How to Gauge Market Sentiment using Put Call Ratio (PCR)?

Any F&O trader will immediately identify a widely used terminology as the Put Call Ratio (PCR) if you ask them. As the name would imply, it is the ratio of puts to calls, although we will go into that more specifically later. Understanding put call ratio options and how to find it for a stock are the more important questions. Reading put call ratio charts is particularly crucial since the alterations they show are important

Put Call Ratio

predictors of future market movement. The PCR ratio is a popular indication of market direction used by most traders. 

What is Put Call Ratio? 

Put call ratio (PCR) is a well-liked derivative indicator that was created expressly to assist traders in determining the general mood (sentiment) of the market. Either the open interest for a given period or the volume of options traded is used to determine the ratio. More puts were traded during the day if the ratio is greater than 1, and more calls were exchanged during the day if the ratio is less than 1. The PCR can be computed for the entire option segment, which includes both specific stocks and indexes. 

How to Interpret Put Call ratio? 

The put call ratio is mostly utilised as a contrarian indicator. Fundamentals are less important in the short term than emotions are. Very high or low PCR are indicators of market greed and fear. Contrary to popular belief, PCR is typically going in the wrong direction. Put options are traded more frequently than call options when the PCR is high. But it is true that a seller is also necessary for a bought option. A transaction must involve both the buyer and the seller at the same time. Without a seller option contract cannot be bought into and vice versa. The meaning will be quite different from the case of buying options if you think of options as sold rather than bought. Put options are purchased more frequently when the PCR is more than one, hence the market should decline. But in practise, the market usually rises in these situations. Only if you suppose that options are being sold rather than bought can you justify this. When the seller undertakes a significant amount of risk for a small amount of reward and also uses a significant amount of cash, the argument seems to be rather straightforward: option writers are smarter than option holders. Thus, you can conclude put option writers are more active than call option writers if the PCR is greater than one. Hence, the market seems positive, and more put option sellers are anticipated to support the upswing. In contrast, PCR values below one show that more call option writers are active than put option sellers, which could cause the market to decline even more. The market may top out and see a reversal or a correction when PCR is too high, since put option sellers may become fatigued. Similar to this, excessively low PCR signals an oversold market that may experience a sharp pullback or reversal. In conclusion, the PCR can be understood as follows. 

Put/Call  Ratio	Interpretation
Put call  ratio more  1.00	Bullish sentiment. It indicates that put writers are actively writingduring dips in anticipation of the trend strengthening.
Put call  ratio less 1.00	Bearish sentiment. It indicates that call option strikes are beingaggressively sold by option writers.

 Put call Overbought situation. The put writers are exhausted and might ratio around 1.50 

book profit. A correction or reversal of the upward trend could happen. 

Put call  ratio around 0.50

Oversold circumstances. The downtrend may have reached itsbottom and a pullback is about to occur.

 Nevertheless, the interpretations are speculative, and the PCR range stated here is not set in stone. The PCR range and interpretations can vary from trader to trader. Just my prior trading experiences were used to inform the aforementioned interpretations. Someone may have the right interpretation if their alternative interpretation yields positive consequences. 

How to Estimate Trading Range with Implied Volatility (IV)? 

It's fascinating to discover that Implied Volatility (IV) provides many insights, the most valuable of which is the expected levels of movement. I'll talk about how we can use Implied Volatility to get a better estimate of this range. However, first, let me define Implied Volatility (IV). The volatility figure implied by the options premium is denoted by IV. A simple calculation yields the IV. 

Option premium calculation involves the following 

1.  Stock Price (Known and Definite Information) 
2.  Strike Price (Factual Input) 
3.  Volatility (Unknown & could have many answers) 
4.  Time to Expiry (Known and Definite Information) 
5.  Risk Free Interest Rate (Not a lot impactful) 

Given an option premium and inputs 1, 2, 3, and 5, the volatility figure calculated and it is referred to as Implied Volatility. The good news about IV is that it does not represent historical volatility, but rather volatility anticipated by option traders. This figure represents the annualised volatility forecasted by Options. This means that if this figure is 20% and the stock on which we are trading options is trading at 100 then the stock is expected to trade at 100 +/- 20%, or in the range of 80 to 120. 

If you want to estimate the trading range for fewer days, say one month, you can reduce the IV figure proportionally to represent the smaller part of the year. Proportionate reduction means that if the rent for a year is ₹12,000, the rent for a month will be ₹1,000. The difference in proportionate volatility reduction is that time cannot be multiplied directly. Volatility can be scaled (apportioned) by multiplying or dividing by the Square Root of time.

Assume there are 252 trading days in a year, you want to find the range for 30 trading days, and your IV is 20%. 

30 days of IV reduction = 20% / Square Root (252) X Square Root (30) = 20% / 15.9 X 5.5 

= 6.9% ~ 7% 

So, using this simple calculation, we can estimate that option traders are expecting 7% volatility. This means that for a 100 rupees stock, a trading range of 93 to 107 is an expected range indicated by IV for the 30 trading days. This calculation is also applicable to index. Instead of simply selling options with a range assumption based on historical data, option writers can now sell higher strike call and lower strike put options based on the range indicated by Expectation of future volatility during the option's life. 

Max Pain Theory 

Maximum pain is a term used to describe the somewhat controversial Maximum Pain Theory, which states that investors who buy and hold option contacts until the expiration date will incur a maximum loss. The occurrence is based primarily on two assumptions. 

1.  The first assumption is based on price movements, which are the result of traders legitimately buying and selling stock options for hedging purposes. During the last few days, the index has moved closer to the strike prices at which the option buyer suffers the greatest loss. 
2.  The second assumption is that option sellers, such as large institutions that hedge large positions in their portfolios, will manipulate the market. Because they are large institutions, they can manipulate index prices, resulting in no obligation to fulfil contracts and thus hedging their payouts to buyers. 

