## Standard Error and Standard Deviation in Finance

In finance, the SEM daily return of an asset measures the accuracy of the sample mean as an estimate of the long-run (persistent) mean daily return of the asset.

On the other hand, the SD of the return measures deviations of individual returns from the mean. Thus, SD is a measure of volatility and can be used as a risk measure for an investment.

Standard deviation measures the variability from specific data points to the mean.Assets with greater day-to-day price movements have a higher SD than assets with lesser day-to-day movements. Assuming a normal distribution, around 68% of daily price changes are within one SD of the mean, with around 95% of daily price changes within two SDs of the mean.

## What is the empirical rule, and how does it relate to standard deviation?

A normal distribution is also known as a standard bell curve, since it looks like a bell in graph form. According to the empirical rule, or the 68-95-99.7 rule, 68% of all data observed under a normal distribution will fall within one standard deviation of the mean. Similarly, 95% falls within two standard deviations and 99.7% within three.

## What is a sampling distribution?

A sampling distribution is a probability distribution of a sample statistic taken from a greater population. Researchers typically use sample data to estimate the population data, and the sampling distribution explains how the sample mean will vary from sample to sample. The standard error of the mean is the standard deviation of the sampling distribution of the mean.

## How are standard deviation and standard error of the mean different?

Standard deviation measures the variability from specific data points to the mean. Standard error of the mean measures the precision of the sample mean to the population mean that it is meant to estimate.