*When you invest in securities whose values fluctuate every day, your investment is prone to volatility risks. Some days your investments may yield positive returns, while the returns can be negative on other days.*

Moreover, the severity of price fluctuations should also be noted to understand how high the volatility is. The concept of standard deviation is used herein to find out the volatility of market-linked securities like stocks, mutual funds, etc.

Let us read this more in detail.

## What is standard deviation?

Standard deviation is the measurement of the deviations of different data points in a data set corresponding to the mean of the data set. If you apply the same concept to the value of securities, standard deviation helps measure how the security values have deviated from their mean.

Confused? Let’s break it down.

A data set is a set of values like the price of a stock on five different days. The mean of the data set is the average of the values. So, if the data set contains the stock price over the last five days, the mean would be the average stock price over that period. Standard deviation is then measured to see how the stock prices have deviated from the average price.

## Calculation of standard deviation

Standard deviation can be calculated using a mathematical formula. It is as follows –

Standard deviation = √Variance

The variance of a set of values is calculated using the following formula –

Variance = ∑(Rv – Rm) ^2 / (N – 1)

In this formula,

Rv = The individual rate of return in the data set

Rm = The average rate of return of data set

N = Number of values contained in the data set

Now, let’s understand the calculation of standard deviation using an example.

Suppose you buy one share of HDFC Bank Limited on 14 March 2022 at the closing price of Rs. 1443. The closing price of the stock over the next five days and your profit/loss per day is as follows –

The average return over the 5-day period is (-1.31 + 0.35% + 2.56% + 3.05% + 3.53%) / 5 = 1.636%

The variance of the return over the 5-day period would be calculated as follows –

∑ {(-1.31 – 1.636) ^ 2 + (0.35 – 1.636) ^ 2 + (2.56 – 1.636) ^ 2 + (3.05 – 1.636) ^ 2 + (3.53 – 1.636) ^ 2} / (5 – 1)

= ∑8.68 + 1.65 + 0.85 + 1.99 + 3.59 / 4

= 4.19%

The standard deviation, on the other hand, would be the square root of the variance.

Standard deviation = √4.19% = √0.0419 = 0.20 = 20%

The standard deviation of 20% means that the value of the stock of HDFC Bank would fluctuate by 20% over a one-day period.

## What does standard deviation measure in a portfolio?

When the concept of standard deviation is applied to a portfolio, it gives you the idea of volatility risk in that portfolio.

Take a mutual fund portfolio, for instance. A higher standard deviation value means that the fund is highly volatile and risky. On the other hand, funds with a low standard deviation have low risks. Thus, you can choose a suitable mutual fund scheme based on your risk appetite by assessing its standard deviation. Here’s how –

- If you have a high-risk appetite and are looking for aggressive returns, you can choose mutual funds that have a high value of standard deviation
- If you have a low-risk appetite and want stable and consistent returns, choose a fund that has a low standard deviation
- For moderate risk appetites, funds with a moderate standard deviation are better

The knowledge of standard deviation can, thus, help you pick the right investments based on your risk appetite.

For instance, say you have a low-risk appetite and are considering investing your money. You have two fund options, both of which have an average rate of return of 10%. The standard deviation, however, of both these funds varies. Fund A has a standard deviation of 6% and Fund B has a deviation of 8%.

Since you have a low tolerance for risk, you should pick Fund A, which has a lower standard deviation and gives a better return in a downward trend.

You can also apply standard deviation to your own portfolio. It would give you an idea of the risk that your portfolio carries. If you consider the standard deviation of each investment, the higher the standard deviation, the more volatile the asset is considered to be. On the other hand, you can also check the standard deviation of your overall portfolio. This is called portfolio standard deviation and is calculated using three main inputs –

- The standard deviation of each asset in your portfolio
- The weight of each asset in your overall portfolio
- The correlation between the assets of your portfolio

If the standard deviation of your overall portfolio is high, it means that you have a high-risk portfolio which is prone to market volatility. On the other hand, a portfolio with a low standard deviation depicts stability in a volatile market.

How does one assess portfolio risk? Read all about it in our article titled How to determine Portfolio Risk in our article on the TejiMandi blog.

## Limitations of standard deviation

Though useful, standard deviation has its limitations too. For starters, the value of standard deviation is calculated using historical data. History alone cannot be an indicator of future performance. While a stock or a fund might be performing poorly in the past, it might correct in the future. As such, standard deviation does not indicate the future performance of the asset.

Secondly, in the case of mutual funds, standard deviation measures the consistency of the fund’s performance. It, however, does not depict how the fund performs against its benchmark. For that, you have to check the fund’s beta along with its standard deviation. It is pretty much the same for smallcases.

Wondering how a smallcase is different from a mutual fund as both are diversified buckets of investments? Read in our article titled Smallcase vs Mutual funds in the TejiMandi blog.

Thirdly, when applying standard deviation to your portfolio, if you have a diversified portfolio, standard deviation might not give an accurate answer.

Lastly, standard deviation is calculated assuming that the values follow a normal distribution pattern. If an asset’s value does not follow the normal distribution pattern, the calculation of standard deviation would not be accurate.

### The bottom line

Though statistical in nature, standard deviation can help you measure the volatility of an asset and even of your overall portfolio. When investing in stocks or mutual funds, it is thus, recommended to check the standard deviation to gauge how risky the asset is. However, do consider other metrics too, along with standard deviation, to correctly assess an asset’s volatility. Remember, investing as per your risk appetite is important when you are investing in market-linked securities so that a rough patch does not cause you immense financial pain.

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