## Delta Hedging Strategy – Overview

How great would it be to see a profit and loss curve against the underlying is shaped like a U? Where, regardless of market movement, you are always making money? It’s rare enough to find a profitable strategy so why don’t we start by drawing up a P&L sheet that looks promising to begin with. This is what I’m going to show you in this post using a strategy called delta hedging.

Now, the basics of Delta Hedging was covered in an earlier post by my colleague Puneet. If you are unsure of what “delta” is and how it works, I suggest you go through his post so that you have a thorough understanding of the concepts.

Finished reading? Okay, let’s start. The basic premise of the delta hedging strategy is you buy a call option and sell the underlying (in Indian markets, it would generally be the equity future or index future). When the market goes down, you want the profits of your short position on the underlying to offset the long position on your call option. Similarly, when the market goes up, you want the profits of your call option position to offset the loss in your underlying. While it may seem that both of these profits and loss should cancel each other, it’s not always the case.

## Delta Hedging on the NIFTY

Let’s start with an example. I will use real market values of the NIFTY from Oct 1, 2013 to show you how this works. I’m going to apply this strategy on NIFTY futures (expiring Oct 31) and NIFTY Call Option 6000 (expiring Oct 31 also). Both are very liquid contracts, hence easily tradable. First we start by calculating the delta of the option. To do so, we need the following data points which can be found on the Internet or calculated by yourself.

NIFTY OCT 31 Closing Price / Underlying Price = 5,828.45 (source: NSE Bhavcopy)
Strike Price = 6,000
NIFTY OCT 31 6000 CE Closing Price = 82.70 (source: NSE Bhavcopy)
Time to maturity (31 OCT 2013 – 1 OCT 2013) = 30 days
Historical Volatility – Current IV of 6000 is around 21 (source: NSE Live Option Chain). Historical Volatility of VIX for the past few days seems to be around 24. (source: NSE India VIX). The present value of NIFTY is between 5,800 and 5,900 and IV generally decreases as strike prices increase. I will use the value of 21.
Risk Free Rate – 7.16% (as per May 31, 2013. source: Macquarie Capital)
Dividend Yield – 1.50% (average of last 30 days dividend yield of NIFTY. source: NSE)

Now that we have these values in hand, we can plug them into an option calculator to get the delta of the option. Option Price has a good calculator that computes these values easily.

Delta Hedging on 6000CE Nifty

Theoretical price is 81.18 which is quite close to the actual price. Just a note — sometimes theoretical price may be well off the actual price. This all depends on what value you use for historical delta. If I had used 23% as my historical volatility value, theoretical price jumps to Rs. 93.68 while option delta jumps to 36.8%. Trading is an art as much as it is a science.

Let’s stick to the value of 35.4%. That means for every 1,000 shares we buy of the option, we need to sell 354 shares of the underlying to be delta neutral. I’m going to draw out a table to show what happens when the NIFTY moves from it’s present value.

NIFTY Price 5,600.00 5,700.00 5,800.00 5,900.00 6,000.00 6,100.00
Option Price25.3744.0771.54109.23157.92217.48
Option P&L (57,331.00) (38,626.20) (11,157.00) 26,530.00 75,220.00 134,780.00
Nifty P&L 79,957.50 44,957.50 9,957.50 (25,042.50) (60,042.50) (95,042.50)
Total P&L 22,626.50 6,331.30 (1,199.50) 1,487.50 15,177.50 39,737.50

Now that’s a pretty table. Notice that whatever side the NIFTY moves, you are making money. However, before we get excited over this strategy, let’s talk about risks involved in this strategy.

## Time Decay Risk

Sadly, there is never such a thing as free money in trading. Every reward comes with its share of risk. In our strategy above, notice how the profits happen as the NIFTY moves away from the present value. If it stays put at the same place, then you fall at risk with the time value of the option. Let’s say that today, we bought 1,000 shares of the Call Option and sold 354 shares of the Future. If the price remained the same, then because of time value of the option, the price of the call option will go down.

Delta Hedging – Value of option 1 day after trading

Your P&L table on T+1 would now look like this:

NIFTY Price560057005800590060006100
Option Price23.9442.1569.16106.52155.03214.63
Option P&L-58,755.90-40,548.30-13,535.1023,821.9072,332.90131,930.50
Nifty P&L79,957.544,957.59,957.5-25042.5-60042.5-95042.5
Total P&L21,201.604,409.20-3,577.60-1,220.6012,290.4036,888.00

## Conclusion

Delta Hedging is a great strategy for high returns, and low risk if you expect the market price to move. You can use this strategy using a timeframe of a several days. Generally, intraday movement won’t be enough to start making a profit. But remember, you are somewhat market neutral with a delta hedging strategy.

## Notes

• Program traders in India use this as a strategy. They put the values we have discussed above into a program. The program watches the market move and executes the order. However, this does not mean that they have an advantage over manual traders. They still have to figure out what historical volatility value to use. Knowing what value to use takes practice and observation of historical prices in the market. Whether you do delta hedging manually or automatically won’t increase your profit or loss without increasing your risk.
• I left out transaction cost in this article to make it simple. Calculating P&L on delta hedging strategies requires you to factor in exchange and brokerage costs on each leg. Use our calculator here to get an idea.

Would love to hear your questions, comments, and experience regarding this strategy.

### Shrinivas Viswanath

Shrinivas enjoys working on web and desktop technology. Developing products that enhance user experience and emphasize simplicity are his passion. While he's not busy fixing code, he's usually listening to music, running or watching movies.

• Sagar

God Article Shrinivas!! You can also add how this strategy would have worked on weekly/monthly basis for past three months with actual prices. It would help more..

• Shrinivas Viswanath

Hi Sagar!

