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 51,200 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 420, which remains constant regardless of the spot value. To have a clear understanding of the profit and loss, we should take into account this expense whilst 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 generalisations about it. Let row 8 be our point of reference for the conversation.

Buying a put option is to capitalise on a declining price. Depending on the strike price of 51,200, benefits rise as the spot market diminishes

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.

When the spot price surpasses 51,200, 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 420

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 utilised 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: 48,950

Value 2: 52,800

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

P&L = [Max(0, 51,200 – 48,950)] – 420

= 2,250 – 420

= +1,830

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

P&L = [Max(0, 51,200 – 52,800)] – 420

= [Max(0, -1,600)] – 420

= -420

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 = 51,200 – 420

= 50,780

According to this breakeven point definition, at 50,780, the put option should neither gain nor lose any money. To validate this, let’s apply the P&L formula:

P&L = [Max(0, 51,200 – 50,780)] – 420

= [Max(0, 420)] – 420

= 420 – 420

= 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 and expiry:

What would be the profit and loss (P&L) if the spot price is 49,500 on the expiry date?

What would be the profit and loss (P&L) if the spot price is 49,500 on a date prior to expiry, or any other date apart from the expiry date?

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

= Max(0, 51,200 – 49,500) – 420

= Max (0, 1,700) – 420

= 1,700 – 420

= 1,280

Moving on to the second question, if the spot rate is 49,500 at any point other than expiration, the P&L won’t be 1,280; 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 generalisations about the profit/loss for buyers of this security.

The chart presents several elements worth noting. Of particular interest is the 51,200 strike price, but there are other details to keep in mind as well:

If the spot price exceeded the strike price of 51,200, the buyer of the Put option would incur a loss, but limited to the premium paid

Conversely, when the spot rate falls below the strike price, the Put option buyer can potentially gain exponentially, with the possibility of unlimited profits

At the breakeven point of 50,780, 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

Beyond this level, the put option buyer starts to generate profits

For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding put option P&L mechanics proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending put option profit and loss structures enables more informed bearish investment strategies.

Visit https://stoxbox.in/ for comprehensive educational resources on put option calculations and market analysis tools.