## 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.

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 Price | 25.37 | 44.07 | 71.54 | 109.23 | 157.92 | 217.48 |

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.

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

NIFTY Price | 5600 | 5700 | 5800 | 5900 | 6000 | 6100 |
---|---|---|---|---|---|---|

Option Price | 23.94 | 42.15 | 69.16 | 106.52 | 155.03 | 214.63 |

Option P&L | -58,755.90 | -40,548.30 | -13,535.10 | 23,821.90 | 72,332.90 | 131,930.50 |

Nifty P&L | 79,957.5 | 44,957.5 | 9,957.5 | -25042.5 | -60042.5 | -95042.5 |

Total P&L | 21,201.60 | 4,409.20 | -3,577.60 | -1,220.60 | 12,290.40 | 36,888.00 |

## 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.