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Chapter 1 Introduction To Volatility

Introduction
One often witnesses heavy price fluctuations in the stocks market. The most common term used by traders to define price fluctuations is volatility.

Volatility is a statistical measure of the dispersion of returns for a given security or market index. It is measured by using variance or the square root of variance i.e. standard deviation.

Volatility is a double-edged sword; a surge in volatility could either benefit a trader or end up triggering his stop loss.

Low volatility indicates that a stock does not swing dramatically, but changes in price at a steady pace over a given period of time. In this chapter, we would cover the types of volatility, the methods to calculate them and how a trader can successfully interpret and benefit from the same.

Let us understand the concept of volatility (Standard Deviation) better with a simple example.

Consider BCCI has to make a selection between two batsmen based on their past 10 scores.

Match Rohit Dhavan
1 27 11
2 42 101
3 47 20
4 52 119
5 39 40
6 61 27
7 55 31
8 34 17
9 43 21
10 46 60
Total 446 447

Rohit’s Average = 446/10= 44.6

Dhavan’s Average = 447/10=44.7

Both the batsmen have scored nearly the same runs and have a similar average over the course of 10 innings, which makes the selection difficult.

The parameter that can be used in such a situation is to determine the consistency of the batsmen calculated through the mathematical formula of standard deviation.

First, we calculate the variance through which the standard deviation can be easily computed.

Variance is simply the ‘sum of the squares of the deviation from the mean divided by the total number of observations'.

Variance for Rohit, who maintains an average of 44.6, is calculated a below:

Variance = [(-17.6) ^2 + (-2.6) ^2 + (2.4) ^2 + (7.4) ^2 + (-5.6) ^2 + (16.4) ^2 + (10.4) ^2 + (-10.4) ^2 + (-1.6) ^2 + (1.4) ^2] / 10

= 902.4 / 10

= 90.24

Next we calculate the Standard Deviation (SD)

Std deviation = √ variance

Standard deviation for Rohit’s turns out to be Square root (90.24) = 9.49

Similarly we calculate the variance and standard deviation of Dhavan

Player Rohit Dhavan
Total in 10 matches 446 447
Average 44.6 44.7
Variance 90.24 1252.21
S.D 9.49 35.38

Once we have obtained the standard deviation, it can be used to predict the possible/probable runs both the players are likely to score in the next match. We can arrive at lower and higher projections by adding and subtracting the S.D from the average.

Player Lower projection Higher projection
Rohit 44.6-9.49=35.11 44.6+9.49=54.09
Dhavan 44.7-35.39=9.31 44.7+35.38=80.08

From this, we can estimate that in the next match Rohit is likely to score between 35 to 54 runs (rounded off), while Dhavan is likely to score between 9 to 80 (rounded off). Rohit is clearly the more consistent of the two; Dhavan could either click or get out cheaply.

From the above example we clearly see how standard deviation and volatility estimation can be used in our day to day activities.

Volatility is a % number as measured by standard deviation.

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