# Standard Deviation in Trading: Calculations, Use Cases, Examples and more

Whether you're a seasoned trader or just starting in quantitative finance, grasping the concept of standard deviation is crucial. Standard deviation helps traders with volatility measures in finance. With this helpful tool, traders can make sense of market fluctuations and manage risks effectively.

In this blog, we break down the idea of standard deviation by imparting all the necessary information related to standard deviation in the trading domain. Let's dive into the exciting journey of understanding standard deviation’s role in trading as we cover:

## What is standard deviation?

Let us see a famous quote defining standard deviation by John Bollinger, a well-known figure in the trading world, primarily recognised for developing the widely-used technical analysis tool known as Bollinger Bands.

"Standard deviation is a key tool for traders to quantify the uncertainty and risk in the market. It allows us to better understand the potential variability of returns and make informed decisions to manage our portfolios effectively." - John Bollinger

Definition of standard deviation

“The standard deviation (σ) is a measure that is used to quantify the amount of variation or dispersion of data from its mean.”

Let's simplify the concept of deviation from the mean.

In essence, deviation refers to how far a data point is from the average. Imagine we have a set of observations represented by the variable X, consisting of various values: x₁, x₂, ..., xn.

Now, let's consider two of these observations (as shown in the image below), x₁ and x₂, and their deviations from the mean of X.

Deviations are straightforward: they tell us if an observation is above or below the mean, shown by positive or negative values respectively.

What if we add up all these deviations?

Interestingly, they would balance out to zero due to the mix of positive and negative values. To overcome this, we square each difference to remove the sign and find their average. This yields the variance, indicating how spread out the data is.

Standard deviation, derived from the variance, provides a standardised measure of dispersion. It involves taking the positive square root of the variance. This process ensures we're dealing with values in the same units as the original data. In the following section, we'll delve into the formula for calculating standard deviation.⁽¹⁾

## Formula of standard deviation

The formula for calculating the standard deviation (denoted by σ) is as follows:

$$σ = \sqrt\sum(x_i-μ)^2/n)$$

$$\text{Where,}\\ σ\;\text{is the standard deviation}\\ x_i\;\text{represents each individual data point}\\ μ\;\text{is the mean of the data set}\\ Σ\;\text{denotes the sum of all the values}\\ n\;\text{is the total number of data points}$$

Going forward, we will discuss the calculation of standard deviation.

## How to calculate standard deviation?

To calculate the standard deviation using Python, you can utilise libraries such as pandas and numpy. Here's a step-by-step guide to calculate the standard deviation using historical price data:

### Step 1: Install Required Libraries and import packages

If you haven't already installed numpy, you can install it using pip:

### Step 2: Define an example data

Here we have taken an array of numbers to show the calculation.

### Step 3: Compute Standard Deviation

Output:

Standard Deviation of Data: 7.0710678118654755

We will now discuss some examples of the applications of standard deviation in general as well as in trading.

## Examples of applications of standard deviation

Let us check out the general examples of applying standard deviation before heading to the trade oriented example.

### General examples

The term standard deviation sounds like something you hear in a statistics class, but don’t dismiss it as an overly technical term just yet. It can be used in different aspects of our lives.

A teacher can use the standard deviation of marks of her students in an exam as a metric to assess the overall level of understanding of the subject. If the mean and standard deviation are both high, it indicates that, on average, students have a good understanding of the subject.

However, there would be many students who have scores that are much above and much below the average scores. In case the mean is high and the standard deviation is low, it indicates that the average scores are similar to the previous case.

The low standard deviation tells her that most students have scores that are close (i.e. slightly above and slightly below) to the mean. In weather forecasting, it can be used to compare the weather patterns in two or more regions.

If we compare the standard deviation of temperatures in Jaisalmer (which has extreme weather) with Mumbai (which has moderate weather), we would find that the former has more variability in temperature around the mean.

### Examples of application in trading

Example: Amazon (AMZN) Stock

• Volatility Analysis: Traders analysing Amazon's stock may calculate the standard deviation of its daily returns over a specific period, such as the past year. A higher standard deviation indicates greater price volatility, implying larger price swings.
For instance, if Amazon's stock has a daily standard deviation of 2% over the past year, it suggests that, on average, the daily price movements deviate by 2% from the mean daily return.
• Options Trading: Standard deviation is a crucial factor in options pricing models like the Black-Scholes model. Traders estimating the implied volatility of Amazon's options contracts may use historical standard deviation as a reference point.
For instance, if the historical standard deviation of Amazon's stock is 20% and the implied volatility of its options is significantly higher, it might suggest that options are relatively expensive, potentially presenting trading opportunities.
• Risk Management: Investors holding Amazon's stock in their portfolio may use standard deviation to assess and manage risk. By calculating the standard deviation of Amazon's daily returns, investors can estimate the potential range of price movements and set stop-loss orders or position sizes accordingly.
For instance, if an investor is comfortable with a certain level of risk, they may adjust their position size based on Amazon's historical standard deviation to align with their risk tolerance.

