Introduction To Volatility

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Introduction

One usually witnesses serious worth fluctuations within the stocks market. the foremost common term employed by traders to outline worth fluctuations is volatility.

Volatility could be a applied math live of the dispersion of returns for a given security or market index. it’s measured by mistreatment variance or the root of variance i.e. variance.

Volatility could be a ambiguous sword; a surge in volatility may either profit a dealer or find yourself triggering his stop loss.

Low volatility indicates that a stock doesn’t swing dramatically, however changes in worth at a gentle pace over a given amount of your time. during this chapter, we’d cowl the categories of volatility, the strategies to calculate them and the way a dealer will with success interpret and like constant.

Let us perceive the conception of volatility (Standard Deviation) higher with a straightforward example.

Consider BCCI needs to build a range between 2 batsmen supported their past ten scores.

MatchRohitDhavan
12711
242101
34720
452119
53940
66127
75531
83417
94321
104660
Total446447

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

PlayerRohitDhavan
Total in 10 matches446447
Average44.644.7
Variance90.241252.21
S.D9.4935.38

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.

PlayerLower projectionHigher projection
Rohit44.6-9.49=35.1144.6+9.49=54.09
Dhavan44.7-35.39=9.3144.7+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.