Put Option Selling: Strategies and Techniques for Profitable Trading

Vega

Vega measures the rate at which option premiums change with respect to volatility. Many traders express the concept of volatility as being synonymous with the “up-down movement of the stock market”. Consequently, it is time we gain a better understanding of this variable.

Moneyball

Have you seen the Hollywood film ‘Moneyball’? It is a depiction of a real-life story centred around the manager of an American baseball team, Billy Beane, and his colleague. To acquire the most skilled players for their team, they implemented a revolutionary strategy that was unheard of in their day, using statistics to pick lower profile but highly talented baseball players. This approach was both innovative and disruptive at the time.

To give an example, I can draw some inspiration from the Moneyball approach to illustrate volatility.

This topic may appear to be unrelated to stock markets, but try not to be disheartened. Rest assured that it is pertinent, and will assist you in understanding the concept of ‘Volatility’ better.

Let’s take into account two batsmen and the runs they have scored in six consecutive matches.

As the captain, you face a decision between Rajesh and Amit for the upcoming game. It is crucial to select a batsman who can consistently score at least 20 runs. In such situations, there are typically two methods used:

Calculate the combined score (referred to as ‘Sigma’) of both batsmen and choose the one with the highest score for the game

Determine the mean (also known as the ‘average’) of the number of scores per game and select the batsman with a superior average

Let’s perform the calculations using the following numbers:

Rajesh’s Sigma = 25 + 28 + 22 + 24 + 21 + 26 = 146

Amit’s Sigma = 38 + 15 + 20 + 14 + 30 + 21 = 138

Based on Sigma, Rajesh appears to be the more likely choice. Now, let’s calculate the mean or average for both players:

Rajesh = 146 / 6 = 24.33

Amit = 138 / 6 = 23

From both the mean and Sigma perspectives, it seems that Rajesh has the advantage. However, it is important not to jump to conclusions just yet. Remember, the goal is to select a batsman capable of consistently scoring at least 20 runs. This cannot be determined solely based on mean and Sigma data. Let’s continue our analysis.

Next, we will find the deviation from the mean for each match. Taking Rajesh as an example, his average is 24.33, and in the first match, he scored 25 runs, resulting in a deviation of +0.67 (0.67 runs above his average). In the second match, there was a deviation of +3.67 with a score of 28.

The average score of Rajesh is represented by the middle black line, and the double-arrowed vertical line indicates the deviation from the mean in each match. Moving forward, we will compute another statistical measure called ‘Variance’.

Calculating variance may seem daunting, but it’s not that complex. We simply sum up the squares of the deviations from the average result and divide by the number of matches played, which is 6 in this case.

For Rajesh, the variance can be calculated as follows:

Variance = [(0.67)² + (3.67)² + (-2.33)² + (-0.33)² + (-3.33)² + (1.67)²] / 6

= 35.33 / 6

= 5.89

We will also calculate another factor called ‘Standard Deviation’ (SD), which is obtained by taking the square root of the variance:

Standard Deviation = √Variance

For Rajesh, the standard deviation is:

Standard Deviation = √5.89

≈ 2.43

Similarly, the standard deviation for Amit is calculated to be 8.72. Now, let’s gather and compare all the numbers and statistics:

While we are familiar with the terms ‘mean’ and ‘Sigma’, what is SD? This statistic quantifies the extent to which values deviate from the average. Standard deviation (SD), often represented by the Greek letter sigma (σ), is a measure in statistics that indicates the spread of a set of data values.

It is important not to confuse the two sigmas. The total is denoted by the Greek symbol ∑, whilst standard deviation is sometimes represented by σ.

To predict the likely number of runs Rajesh and Amit will score in their next game, we can utilise the standard deviation (SD). By adding and subtracting the SD from their mean, we can obtain a range of predictions.

The figures indicate that in the upcoming 7th match, Rajesh is likely to score between 21.9 and 26.76 runs, whilst Amit’s potential range is wider, spanning from 14.28 to 31.72 runs. With Amit’s scoring range being more diverse, it becomes challenging to determine if he will reach or exceed 20 runs. He could end up scoring anywhere between 14 and 32 runs.

Considering Rajesh’s consistent performance and narrower range, he is a safer choice for the 7th match. His scores are likely to fall between 21 and 27, whilst Amit’s performance can be more unpredictable. Choosing Amit may involve a higher level of risk.

In conclusion, when considering who has a better chance of scoring 20 or more runs, Rajesh is undoubtedly the clear choice. He is reliable and less prone to taking unnecessary risks, unlike Amit.

We have assessed the risk associated with these players through “Standard Deviation.” In the realm of the stock market, the riskiness of equities or indices is referred to as volatility, which is represented as a percentage calculated using standard deviation.

Here’s a definition:

“A statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly higher the standard deviation, higher is the risk”.

According to the given definition, if the volatility of Wipro is 25% and HCL Technologies is 45%, it is evident that Wipro demonstrates more stable price fluctuations in comparison to HCL Technologies.

Before concluding this chapter, let’s make some predictions based on the following information:

Today’s Date: 1st June 2024

Nifty Spot: 23,500

Nifty Volatility: 18%

Wipro Spot: 450

Wipro Volatility: 30%

Given this information, can we predict the likely trading range for Nifty and Wipro one year from now? Let’s put these numbers to good use.

According to the above calculations, in the next 1 year, Nifty is expected to trade within the range of 19,270 and 27,730, with varying probabilities for values in between. For example, the probability of Nifty being around 20,500 could be 25%, whilst around 25,000 it could be 40% by 1st June 2025.

This leads us to an exciting platform:

We have estimated the range for Nifty over 1 year

Now, can we estimate the range within which Nifty is likely to trade over the next few days or until the series expiry?

If we can do this, we will be in a better position to identify options that are likely to expire worthless, allowing us to sell them today and pocket the premiums

Whilst we have determined the range for Nifty based on a volatility estimate of 18%, we should consider what happens if the volatility changes

In the upcoming chapters, we will answer these questions and explore easier methods, such as using MS Excel, to calculate volatility.

For those exploring equity investment opportunities through a stock broker or consulting with a financial advisor, understanding volatility and Vega proves essential when navigating the stock market. Whether evaluating trading calls or utilising a stock screener to identify opportunities, comprehending how volatility affects option premiums enables more sophisticated options pricing analysis and risk assessment.