Standard Deviation

Standard deviation is a statistical measure, expressed as a percentage, that indicates how much the returns of a mutual fund scheme are expected to deviate from its average annual returns. Mutual funds with a lower standard deviation, typically in the range of 1-10, are considered less volatile.
EXPLORE FUNDS
Standard Deviation in Mutual Fund
EXPLORE FUNDS
3 mins read
02-January-2026

Standard deviation, typically presented as a percentage, indicates the extent to which the returns of a mutual fund scheme may differ from its average annual returns. Utilised with historical returns, it serves as a gauge for the fund's volatility over a specific timeframe. Let us navigate through its definition, formula and inner workings to grasp its significance in the financial markets and its impact on institutions.

What is Standard Deviation?

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.

How does Standard Deviation work?

Consider an example to elucidate the concept of standard deviation: If a mutual fund scheme displays a standard deviation of 5 and an average return of 15%, it implies that the returns may fluctuate by up to 5% above (20%) or below (10%) the average.

Furthermore, a mutual fund exhibiting a low standard deviation over a period of 3 to 5 years suggests that the fund has maintained consistent returns over the long term.

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

How to calculate standard deviation of mutual fund?

Calculating the standard deviation of a mutual fund involves several steps:

  1. Collect historical returns: Gather the mutual fund's historical returns for a chosen period.
  2. Calculate the mean return: Sum all the returns and divide by the number of periods to find the average return.
  3. Find deviations: Subtract the mean return from each individual return to get the deviations.
  4. Square the deviations: Square each deviation to eliminate negative values.
  5. Average the squared deviations: Sum the squared deviations and divide by the number of periods, resulting in the variance.
  6. Square root of variance: Take the square root of the variance to obtain the standard deviation.

This metric measures the volatility of the fund's returns, helping investors assess the risk involved. A higher standard deviation indicates greater volatility, while a lower one suggests more stable returns.

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.

Importance of Standard Deviation in mutual funds

Here's the significance of standard deviation in mutual funds:

  • Comprehensive risk assessment: Standard deviation offers a holistic evaluation of total risk, encompassing factors beyond market-related volatility, thus providing a broader perspective compared to beta.
  • Applicability across asset classes: Whether considering equity or debt schemes, standard deviation serves as a valuable tool to assess the variability in returns across different investment vehicles.
  • Risk alignment: Utilising standard deviation allows investors to align the risk level of a mutual fund with their individual risk tolerance, aiding in informed decision-making.
  • Predictive performance indicator: Standard deviation serves as a predictive indicator of a mutual fund's future performance. By analyzing the standard deviation value, investors can anticipate potential deviations in returns from the fund's mean or average returns.
  • Comparative analysis: Investors can employ standard deviation to compare funds within the same category. Significant deviations in standard deviation from similar funds may signal operational differences, offering insights into the relative performance of funds within the same segment.

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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 crucial metric in mutual funds, indicating the degree of variation or volatility in the fund's returns. A higher standard deviation signifies greater volatility, implying that the fund's returns fluctuate significantly from the average, presenting higher risk. Conversely, a lower standard deviation suggests more stable and predictable returns.

This measure helps investors assess the total risk associated with a mutual fund and compare it with other funds. By understanding standard deviation, investors can align their risk tolerance with their investment choices, ensuring a well-balanced portfolio.

Conclusion

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.

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Frequently asked questions 

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.

What is standard deviation in mutual funds?

Standard deviation is a statistical measure that reflects how much a mutual fund's returns deviate from its average return over time. In simpler terms, it tells you how volatile or risky the fund's performance can be.

Which standard deviation is good in a mutual fund?

A lower standard deviation generally indicates a less volatile fund with returns that stay closer to its average. Conversely, a higher standard deviation suggests a more volatile fund with returns that can fluctuate significantly. There's no single "good" standard deviation, as it depends on your risk tolerance. Aggressive investors might be comfortable with higher volatility (higher standard deviation) for potentially higher returns, while conservative investors may prefer lower volatility (lower standard deviation) for more stability.

How do you calculate standard deviation for mutual funds?

Calculating standard deviation involves complex statistical formulas. However, you don't necessarily need to do it yourself. Most financial websites and mutual fund platforms display the standard deviation of a fund over various periods (e.g., 1 year, 5 years).

What does the standard deviation of a fund tell you?

The standard deviation of a mutual fund provides valuable insights into the fund's risk profile. Here's what it tells you:

  • Potential Volatility: A higher standard deviation suggests the fund's returns could swing more dramatically, with periods of high gains and losses.
  • Risk-Return Trade-off: Generally, funds with higher potential returns tend to have higher standard deviation (more risk).
  • Investment Strategy: The type of assets a fund invests in can influence its standard deviation. For example, aggressive growth funds typically have higher standard deviation compared to stable value funds.

By understanding standard deviation, you can make more informed investment decisions based on your risk tolerance and financial goals.

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.

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.

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