## Use cases of standard deviation

Here are the use cases of standard deviation in risk assessment, volatility analysis, and portfolio management:

### Risk Assessment

• Credit Risk Evaluation: In financial institutions, standard deviation is used to assess the variability of returns on loans or investments. A higher standard deviation indicates higher volatility, implying greater risk. Lenders may use standard deviation to evaluate the creditworthiness of borrowers and determine appropriate interest rates.
• Market Risk Management: Standard deviation helps quantify market risk by measuring the variability of asset prices or portfolio returns. Traders and investors use standard deviation to assess the potential downside risk of their investments and implement risk mitigation strategies accordingly.

### Volatility Analysis

• Options Pricing: Standard deviation is a key input in options pricing models like the Black-Scholes model. A higher standard deviation implies higher implied volatility, leading to higher option premiums. Traders use standard deviation to estimate the future volatility of underlying assets and determine the fair value of options contracts.
• Technical Analysis: Standard deviation is used to calculate volatility indicators such as Bollinger Bands. These bands consist of a moving average and upper and lower bands representing standard deviations from the mean. Traders use Bollinger Bands to identify potential buy or sell signals based on volatility levels.

### Portfolio Management

• Diversification: Standard deviation is used to measure the risk of individual assets and portfolios. By diversifying investments across assets with low or negatively correlated returns, investors can reduce portfolio risk. Standard deviation helps investors assess the effectiveness of diversification strategies and optimise asset allocation to achieve desired risk-return profiles.
• Risk-adjusted Performance: Standard deviation is used to calculate risk-adjusted performance measures such as the Sharpe ratio and the Sortino ratio. These ratios quantify the excess return generated per unit of risk (measured by standard deviation). Portfolio managers use these metrics to evaluate investment strategies and compare the risk-adjusted returns of different portfolios.⁽²⁾

Let us now head to the essential components concerning standard deviation that are used in the calculation part.

## Essential components of standard deviation

Let us now see the essential components that are required for calculating standard deviation in the trading domain.

These are:

### Unit of standard deviation

The unit of standard deviation would be the same as the unit of our data. This makes it easier to interpret compared to the variance. In the next section, we do a detailed comparison between these two measures of dispersion.

### Standard deviation vs Variance

$$The\;variance(σ ^2)\;of\;a\;random\;variable\;X\;is\;given\;by\;the\;formula\;below:\\Variance=\frac{\sum_{i=1}^N(x_i-μ)^2}{N}$$

As we can see, by its very construction, the variance is in the square of the original unit. This means that if we are dealing with distances in kilometres, the unit of variance would be in square kilometres.

Now, square kilometres may be easy to visualise as a unit, but what about year2 or IQ2, if we are working with ages or IQs of a group? They are harder to interpret. Hence, it makes sense to use a measure that can be comparable to the data on the same scale/units, like the standard deviation.

Standard deviation is calculated as the square root of variance. It has the same unit as our data and this makes it easy to use and interpret. For example, consider a scenario where we are looking at a dataset of the heights of residents of a neighbourhood. Assume that the heights are normally distributed with a mean of 165 cm and a standard deviation of 5 cm.

We know that for a normal distribution,

• 68% of the data points fall within one standard deviation,
• 95% within two standard deviations, and
• 99.7% fall within three standard deviations from the mean.

Thus, we can conclude that the height of almost 68% of the residents would lie between one standard deviation from the mean, i.e., between 160 cm (mean – sd) and 170 cm (mean + sd).⁽³⁾

### Standard deviation for sample data - Bessel's correction

When calculating the standard deviation of a population, we use the formula discussed above. However, we modify it slightly when dealing with a sample instead.

This is because the sample is much smaller compared to the entire population. To account for differences in a randomly selected sample and the entire population, we ‘unbias’ the calculation by using '(n-1)' instead of 'n' in the denominator of equation 1. This is referred to as Bessel's correction.⁽⁴⁾

Thus, we use the following formula to calculate the sample standard deviation (s).

$$s= \sqrt\frac{\sum_{i=1}^n (x_i-\bar x)^2}{n-1}$$

$$\text{Where,}\\ x_i = \text{value of the } i\text{th point in the sample}\\ \bar{x} = \text{sample mean}\\ n = \text{total number of data points in the sample}\\ \text{Do note that as the sample size } n \text{ gets larger, the impact of dividing by } (n - 1) \text{ or } n \text{ will become lesser.}$$

Now, we can discuss the standard deviation in trading as a measure of the volatility.

## Standard deviation in trading as a measure of volatility

In trading and finance, it is important to quantify the volatility of an asset. An asset’s volatility, unlike its return or price, is an unobserved variable.

Standard deviation has a special significance in risk management and performance analysis as it is often used as a proxy for the volatility of a security. For example, the well-established blue-chip securities have a lower standard deviation in their returns compared to that of small-cap stocks.

On the other hand, assets like cryptocurrency have a higher standard deviation, as their returns vary widely from their mean.