Alternatively, as the strategy nears its end, different groups compete based on purchasing power to drive prices towards a more profitable closing price. When market makers reach a net positive position of call and put options at a strike price where option holders stand to lose the most money, this is known as max pain. Option sellers, on the other hand, may profit the most if they sell more options than they buy, causing them to expire worthless. 

The Maximum Pain Theory is a bit contentious. The theory's naysayers disagree on whether the maximum pain behaviour of close stock prices is accidental or the result of market manipulation. The latter reason raises more serious concerns about market oversight. 

Max Pain Calculation

To understand this, consider a simple example. For the sake of this example, I'll assume the market has only three Nifty strikes available. I've taken note of the open interest for both call and put options at each strike. 

Strike	Call Option OI	Put Option OI
17900	1,41,963	1,33,103
18000	1,26,673	1,38,707
18100	1,00,174	58,663

 Case 1: Markets expire at 17900. 

Keep in mind that if you write a Call option, you will only lose money if the market rises above the strike price. Similarly, if you write a Put option, you will only lose money if the market falls below the strike price. 

As a result, if the market closes at 17900, none of the call option writers or sellers will be out of money. This means that call option sellers with strikes of 17900, 18000, and 18100 will keep the premiums received. 

Put option sellers, on the other hand, will be in big trouble. Let us begin with the 18100 PE sellers. 

18100 PE seller would lose 200 points if Nifty expires at 17900. Because the OI is 58,663, the loss in Rupees is – 

= 200 X 58,663 = ₹1,17,32,600/- 

18000 PE Seller will lose 100 points, in terms of Rupee it would be = 100 X 1,38,707 = ₹1,38,70,700/- 

17900 PE seller won’t lose any money. 

So, the total amount of money lost by option seller if the markets expire at 17900 is – 

Total money lost by Call Option seller + Total money lost by Put Option seller = 0 + 1,17,32,600 + 1,38,70,700 

= ₹2,56,03,300/- 

Remember that the total amount of money lost by Call Option sellers equals the sum of the amounts lost by 17900 CE sellers, 18000 CE sellers, and 18100 CE sellers. Similarly, the total amount lost by Put Option sellers is equal to the sum of the 

amounts lost by 7700 PE sellers, 7800 PE sellers, and 7900 PE sellers. 

Case 2: Markets expire at 18000 

At 18000, the call option sellers listed below would lose money - 17900 CE sellers would lose 100 points, which we can multiply by the Open Interest to get the Rupee value of the loss. 

100 X 1,41,963 = ₹1,41,96,300 /- 

Both 18000 CE and 18100 CE seller will not lose money. 

The 17900 and 18000 PE seller wouldn’t lose money 

The 18100 PE will lose 100 points, multiplying with the Open Interest, we get the Rupee value of the loss.

100 X 58,663 = ₹58,66,300/- 

So, the total loss for option sellers if the market expires at 18000 is – = 1,41,96,300 + 58,66,300 

= ₹2,00,62,600/- 

Case 3: Markets expire at 18100 

At 18100, the call option sellers listed below would lose money - 17900 CE sellers will lose 200 points, with a monetary value of - 

200 X 1,41,963 = ₹2,83,92,600/- 

18000 CE seller will lose 100 points, with a monetary value of - 

100 X 1,26,673 = ₹1,26,67,300/- 

18100 CE sellers will keep the premiums received. 

Because the market expires at 18100, all put option seller will keep the premiums received. 

As a result, the total loss of option seller would be - 

= 2,83,92,600 + 1,26,67,300 = ₹4,10,59,900/- 

So far, we've calculated the total rupee value loss for option writers at each possible expiry level. The above calculations can now be summarised in a table format – 

Strike	Call  Option OI	Put  Option OI	Loss of  Calls (₹)	Loss of  Puts (₹)	Total loss  (₹)
17900	1,41,963	1,33,103	0	2,56,03,300	2,56,03,300
18000	1,26,673	1,38,707	1,41,96,300	58,66,300	2,00,62,600
18100	1,00,174	58,663	4,10,59,900	0	4,10,59,900

 Now, we can easily identify the point at which the market is likely to expire. We have identified the combined loss that option writers would experience at various expiry levels. According to the option pain theory, the market will expire at the point where option sellers experience the least amount of pain i.e. the least amount of loss. 

According to the table above, this point is 18000, where the combined loss is around 2,00,62,600 which is less than the combined loss at 17900 and 18100. That's all there is to the calculation. However, for the sake of simplicity, only three strikes were considered in the example. However, there are numerous strikes for any given underlying, particularly the Nifty. Calculations become cumbersome and confusing, necessitating the use of a tool such as Excel. 

As a result, real open interest build-ups of the Nifty option chain were calculated on March 23rd, 2023 for the March 29th expiry. Only ten strike prices and strike prices with 100 multiples are considered for simplicity. Take a look at the image below.

It assumed that the market would expire at that point for all available strikes and then computed the rupee value of the loss for CE and PE option writers. This number is shown in the final column, titled "Total Pain." Once you've calculated the total pain, you can simply identify the point at which the option writer loses the least amount of money. This can be determined by plotting a 'bar graph' of total pain. The bar graph would look something like this - 

Max Pain

As you can see, the 17100 strike is where option writers would lose the least money, hence in accordance with the theory of option pain, this is the strike where the market for the March series is most likely to expire. 

Now, how can you put this knowledge to use now that you've determined the expiry level? Well, there are many applications for this knowledge. The majority of traders identify the strikes they can write using this maximum threshold for pain. As

17100 is the anticipated expiration level in this scenario, one can choose to write call options above 17100 or put options below 17100 and keep all of the premiums.