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?
Standard deviation, often abbreviated as "std," is a key statistical measure that assesses the dispersion or variability of a set of data points. In simpler terms, it indicates how much individual data points differ from the mean (average) value. A low standard deviation signifies that the data points tend to be close to the mean, suggesting stability, while a high standard deviation indicates greater variability and potential volatility.
In the context of investments, particularly mutual fund schemes, standard deviation serves as a crucial tool for evaluating the risk associated with a fund’s returns over a specified period. Investors use this measure to understand how much the returns can fluctuate, which in turn informs their decision-making process. A fund with a high standard deviation may offer the potential for higher returns but also comes with increased risk due to its volatility. Conversely, a fund with a low standard deviation is typically seen as a more stable investment, albeit with potentially lower returns. Therefore, understanding standard deviation helps investors assess their risk tolerance and make informed choices aligned with their financial goals.
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:
- Collect historical returns: Gather the mutual fund's historical returns for a chosen period.
- Calculate the mean return: Sum all the returns and divide by the number of periods to find the average return.
- Find deviations: Subtract the mean return from each individual return to get the deviations.
- Square the deviations: Square each deviation to eliminate negative values.
- Average the squared deviations: Sum the squared deviations and divide by the number of periods, resulting in the variance.
- 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.
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.
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.
How does standard deviation help in portfolio management?
Standard deviation plays a vital role in portfolio management by providing insights into the risk and volatility of investment returns. It quantifies the degree of variation in asset prices, helping investors assess how much the returns of individual securities or the entire portfolio can deviate from the expected average. By understanding the standard deviation, portfolio managers can gauge the potential risk associated with different investments, enabling them to make informed decisions about asset allocation.
In portfolio construction, standard deviation aids in identifying the right balance between risk and return. For example, a portfolio heavily weighted in high-standard deviation assets may offer higher returns but also exposes investors to significant volatility. Conversely, a portfolio composed of low-standard deviation assets tends to be more stable but may generate lower returns.
Additionally, standard deviation assists in diversification strategies. By combining assets with varying standard deviations, managers can reduce overall portfolio risk. This diversification effect occurs because assets often do not move in tandem; when one investment declines, another may rise, thereby smoothing overall portfolio returns. Ultimately, standard deviation is essential for assessing risk, enhancing decision-making, and achieving optimal investment outcomes in portfolio management.
Things to remember about standard deviation
When considering standard deviation, several key points are essential to understand its significance and application. Firstly, standard deviation measures the dispersion of data points around the mean, indicating the degree of variability within a dataset. A smaller standard deviation suggests that the data points are clustered closely to the mean, indicating lower volatility, while a larger standard deviation indicates greater variability and risk.
Secondly, standard deviation is sensitive to outliers. Extreme values can disproportionately influence the measure, leading to potential misinterpretations of risk. Therefore, it's important to consider the overall distribution of data when evaluating standard deviation.
Thirdly, in the context of investments, standard deviation is often used to assess the risk associated with returns on mutual funds or other securities. While a higher standard deviation may signal greater potential for return, it also implies increased risk, so investors should align their investments with their risk tolerance.
Lastly, standard deviation should not be viewed in isolation. It is most effective when used alongside other statistical measures, such as the mean, variance, and correlation, to gain a comprehensive understanding of investment performance and risk.
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.
