# What is a Standard Deviation?

Standard deviation quantifies the extent to which returns of mutual funds diverge from their average annual returns. Explore further into the formula and calculation methods of standard deviation.
What is a Standard Deviation?
30 March 2024

Standard deviation plays a crucial role in assessing the risk associated with investments, particularly mutual funds. Seasoned investors and beginners, all can benefit from its understanding. This article aims to demystify standard deviation, breaking down its complex concept into easily understandable parts. Let us navigate through its definition, formula and inner workings to grasp its significance in the financial markets and its impact on institutions.

## Standard Deviation definition

So, what is standard deviation? Sometimes abbreviated as "std", it is a statistical measure that quantifies the dispersion or variability of a set of data points. In simpler terms, it tells us how much the data deviates from the mean (average) value. When it comes to investments, particularly mutual funds schemes, standard deviation is used to gauge the volatility of the fund's returns over a period.

## What does Standard Deviation do?

The essence of standard deviation lies in its ability to measure risk. It provides a numerical value that helps investors understand the amount of uncertainty or risk involved in an investment option. A higher standard deviation indicates greater volatility, meaning the investment's returns can vary widely from the average return. Conversely, a lower standard deviation signifies less volatility, suggesting the returns are more likely to be close to the average. Adding established mutual funds to your portfolio, whether through a single lump sum investment or a SIP investment, can play a crucial role in helping you meet your overall financial goals in several different ways.

## Formula of Standard Deviation

The formula for standard deviation is a mathematical representation that calculates the square root of the variance. The variance measures the average of the squared differences from the Mean. The formula is given by:

SD = √Σ (xi - x̄ )² / N

or

σ2 = Σ(xi - μ)2
N

Where:

SD is the standard deviation,

N is the number of observations,

xi represents each value in the dataset,

x̄ is the mean of the data

## An example of Standard Deviation

Let's illustrate the concept of standard deviation in mutual funds with a practical example from the Indian market. Assume we are analysing the annual returns of a hypothetical Indian equity mutual fund over 5 years. The annual returns for these years are as follows:

• Year 1: 8%
• Year 2: 12%
• Year 3: 15%
• Year 4: 7%
• Year 5: 10%

First, we calculate the mean (average) annual return of the fund over these 5 years.

Mean = 8+12+15+7+10/5 = 10.4%

The mean (average) annual return of the mutual fund over the 5 years is 10.4.

Next, we apply the standard deviation formula, which involves several steps:

• Calculate each year's deviation from the mean (subtract the mean from each year's return
• Square each of these deviations (to eliminate negative values and give more weight to larger deviations).
• Sum up all the squared deviations.
• Divide this sum by the total number of observations (in this case, 5 years).
• Take the square root of this quotient to get the standard deviation.
• Let us go through these steps with our example data.

SD = √(((8-10.4)2 + (12-10.4)2 + (15-10.4)2 + (7-10.4)2 + (10-10.4)2 )/5)

SD = √(41/5)

SD = 2.87

By applying the standard deviation formula, we find that the standard deviation of the fund's annual returns is approximately 2.87%.

This means that, on average, the annual returns of this hypothetical Indian equity mutual fund deviate from the mean annual return by about 2.87 percentage points. In the context of mutual funds in the Indian market, this standard deviation figure helps investors understand the volatility of the fund. A standard deviation of 2.87 indicates that the fund's annual returns have fluctuated within a relatively moderate range around the average return, providing insights into the risk and variability investors might expect. ​

## Using Standard Deviation to compare investments

Investors often compare the standard deviation of different investments to understand their risk profiles better. A mutual fund with a lower standard deviation is considered less risky than one with a higher standard deviation, assuming the average returns are similar. This comparison helps in constructing a diversified investment portfolio that aligns with an investor's risk tolerance.

## Why care about Standard Deviation?

Understanding standard deviation is crucial for investors as it provides insights into the risk associated with different investment vehicles. It helps assess whether an investment's potential returns justify the risk involved, facilitating better investment choices.

## When Standard Deviation does not tell the whole story

While standard deviation is a powerful tool for risk assessment, it has its limitations. It assumes that returns are normally distributed, which might not always be the case. Furthermore, it doesn't account for the direction of the volatility, meaning it treats both upward and downward deviations equally.

## Key points on Standard Deviation

• Standard deviation is a measure of volatility, not a predictor of investment performance.
• It is essential to consider other factors alongside standard deviation when evaluating investments.
• Understanding the context and the type of data analysed is crucial when interpreting standard deviation values.

While navigating the complexities of financial investments, the understanding of standard deviation is indispensable. However, the journey does not end here. With Bajaj Finserv Mutual Fund Platform you can leverage your insights into making informed investment decisions. Whether you are looking to expand your business or diversify your investment portfolio, Bajaj Finserv Platform provides the financial backing you need to achieve your goals. Explore your options today and take the next step towards financial success.

What do standard deviation and variance tell us?

Standard Deviation is the square root of variance, which measures the average squared deviations from the mean. Both quantify data spread or variability.

What makes a standard deviation 'good'?

A ‘good’ standard deviation varies depending on context and objectives. For investments, it depends on the investor's risk tolerance.

How can we understand what standard deviation means?

A higher standard deviation indicates more variability or risk, whereas a lower standard deviation suggests less variability around the mean.

What does having a standard deviation less than 1 indicate?

It indicates that the data points are closely clustered around the mean, implying low variability.

Why should we care about standard deviation?

It is a key measure of risk that helps investors understand the volatility of their investments.

What is the difference between mean deviation and standard deviation?

Mean deviation calculates the average absolute deviation from the mean, while standard deviation squares these deviations before averaging, providing a measure of spread that gives more weight to outliers.