Thanks for the comments. Working this strategy for a weekly/monthly basis would not be easy on a blog since there are multiple future prices to choose, and many strike prices to pick from. Also, part of it involves accurately estimating historical volatility for each test. That part is more of an art than a hard science

However, I wanted to lay down all the variables and tools needed for the reader to pursue it on his/her own and make it profitable. Hope that helps!

• amitkumar

banknifty support

• shankar

Hi there, I just wanted to confirm your post did you recommend to sell 354 shares at 5828 of NIFTY futures and buy 1000 shares of 6000 call at 81.18?

Thanks

Shankar

• Shrinivas Viswanath

Hi Shankar,

No this is not a recommendation to buy or sell a stock/derivative. I just used those historical market prices to show how you can construct a delta hedging strategy.

Regards

• shankar

I am sorry, if I meant it any other way, I just couldn’t understand the blog so wanted to know how to construct a delta hedging strategy, according to the study you explained was it identified as ” sell 354 shares at 5828 of NIFTY futures and buy 1000 shares of 6000 call at 81.18″?
Just wanted to make sure that I understood it properly.

• shankar

I am sorry, if I meant it any other way, I just couldn’t understand the blog so wanted to know how to construct a delta hedging strategy, according to the study you explained was it identified as ” sell 354 shares at 5828 of NIFTY futures and buy 1000 shares of 6000 call at 81.18″?
Just wanted to make sure that I understood it properly.

• Shrinivas Viswanath

Sorry if it was confusing. Let me try to clear it up. Yes for every 1000 shares you buy of the call, you should sell 354 shares of the NIFTY. The call price I used was 82.70.

81.18 is the theoretical price that OptionCalc showed me. I wanted to make sure that the theoretical price is close to the actual market price. That way, I can then use OptionCalc to get the theoretical price of the call option when the market moves to 5800 or 6000. On the first table, I have listed the option price with a price of Rs. 71.54 when the NIFTY is at 5800. I got that by looking at the theoretical price on OptionCalc after setting the underlying price to 5800.

I hope that helps.

• shankar

I am sorry, I don’t mind to disturb any study but when I calculated the whole thing showed a different risk graph.
I have put the profit and loss at different spot prices for NIFTY, please correct me if I am wrong.
5400 +68812
5500 +33412
5600 -1988
5700 -37388
5800 -72788
5900 -108188
6000 -143588
6100 -78988
6200 -14388
6300 +50212
6400 +179412.
I have come up with this profit and loss table when I sold 354 shares at 5828 and bought 6000 call at 82.7 for 1000 quantity.

• Shrinivas Viswanath

Are you using http://www.option-price.com/flash-calculator.php? What values are you using for days to expiration, historical volatility, risk free rate, dividend yield?

• shankar

I am sorry I am not using any of the calculators that are available online, I have calculated these prices manually using a simple excel, these will be the profit or loss numbers on expiry day. Hope I am correct so far.

• Shrinivas Viswanath

Ah okay. How are you calculating the option price when Nifty moves to 5,600 or 6,100? We would need to use an option calculator to get the price of the option.

Since it was bought at 82.7 when Nifty was around 5845, we need to calculate the new option price when Nifty moves up or down. For that, we need to use an option calculator.

• HARIHAR SHARMA

sir ji hindi me likha hoga to jyada acha samajh aayega

• shankar

I have calulated the NIfty price for 7.08 lots but this is not feasible in reality we either can sell 7 lots or 8 lots, but still since this was looking like a interesting discussion I thought I would go ahead for theoretical calculations, when I sell 7.08 lots of NIFTY at 5828, the profit and loss will be as below

5400 +151512
5500 +116112
5600 +80712
5700 +45312
5800 +9912
5900 -25488
6000 -60888
6100 -96288
6200 – 131688

accordingly when I buy 6000 call for 20 lots at 82.7 I will be sitting at -82700 below 6000 and sitting in profit about 6082.7
the profit will be as below
6100 +17300
6200 +117300
6300 +217300

adding both of these at expiry the table that we got in my earlier post will be seen. Anyhow I am starting to assume that Delta Hedge spreads cannot be calculated till expiry, let me check more into it and understand it properly, sorry if I am sounding a little dumb, I would really find it helpful if you could help me to find some articles or anthing that would help me understand Delta Hedging and other complicated process that would make trading even more interesting and profitable.

regards

Shankar

• Shrinivas Viswanath

Hi Sir,

First of all, no such thing as dumb questions. Sorry I wasn’t clear on my earlier post. We have a column on how delta works at (http://www.rksv.in/blog/2013/03/importance-of-delta-hedging-in-options/).

Sorry again, let me know once it makes sense. Always here to share our thoughts and hear yours out as we all learn more about trading.

• vihar

hello sir, nice article. i have a practical rate below , if you explain on below position please

power grid spot 94.5

95 call 1.20
95 put 4.5

how did we can apply delta hedging on this?

• Shrinivas Viswanath

Hi sir,

Delta hedging is applied on either call or put contract, not both. You would have to get the historical volatility (as shown above) and create the tables.

The delta calculation will tell you: for every share of call option I buy, how much of the underlying should I sell.

• Roomy Daruwalla

i need to know which softwares are available for realtime IV charting and historical volatility along with the historical data availability for last three years.Pls suggest

• Prakash Sonani

Is there any software available in the market, which scan the many scripts and suggest about suitability for Delta hedging by checking IV w.r.t historical volatility [IV can be found high though stock price is not moved, this could be due to some news expected in stock] and with other all the real time data of IV, Delta, Gamma, Vega etc. displayed ?

• Yashodhan

Thanks Shrinivas…Its a wonderful article…

• Shrinivas Viswanath

Thanks for your comments! If you found it useful, and don’t mind, do share it so we can get more thoughts on the topic 🙂