Put option profit formula: P&L Analysis and Break-Even Point

• The profit and loss (P&L) pattern of the Put Option buyer

By keeping in mind, the intrinsic value of a put option, let’s create a table that helps us determine the potential profit or loss for the buyer of Bank Nifty’s 18400 put option upon expiry, considering different changes in the spot market. It’s crucial to remember that the premium paid for this option was Rs 315, which remains constant regardless of the spot value. To have a clear understanding of the profit and loss, we should consider this expense while constructing our profit and loss table.

Please note that the negative sign preceding the premium paid indicates a cash outflow from the trading account.

Let us take note of the P&L’s behaviour and make some generalizations about it. Let row 8 be our point of reference for the conversation.

1. Buying a put option is to capitalize on a declining price. Depending on the strike price of 18400, benefits rise as the spot market diminishes.
   1. Those who purchase put options make a profit if the spot rate drops beneath the strike price. In other words, one should only consider this avenue of investment when expecting the underlying to decline.
2. When the spot price surpasses 18400, the position begins to accumulate a deficit. Nevertheless, this loss is restricted to how much was paid for the premium, which in this case was Rs.315/-
   1. When the spot price exceeds the strike price, a put option buyer will indeed incur a loss. However, it’s important to note that this loss is restricted to the amount of premium they initially paid.

This general formula can be utilized to calculate the profit and loss (P&L) from a put option position when held until expiration. Remember:

P&L = [Max (0, Strike Price – Spot Price)] – Premium Paid

Let’s take two random values and evaluate if the formula holds true:

Value 1: 16510

Value 2: 19660

For Value 1 (spot below strike, position expected to be profitable):

P&L = [Max (0, 18400 – 16510)] – 315

     = 1890 – 315

     = +1575

For Value 2 (spot above strike, position expected to incur a loss, limited to the premium paid):

P&L = [Max (0, 18400 – 19660)] – 315

     = [Max (0, -1260)] – 315

     = -315

Both results align with the expected outcomes.

Now, let’s understand how to calculate the breakeven point for a put option buyer. As we discussed this in a previous chapter, I will provide you with the formula:

Breakeven Point = Strike Price – Premium Paid

For the Bank Nifty, the breakeven point would be:

Breakeven Point = 18400 – 315

                       = 18085

According to this breakeven point definition, at 18085, the put option should neither gain nor lose any money. To validate this, let’s apply the P&L formula:

P&L = [Max (0, 18400 – 18085)] – 315

     = [Max (0, 315)] – 315

     = 315 – 315

     = 0

The outcome confirms the expectation of the breakeven point.

It is essential to note that all calculations of intrinsic value, profit and loss, and breakeven point are with regard to the expiry date. We have presumed that you, as an option buyer/seller, plan to keep the trade until its expiration.

Soon, you’ll discover that more often than not, you will open an options trade, but close it much earlier than expiration. Calculating the break-even point in such a scenario may not be important; however, working out the P&L and intrinsic value is significant and requires a different formula.

Let us look at two scenarios on the Bank Nifty Trade with its start date of 7 April 2015 and expiry of 30 April 2015.

1. What would be the profit and loss (P&L) if the spot price is 17000 on 30th April 2015? 
2. What would be the profit and loss (P&L) if the spot price is 17000 on 15th April 2015, or any other date apart from the expiry date?

The first question’s answer is quite easy. We can directly apply the profit and loss (P&L) formula: 

= Max (0, 18400 – 17000) – 315

= Max (0, 1400) – 315

= 1400 – 315

= 1085

Moving on to the second question, if the spot rate is other than 17000 at any point other than expiration, the P&L won’t be 1085; it will actually be greater. We’ll explore why at a later stage, but just keep that in mind for now.

– Put option buyer’s P&L payoff

By connecting the P&L points of the Put Option and plotting it on a line graph, we should be able to confirm our generalizations about the profit/loss for buyers of this security.

The chart presents several elements worth noting. Of particular interest is the 18400-strike price, but there are other details to keep in mind as well.

1. If the spot price exceeded the strike price of 18400, the buyer of the Put option would incur a loss, but limited to the premium paid. 
2. Conversely, when the spot rate falls below the strike price, the Put option buyer can potentially gain exponentially, with the possibility of unlimited profits. 
3. At the breakeven point of 18085, there is no financial gain or loss for the put option buyer. It is at this point that the P&L graph transitions from negative to neutral. 
4. Beyond this level, the put option buyer starts to generate profits.