumar

    Sir,

    I have gone through your article on delta hedging. That is very good article for the persons engaged in options trading but do not have enough knowledge about delta hedging. Same is the case with me. Sir, may I know how the delta may remain neutral(zero) on next day(in case of positional trading) when stock/index opens with gap up/down.

    Thanks and regards,

    Pardeep Kumar

    • Puneet Maheshwari

      Mr. Pardeep that’s a very good question you have asked . Let me explain it to you further.

      The objective of Delta Neutral trading is to remove price risk regardless of how the stock moves. The Delta neutral strategy is achieved by combining options and stocks/futures together so that your overall delta is as close to zero as much possible. Let’s say ABC company is trading at Rs.100. You buy 100 shares of company ABC which is +100 Deltas now you need -100 Deltas to offset the +100 risk. By buying 2 at the money PUTs you should be close to -100 deltas which offsets the initial +100 Deltas. Let’s say the at the money Puts are worth 5.00 (Lot size 100)

      Buy 100 shares ABC at 100 (+100 delta)
      Buy 2 At the money PUTs at 5.00 (-100 delta)

      You invested 10 000 in the stock and 1000(200@5) in the Puts. Total investment worth Rs.11000.

      Now what will happen is if the stock moves up by one rupee, you are making Rs.100 with your shares, but you lose 50 with each Put, so Rs. 100 lost in the Puts. However, the delta of your Puts decreases as the stock moves against them. So instead of 50 negative deltas per Put, let’s assume it is now 40 negative Deltas per Put. If the stock moves up another rupee you make Rs.100 again in your shares position but this time you lose only 80 on your Puts (40 loss on each Put per the -40 delta). If the stock keeps moving up you make 100 on your shares position for each rupee move and you lose less and less on your Puts and this results in a profit. You keep making the same money on your shares moving up, while the Puts lose less money than what you are making on your shares.

      For example ABC moves from 100 to 105 next day with the gap up opening. Your Puts are now almost close to Out of the Money and instead of 5.00 they are now worth 3.00 and have a Delta of 0.35. That means you have 600 in your Puts with -70 Deltas. You also have Rs.10500 of value in your shares, with +100 Deltas.

      100 shares of ABC at 105 = 10500 (+100 Deltas)
      2 lots Puts Strike 100 at 3.00 = 600 (-70 Deltas)

      Overall you now have 11100 and +30 Deltas. And you have made 100 in profit. You can close the whole position now, and go home with 100 or you can re-balance your deltas and get back to neutral. Having +30 deltas by further buying a Put with 0.30 negative deltas.

      Note :-If the stock doesn’t move, the options will lose value, resulting in overall loss.

  • agam doshi

    Sir right now I am in commodities market but as u know the tax has been laid by the government in June month so is it good to take entry in market by doing delta …plz rep sir.
    Sir can u plz help me by giving me your contact number on my email address….thank you

  • naily

    wanna work with these pls leave ur contact

  • Gourav Sharma

    Sir mein aapse delta ratio strategy samjhna chahta hu…..kya aap mujhe btayenge ki Greek automated software mein delta ratio ki trading kaise hoti h?

  • sundar raman p

    dearsir, please tell me how to do straddle trading in option ,because I am unable judge the market wheather it is in uptrend or downtrend, and also I want to protect my capital.

  • Puneet Maheshwari

    Dear Sundar Raman,

    With reference to your query regarding straddle strategy along with the capital protection, following is the example:

    A Nifty straddle can be done by buying a 6300 call and put expiring on 26th Dec 2013 as nifty is currently trading at 6270. We can make a straddle strategy which will involve buying a 6300 call and 6300 put. A 6300 call will cost Rs 75 and a 6300 put will cost Rs 85. Thus the total investment i.e. the premium paid is Rs 160. For this strategy to be profitable, the index has to close either at 6140 or 6460. The maximum loss for this strategy will be Rs. 160 i.e. the premium paid to buy the call and put.

  • p.kailash

    sir
    can i buy both call put option at time of in-the money two days before the 2014 election result IAM THINKING OF BUYING BOTH CALL PUT AT SAME PREMIUM PL
    SUGGEST ME HOW FAR THIS STRAEGY WILL WORK

  • Subhendu

    Sometime we see both call and put option for a strike price changes in same direction, means, both premium prices reducing or both increasing. When does this happen? if delta is always positive for call and negative for put, why this happens?

    • Hi Subhendu,

      That’s a great question.

      This happens in case there is a sudden jump in volatility, which can happen due to a variety of reasons that can cause the market to react abnormally. For example, when an important policy announcement is released or a critical event is about to occur .

      In such a scenario there are cases when market participants rush for protection and consequently, the demand for puts rises without an actual rise or fall in the underlying. In order to keep the arbitrage pricing theory (APT) in tact, the price of the call also rises in the same direction.

      The adjustment happens as per the formula X+C-P = F
      If F (future) doesn’t change and X(strike price) is constant, a rise in C or P has to correspondingly cause the value of P or C to also rise.

      Hope that answers your question.

      Cheers,
      -Raghu

      • Subhendu

        Thanks Raghu, this answers my question.

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  • Anees Kalsekar

    Can you please also add some examples with numbers to explain Delta hedging clearly? I guess, examples will help readers to understand the strategy well. Anyway, thanks for your time in putting up this excellent post.