**Chapter 4**

# Long Put Option Strategy

Amit has a farm on which he grows potatoes. His neighbours, all farmers, also grow potatoes. Now one year, with about a month to harvest, Amit realises that he is looking at a bumper crop. That’s the good news. The bad news - every farmer around him would also have a bumper crop, meaning a supply glut of potatoes in the market. That could cause prices to fall.

Amit enters into a contract with a potato chip manufacturer to supply potatoes at last season’s prices - ₹2,000 per quintal. As expected, he has a bumper harvest, there is a glut in the market and prices fall to ₹1,800 per quintal. But that doesn’t bother Amit. He is still able to sell his crop at ₹2,000 per quintal - the contracted price with the chip company- and earn a tidy profit.

A long put option strategy works in a similar fashion. Like Amit the farmer, you believe the value of the underlying will fall and prepare to profit from it.

**Why would a trader use this strategy? **

You buy or ‘go long’ on a Put Option if you believe two things:

1) The underlying stock or index will move downward.

2) You expect this downward move to occur prior to the selected expiration date of the option.

While put options allow traders to benefit from bearish movements in stocks or indices, put options aren’t assets. This means that upon expiration, the put option will no longer exist and if the underlying price didn’t move favourably, the trader could end up losing 100% of what they paid for the put option. By comparison, if you were to buy a stock, the only way you could lose 100% of your capital is if the price of the stock went to zero.

**How do you construct it? **

The table below is an example of an option chain with bid and offer prices for 5 strikes associated with calls and puts on one expiration date.

If you were ready to place a trade for a long put option, you would look to the right side of the option chain for the put option section. You could select from any of the strikes listed. For example, if you wanted to buy the put option with the strike price of 390, this would cost you 4.46 which is the asking price for this option contract.

*Illustration 1*

**What is maximum gain? **

The maximum gain you can have with a long put option is the price of the underlying. When you buy a put option, you are anticipating a price decrease in the underlying stock or index. The lowest price that a stock or index can go to is 0. If the price of a stock is 250, the most you can gain with a put option is 250 which is the current price of 250 minus 0.

This is different from a call option that has a theoretically unlimited upside. Because of the disparity in maximum gain, put options could seem less attractive.

But, a concept to remember here is that stocks tend to fall faster than they rise. The fear that drives irrational selling is greater than the ‘fear of missing out’ that drives irrational buying. The table in illustration 2 shows the Nifty 50 rolling 1-week returns for the last 15 years ranked by largest gain and largest loss. As you can see, the top 10 losses are always bigger than the top 10 gains.

*Illustration 2*

**What is the maximum loss?**

The maximum loss is capped at the price at which you purchased the option. In the option chain above, if you selected the at-the-money strike of 400, the premium or cost that you paid to buy the call option is 8.91. This cost is the maximum you can lose in this trade.

**What is the break-even point? **

The break-even point is the strike minus the cost to buy the put option.

**Key Formulae**

- Break-even Point = Strike Price – Cost of Put Option

In the example table above, if you bought the 400-strike, this would cost you 8.91 (the ask price). The break-even price is 391.09 =400 - 8.91. To achieve break-even, the underlying would need to fall by 0.99% from its current price of 395.

Alternatively, you could choose to purchase an out-of-the-money put option. If you purchased the 385-strike, this would cost 3.06 for a break-even price of 381.94. This would require a drop of 3.3% in the underlying to break-even.

The illustration below shows the profit diagram of the purchasing the at-the-money put call option. This would have a cost of 6.37 and a break-even price of 388.63 (395 - 6.37).

*Illustration 2*

**How do you calculate the profit of a long put? **

The formula for the payoff of a long put is the maximum of zero or the difference between the strike price and the underlying price. The reason we need to calculate the maximum between two values is because a long put cannot have a value less than zero when it comes to the payoff of the option.

The profit formula for a long put is the long put’s payoff minus less the cost to purchase the option. The two formulae are below.

**Key Formulae**

- Long Put Payoff = Max(0, Strike Price – Underlying Price)
- Long Put Profit = Max(0, Strike Price – Underlying Price) – Option’s Cost

**Put Option Scenarios using Historical Data**

To conclude this chapter, we will walk through a few examples using real market data to understand the opportunities and risks of long put options.

**Scenario 1 – Underlying is below the break-even price at expiration**

#### The Situation:

- The trader is bearish on the Nifty which is trading at 17,807.65
- The trader buys a 2-week until expiration put option with a strike price of 17,800.
- The put option costs 222.35.
- The break-even price for the put option is when the Nifty is at 17,577.65 (17,800 – 222.35).

#### What happens:

- The Nifty trends downward throughout the first week and by the end of the week, the trade is profitable as the Nifty hits 17,530.
- Throughout the second week, the Nifty continues to move downward another 1%.
- The trader holds the option until expiration when the Nifty closes at 17,392.60.

#### Trade Results:

- The call option is in-the-money and has an intrinsic value of 407.40 at expiration. This is calculated as the strike price of 17,800 minus the Nifty price of 17,392.60.
- This trade is profitable with a net gain of 185.05. This is the intrinsic value minus the cost of 222.35 to buy the put option.
- This trade is successful with a return of 83.2% as the underlying closed below the break-even price.

