The simple answer is the standard deviation of periodic returns. This video takes some sample data for closing prices of a stock and demonstrates how volatility is calculated in Excel. In finance, such as for price series, usually log returns are used, where log is the natural logarithm.

# Introduction to Quantitative Finance

## What is the Square Root Rule?

Volatility and VaR can be scaled using the square root of time rule. According to this rule, if the fluctuations in a stochastic process are independent of each other, then the volatility will increase by square root of time. It provides exact volatilities if the volatilities are based on lognormal returns. In case of simple […]

## Why Use Lognormal Returns in Finance (Stock Prices)?

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 100 to base 10 is 2, because 100 is 10 to the power 2: 1000 = 10 × 10 = 103. More generally, if x = by, then y […]

## How to Scale Autocorrelated Returns?

We know that the square root rule can be used to scale volatility with time. This rule assumes that the returns are independent and identically distributed. However, this assumption is not very realistic. This video illustrates a scaling factor that adjusts the square root rule for for autocorrelation. This video is developed by David from […]

## Arithmetic Vs. Geometric Stock Returns

This video provides clarity about the confusion over the stock returns. The expected return of a stock is ambiguous because, if we assume returns are normal, then price levels are lognormal. In which case, the mean does not equal the median future stock price. Consider these two questions: 1. What is the average return per […]

## Extreme Value Theory

Extreme value theory (EVT) aims to remedy a deficiency with value at risk (i.e., it gives no information about losses that exceed the VaR) and glaring weakness of delta normal value at risk (VaR): the dreaded-fat tails. The key is the idea that the tail has it’s own “child” distribution. This video explains the extreme […]