INTRODUCTION
TO
VOLATILITY
• Volatility is a measure of the rate of
fluctuations in the price of a security
over time. It indicates the level of risk
associated with the price changes of
a security. Investors and traders
calculate the volatility of a security to
assess past variations in the prices to
predict their future movements.
Range from -3 and 6%
Range from -20 and 15%
UNDERSTANDING VOLATILITY
Volatility often refers to the amount of uncertainty or
risk related to the size of changes in a security's value.
A higher volatility means that a security's value can
potentially be spread out over a larger range of values.
This means that the price of the security can change
dramatically over a short time period in either direction.
A lower volatility means that a security's value does
not fluctuate dramatically, and tends to be more steady
TYPES OF VOLATILITY
1. HISTORICAL VOLATILITY
-This measures the fluctuations in the security’s prices in the past.
It is used to predict the future movements of prices based on previous
trends. However, it does not provide insights regarding the future trend
or direction of the security’s price.
2. IMPLIED VOLATILITY
-This refers to the volatility of the underlying asset, which will
return the theoretical value of an option equal to the option’s current
market price. Implied volatility is a key parameter in option pricing. It
provides a forward-looking aspect on possible future price
fluctuations.
Calculating Volatility
The simplest approach to determine the volatility of a
security is to calculate the standard deviation of its
prices over a period of time. This can be done by using
the following steps:







Gather the security’s past prices.
Calculate the average price (mean) of the security’s
past prices.
Determine the difference between each price in the
set and the average price.
Square the differences from the previous step.
Sum the squared differences.
Divide the squared differences by the total number
of prices in the set (find variance).
Calculate the square root of the number obtained in
the previous step
Sample Calculation
You want to find out the volatility of the stock of ABC Corp. for
the past four days. The stock prices are given below:
Day 1 – $10
Day 2 – $12
Day 3 – $9
Day 4 – $14
To calculate the volatility of the prices, we need to:
Find the average price:
$10 + $12 + $9 + $14 / 4 = $11.25

Calculate the difference between each price and the
average price:
Day 1: 10 – 11.25 = -1.25
Day 2: 12 – 11.25 = 0.75
Day 3: 9 – 11.25 = -2.25
Day 4: 14 – 11.25 = 2.75

Square the difference from the previous step:
Day 1: (-1.25)2 = 1.56
Day 2: (0.75)2 = 0.56
Day 3: (-2.25)2 = 5.06
Day 4: (2.75)2 = 7.56

Sum the squared differences:
1.56 + 0.56 + 5.06 + 7.56 = 14.75

Find the variance:
Variance = 14.75 / 4 = 3.69

Find the standard deviation:
Standard deviation = 1.92 (square root of 3.69)

The standard deviation indicates that the stock price of
ABC Corp. usually deviates from its average stock price
by $1.92.
SAMPLE CALCULATION
1.You want to find out the volatility of the stock of ABC Corp. for the past four days. The stock
prices are given below:
Day 1 – $10
Day 2 – $12
Day 3 – $9
Day 4 – $14
CONCLUSION
-The standard deviation indicates that the
stock price of ABC Corp. usually deviates from its
average stock price by $1.92. The average price is
11. 25, the variance is 3.69.
Sample Calculation #2
Find the following:
A. Find the Variance
B. Find the Standard
Deviation
Sample Calculation #3
Below are the daily stocks of Shoes
Company.
Find the Average Price ;
Find the Variance ;
Find theStandard Deviation ;

Formula for Daily Volatility

Daily Volatility formula = √Variance

If the daily variance of the Apple Inc. is 66.1229 in July 2006,
its Daily Volatility will be :

Daily Volatility = √66.1229 = 8.1316

Therefore, the Daily Volatility for the S&P 500 in 2015 is
8.1316
Formula for Annualized Volatility
Annualized Volatility = Standard Deviation * √252
If the daily standard deviation of the S&P 500 benchmark is
1.73% in August 2015, its Annualized Volatility will be :
Annualized Volatility = 1.73 * √252 = 27.4
Therefore, the annualized volatility for the S&P 500 in 2015 is
27.4%, based on the daily volatility or daily price movements
in August 2015.
How to Calculate Volatility Using Expected
Returns
Firm A
50% chance of an 11% return
50% chance of a 9% return
Expected Return = (0.5 )(0.11) + (0.5)(0.09) = 0.1 or 10%
Variance = (0.5)(0.11- 0.1)2 + (0.5)(0.09 - 0.1)2 = 0.0001
Standard Deviation = √0.0001 = 0.01 or 10%
Firm B
50% chance of an 80% return
50% chance of a -60% return
Expected Return = (0.5)(0.8) + (0.5)(-0.6) = 0.1 or 10%
Variance = (0.5)(0.8-0.1)2 + (0.5)(-0.6-0.1)2 = 0.49
Standard Deviation = √0.49 = 0.7 or 70%
Calculating Volatility Using Historical Returns
S&P 500
2004 10.9%
2005 4.9%
2006 15.8%
2007 5.5 %
Average Return = 0.109 + 0.049 + 0.158 +0.055 / 4 = 0.09275
Variance = (0.109 - 0.09275)2 + (0.049 - 0.09275)2 + (0.158 - 0.09275)2 +
(0.055 - 0.9275)2 / 4-1 = 0.00262
Standard Deviation = √0.00262 = 0.0571859 or 5.71859%
Prepared by Group 9: BSAM 3-1
Ma. Pamela Roldan
Cheche Cuare
Judy Ann De Jose
Mark Sta. Maria