**Scenario 2 – Underlying is below the strike price but above the break-even price at expiration**

#### The Situation:

- Trader is bearish on the Nifty which is trading at 17,670.
- Trader selects a 1-week expiration put option with a strike price of 17,650.
- This put option costs 127.60.
- The break-even is when the Nifty is at 17,522.40 (17,650 – 127.60).

#### What happens:

- The day after entering this trade, the underlying moves upward by 2.1%.
- The movement of the underlying changes the delta of the purchased strike from -0.47 to -0.14, meaning that the likelihood of the strike price being in-the-money at expiration is approximately 14%.
- Over the next several days, the Nifty slowly drifts downward from -0.50% to -1.0% each day.
- On expiration, the Nifty is trading at 17,639.55

#### The Trade Results:

- The put option is in-the-money and has an intrinsic value of 10.45 at expiration (17,650 – 17,639.55).
- This trade results in a loss of 117.15. This is the intrinsic value of 10.45 minus the cost to buy the put option of 127.60.
- This trade is unprofitable because while the underlying moved above the strike, it didn't reach the break-even point.

**Scenario 3 – Underlying is above the strike at expiration**

#### The Situation:

- Trader is bearish on the Nifty which is trading at 17,532.05.
- Trader buys a 1-week expiration put option with a strike price of 17,550.
- This put option costs 135.30.
- The break-even is when the Nifty is at 17,414.70 (17550 + 135.30).

#### What happens:

- In the days following the purchase of the put option, the Nifty moved upward to 17,822. With this move, the delta for the strike moved from -0.52 to -0.02.
- This means that the strike purchased initially had a 51% likelihood of moneyness, but within 2 days, this has dropped to 2%.
- The trader decides to hold until expiration when the Nifty closes at 17,790.35.

#### The Trade Results:

- The call option is deep out-of-the-money and has no intrinsic value at expiration.
- This trade results in a loss of the original premium paid of 135.30.

**Scenario 4 – The trade is profitable shortly after entry**

#### The Situation:

- The trader is bearish on the Nifty which is trading at 16,167.10.
- The trader buys a 1-week until expiration put option with a strike price of 16,150.
- This put option costs 190.5.
- The break-even price for the put option is when the Nifty is at 15,959.50 (16,150 - 190.50).

#### What happens:

- The Nifty moves downwards 2.2% the day after entry. The next day, the Nifty is flat to slightly down.
- The Nifty is at 15,782 and the trader decides to close out the put option that is trading at 409.05.

#### Trade Results:

- The put option is in-the-money and has an intrinsic value of 367.85 which is calculated by subtracting the underlying price of 15,782 from the strike price of 16,150.
- The put option is sold for 409.05. Since the intrinsic value is 367.85, the time value is 41.20 (409.05 – 367.85).
- The profit for this trade was 218.55 which is the difference between what we sold the option for (409.05) and what we bought the option for (190.50).

**What is the impact of time decay and volatility on a long put option?**

A purchased put option will lose time value similar to how a call option will lose time value. This loss in time value won’t be linear and will decay exponentially when an option is a few days away from expiry.

Also similar to call options, put options are ‘long volatility’. This means that there is a positive relationship between implied volatility and the price of an option. If volatility goes up and there is negligible change to the underlying price or time, the price of the put option will increase due to this positive relationship between volatility and the price of put options. The reverse is also true where a decrease in volatility will lead to a decrease in the value of the put option.

Both the change in time remaining in the life of the option and the implied volatility of the underlying only impacts the time value of an option. At expiration, time value is zero so these two factors are irrelevant.

However, as you manage your option trades, these are important factors. If the underlying price moves and it moves enough such that the implied volatility goes up, this could increase the value of your option potentially to the point of turning a profit. If this takes several days to happen, this movement in price and volatility could be offset by time decay loss.

**To Conclude: **

- You buy a Put Option if you believe the underlying stock or index will move downward before expiry.
- Traders could lose 100% of the cost of the put option if the underlying moves against them.
- Put options are listed to the right of the Options chain.
- Maximum gain in a long put option is the price of the underlying.
- Maximum loss is capped at the price at which you purchased the put option.
- Put option loses Time value exponentially when closer to expiry.
- There is a positive relationship between implied volatility and the price of a put option.

Key Formulae

*Key Formulae*

Break-even Point = Strike Price – Cost of Put Option

Long Put Payoff = Max(0, Strike Price – Underlying Price)

Long Put Profit = Max(0, Strike Price – Underlying Price) – Option’s Cost

Long put option strategies work best in a bear market and can be used to offset any losses from trading in equities in such a scenario. The following checklist could help you 'weigh your options' before you execute such a strategy.

- Zero in on a strike price
- Calculate potential break-even, profit and payoff for the strike price
- Factor in time decay and volatility

This concludes our chapter on Long Put strategies to trade in options. See you in the next chapter on Bear Put Spread strategies.

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