Standard Deviation in Portfolio Management: Meaning, Formula & Example

What is Standard Deviation?

Standard deviation in investing is a statistical measure that shows how much an investment’s returns deviate from its average return over a given period. In simple terms, it tells investors how much a stock, mutual fund, or portfolio’s returns fluctuate. A higher standard deviation means wider price swings, while a lower standard deviation indicates more stable and predictable returns.

Standard deviation is important because it enables investors to assess volatility, compare different investments, and understand the consistency of returns relative to expectations. Since volatility reflects how sharply prices move up or down, it is closely linked to risk. Investments with higher volatility and standard deviation carry greater uncertainty and a potential for sharp losses, while lower volatility generally suggests lower risk and steadier performance, making standard deviation a key tool in risk-aware investment decision-making.

How Standard Deviation Measures Portfolio Risk

Standard deviation measures portfolio risk by showing how widely a portfolio’s returns move around their average (mean) return. A high standard deviation indicates large fluctuations, meaning the portfolio is more volatile and carries higher risk, while a low standard deviation suggests returns stay closer to the mean, reflecting stability and lower risk.

The mean represents the portfolio’s average return, and standard deviation measures how consistently actual returns differ from this average, helping investors judge the reliability of performance. While variance and standard deviation both measure dispersion, variance is the average of squared deviations from the mean and is expressed in squared units, making it harder to interpret.

Standard deviation is simply the square root of variance, expressed in the same units as returns, which is why it is more commonly used by investors to evaluate portfolio risk.

How to Calculate 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.

Standard Deviation vs Other Risk Indicators

Standard Deviation vs Beta

Standard deviation measures the total volatility of an investment or portfolio by capturing both market-wide and asset-specific fluctuations, while beta measures only systematic risk, showing how sensitive an asset is to overall market movements. A high standard deviation indicates large price swings, whereas a high beta suggests the asset tends to move more aggressively than the market. While standard deviation is useful for understanding absolute risk, beta is better suited for comparing market-related risk relative to a benchmark index.

Standard Deviation vs Sharpe Ratio

Standard deviation focuses solely on volatility, whereas the Sharpe ratio combines risk and return to evaluate risk-adjusted performance. The Sharpe ratio uses standard deviation as its risk component but adds excess return over the risk-free rate, making it more practical for comparing investments with different return profiles. An investment may have high standard deviation, but if returns are strong enough, it can still deliver an attractive Sharpe ratio.

Standard Deviation vs Sortino Ratio

Standard deviation treats both upward and downward price movements as risk, while the Sortino ratio considers only downside volatility. This makes the Sortino ratio more relevant for investors concerned primarily with losses rather than overall fluctuations. While standard deviation provides a broad view of volatility, the Sortino ratio offers a more refined measure of risk by focusing only on negative deviations from the target or minimum acceptable return.

Final Thoughts

Standard deviation is a crucial risk metric that helps investors understand return volatility and make informed investment decisions. Investors should track standard deviation when comparing mutual funds, building portfolios, and assessing risk tolerance, especially during volatile market phases. Standard deviation metrics can be easily viewed on mutual fund fact sheets, brokerage platforms, financial websites, and tools like fund screeners, making it a practical and accessible indicator for everyday investing.

*The article is for information purposes only. This is not investment advice. 

*Disclaimer: Teji Mandi Disclaimer

FAQs

What is the standard deviation in investment?

In investing, standard deviation measures an asset’s volatility by showing how much returns fluctuate from the average; higher values indicate greater risk, while lower values suggest steadier, more predictable returns.

How to calculate standard deviation in a portfolio?

Portfolio standard deviation is calculated using asset weights, individual asset standard deviations, and the correlation between assets, applied through the portfolio standard deviation formula.

What is a good standard deviation for a mutual fund?

A good standard deviation depends on the fund category; lower SD is generally preferred for debt and conservative funds, while higher SD may be acceptable for equity funds with higher return potential.

Does diversification reduce standard deviation?

Yes, diversification can reduce overall portfolio standard deviation when assets with low or negative correlation are combined.

Does high standard deviation always mean high risk?

Not always; high standard deviation indicates higher volatility, but if accompanied by strong and consistent returns, the investment may still offer attractive risk-adjusted performance.