Volatility - Significance for options Part-I

Question :Why is Volatility significant for Options?

Answer :The value of an Option, apart from other factors, depends upon the Volatility of the underlying. Higher the Volatility of the underlying, higher the Option Premium.

Question :What is Volatility?

Answer :Volatility is the fluctuation in the price of the underlying. For example, the movement in the price of Satyam is quite high as compared to the Sensex. Thus, Satyam is more volatile than the Sensex.

Question :How do you measure Volatility?

Answer :Volatility is the standard deviation of the daily returns on any underlying.

Question :This is too complicated ! What is Daily Return?

Answer :Ok – let me restate in simple language. Every day, every scrip moves up or down by a certain percentage. For example, if Satyam closed at Rs 280 yesterday and today it closed at Rs 285, the percentage change is 5/280 x 100 = +1.79%. This percentage is called ‘daily return’.

Let me make a slightly elaborate calculation and show you.

Fine, what next?

Now you find out the standard deviation of these Daily Returns.

Question :What is Standard Deviation?

Answer :Standard deviation is a measure of dispersion and comes from statistics. Dispersion indicates how widely ‘dispersed’ a set of data is. For example, if you look at heights of adult males in India, you will find that the heights of various people are not too far off from each other. While the average male is about five and a half feet tall, the others are not too far off. While some may be one feet above this average, others might be one feet below.

You are unlikely to find people twenty feet tall, nor two feet tall. Thus, if you were to work out the Standard Deviation of this data, this figure will be a small number, because the data is not too dispersed.

On the other hand, if you try and plot the wealth of various Indian males, you might find a wide dispersion, as somebody might have a wealth of Rs 100 while somebody else might possess Rs 1 crore. Thus, standard deviation of wealth will be high.

Question :How is it calculated?

Answer :In these days of computerized living, it might be simpler to use an Excel spreadsheet and key in the formula for standard deviation. You will get the figure in a second.

The technical formula goes like this:

Identify the basic data (in our case the percentage daily returns)

Work out the average

Work out the deviations of each observation from the average (these deviations might be positive or negative)

Take a square of these deviations

Sum up these squares

Divide the sum by the number of observations

Work out the square root of this number

Let me show you from the above example:

Divide the sum by the number of observations: 0.1966%

Square root of above: 4.43%

Thus the standard deviation of the above data comes to 4.43%.

This is the daily standard deviation, as it is based on daily returns data.

I have heard that Volatility is 50%, 80% etc. Your volatility is far lower at only 4%.

You have heard correct. What we have calculated above is the Daily Volatility. If you want to know the Annual Volatility, you should multiply with the square root of the number of working days in a year. For example, if one year has 256 working days, square root of 256 days is 16 days. Thus in the above case the Annual Volatility is 4.43% x 16 = 70.88%.

In a similar manner, if you want to know the Volatility of the next 9 days, the 9-day Volatility will be 4.43% x 3 = 13.29%.

Question :Having derived the Volatility, how do I interpret it?

Answer :The concept of Normal Distribution states that you can derive a deep understanding of possible movements in the share price from this figure of Volatility. The movement will be within 1 standard deviation 66% of the time, within 2 standard deviations 95% of the time and within 3 standard deviations 99% of the time.

Question :Can you elaborate using examples?

Answer :If Satyam’s closing price today is Rs 287, expected movement in the next one day can be tabulated as under:

Similarly possible movement over the next nine days can be forecasted as under:

Question :What are we predicting here?

Answer :Predicting is a rather difficult science. First of all, we are not looking at direction at all. We are not saying whether Satyam will move up or down. Secondly, we are forecasting possible maximum swing in magnitude irrespective of direction.

For example, we are saying that Satyam will close between Rs 249 to Rs 325 tomorrow and the probability of this happening is 99%. The implication is that the probability of Satyam closing below Rs 249 or above Rs 325 is 1%.

Question :How many days of data should we consider for calculating Volatility?

Answer :There is a difference of opinion among traders as to the number of days that should be considered. In the Indian context, we currently find that Options are available for 3 months. However, most of the trading happens in the first month. Thus, the relevant period for forecasting is one month or lower. Accordingly, it would be sensible to consider Volatility based on the past 10 trading days and for the past 20 trading days. Longer periods would perhaps not be relevant in the present context.

Question :How do we use Volatility in our trading strategies?