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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