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.
Have you seen the Hollywood movie ‘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 consider two batsmen and the runs they have scored in six consecutive matches.
As the captain, you face a decision between Billy and Mike 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:
Let’s perform the calculations using the following numbers:
Billy’s Sigma = 25 + 28 + 22 + 24 + 21 + 26 = 146
Mike’s Sigma = 38 + 15 + 20 + 14 + 30 + 21 = 138
Based on Sigma, Mike appears to be the more likely choice. Now, let’s calculate the mean or average for both players:
Billy = 146 / 6 = 24.33
Mike = 138 / 6 = 23
From both the mean and Sigma perspectives, it seems that Mike 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 Billy 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 -3.33 (-3.33 runs below his average) with a score of 28.
The average score of Billy 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 Billy, the variance can be calculated as follows:
Variance = [(0.67)^2 + (-3.33)^2 + (-1.33)^2 + (+0.67)^2 + (-3.33)^2 + (+1.67)^2] / 6
= 35.33 / 6
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 Billy, the standard deviation is:
Standard Deviation = √5.89
Similarly, the standard deviation for Mike is calculated to be 3.46. 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 ∑, while standard deviation is sometimes represented by σ.
To predict the likely number of runs Billy and Mike will score in their next game, we can utilize 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, Billy is likely to score between 21.9 and 26.76 runs, while Mike’s potential range is wider, spanning from 19.54 to 26.46 runs. With Mike’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 19 and 27 runs.
Considering Billy’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, while Mike’s performance can be more unpredictable. Choosing Mike may involve a higher level of risk.
In conclusion, when considering who has a better chance of scoring 20 or more runs, Billy is undoubtedly the clear choice. He is reliable and less prone to taking unnecessary risks, unlike Mike.
We have assessed the risk associated with these players through “Standard Deviation.” In the realm of the stock market, the riskiness of stocks or indices is referred to as volatility, which is represented as a percentage calculated using standard deviation.
Here’s Investopedia’s 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 Infosys is 25% and TCS is 45%, it is evident that Infosys demonstrates more stable price fluctuations in comparison to TCS.
Before concluding this chapter, let’s make some predictions based on the following information:
Today’s Date: 1st June 2023
Nifty Spot: 12,500
Nifty Volatility: 18%
TCS Spot: 3,000
TCS Volatility: 30%
Given this information, can we predict the likely trading range for Nifty and TCS one year from now? Let’s put these numbers to good use.
According to calculations, in the next 1 year, Nifty is expected to trade within the range of 10,250 and 14,750, with varying probabilities for values in between. For example, the probability of Nifty being around 11,000 could be 25%, while around 13,000 it could be 40% by 1st June 2024.
This leads us to an exciting platform.
In the upcoming chapters, we will answer these questions and explore easier methods, such as using MS Excel, to calculate volatility.