Moving forward, let us discuss the computation of the annualised volatility of stocks using Python.

## Computing annualised volatility of stocks using Python

Let us now compute and compare the annualized volatility for two Indian stocks namely, ITC and Reliance. We begin with fetching the end of day close price data using the yfinance library for a period of the last 5 years:

Output:

Date           Adj Close
2021-10-19     245.949997
2021-10-20     246.600006
2021-10-21     244.699997
2021-10-22     236.600006
2021-10-25     234.350006

Output:

Date          Adj Close
2021-10-19   2731.850098
2021-10-20   2700.399902
2021-10-21   2622.500000
2021-10-22   2627.399902
2021-10-25   2607.300049

Below, we calculate the daily returns using the pct_change() method and the standard deviation of those returns using the std() method to get the daily volatilities of the two stocks:

Output:

Date         Adj Close   Returns
2016-10-25   511.991608       NaN
2016-10-26   508.709717 -0.006410
2016-10-27   506.127686 -0.005076
2016-10-28   509.144104  0.005960
2016-11-01   507.237701 -0.003744
...                 ...       ...
2021-10-19  2731.850098  0.008956
2021-10-20  2700.399902 -0.011512
2021-10-21  2622.500000 -0.028848
2021-10-22  2627.399902  0.001868
2021-10-25  2607.300049 -0.007650

Output:

Date            Adj Close	 Returns
2016-10-26	508.709717	-0.006410
2016-10-27	506.127686	-0.005076
2016-10-28	509.144104	 0.005960
2016-11-01	507.237701	-0.003744
2016-11-02	494.086243	-0.025928

In general, the volatility of assets is quoted in annual terms. So below, we convert the daily volatilities to annual volatilities by multiplying with the square root of 252 (the number of trading days in a year):

Output:

The annualized standard deviation of the ITC stock daily returns is: 27.39%
The annualized standard deviation of the Reliance stock daily returns is: 31.07%

Now we will compute the standard deviation with Bessel's correction. To do this, we provide a ddof parameter to the Numpy std function. Here, ddof means 'Delta Degrees of Freedom'.

By default, Numpy uses ddof=0 for calculating standard deviation- this is the standard deviation of the population. For calculating the standard deviation of a sample, we give ddof=1, so that in the formula, (n−1) is used as the divisor. Below, we do the same:

Output:

The annualized standard deviation of the ITC stock daily returns with Bessel's correction is: 27.39%

The annualized standard deviation of the Reliance stock daily returns with Bessel's correction is: 31.07%

Thus, we can observe that, as the sample size is very large, Bessel's correction does not have much impact on the obtained values of standard deviation. In addition, based on the given data, we can say that the Reliance stock is more volatile compared to the ITC stock.

Note: The purpose of this illustration is to show how standard deviation is used in the context of the financial markets, in a highly simplified manner. There are factors such as rolling statistics (outside the scope of this write-up) that should be explored when using these concepts in strategy implementation.

### The z-score

Z-score is a metric that tells us how many standard deviations away a particular data point is from the mean. It can be negative or positive. A positive z-score, like 1, indicates that the data point lies one standard deviation above the mean and a negative z-score, like -2, implies that the data point lies two standard deviations below the mean.

In financial terms, when calculating the z-score on the returns of an asset, a higher value of z-score (either positive or negative) means that the return of the security differs significantly from its mean value. So, the z-score tells us how well the data point conforms to the norm.

Usually, if the absolute value of a z score of a data point is very high (say, more than 3), it indicates that the data point is quite different from the other data points. We use standard deviation to calculate the z-score using the following formula in case we have sample data:

$$z=\frac{x_i-\bar x}{s}$$

$$Where,\\ x_i = a\; single\; data\; point \\ \bar x = the\; sample\; mean\\ s = the\; sample\; standard\; deviation$$

Below we calculate and plot the z-scores for the ITC stock returns using the above formula in Python:

Output:

From the above figure, we observe that around March of 2020, the ITC stock returns had a z-score reaching below -3 several times, indicating that the returns were more than 3 standard deviations below the mean for the given data sample. As we know this was during the sell-off triggered by the COVID pandemic.

In addition, a standardised measure like the z-score is used widely to generate signals for mean-reverting trading strategies such as pairs trading.

Also, one can use the z score function from the scipy.stats module to calculate the z-scores as follows:

Output:

Date		 Adj Close	 Returns     Returns_zscore
2021-10-19	2731.850098	 0.008956	 0.380491
2021-10-20	2700.399902	-0.011512	-0.665617
2021-10-21	2622.500000	-0.028848	-1.551575
2021-10-22	2627.399902	 0.001868	 0.018247
2021-10-25	2607.300049	-0.007650	-0.468222

### Value at Risk

Value at Risk (VaR) is an important financial risk management metric that quantifies the maximum loss that can be realized in a given time with a given level of confidence/probability for a given strategy, portfolio or trading desk.

It can be computed in three ways, one of which is the variance-covariance method. In this method, we assume that the returns are normally distributed for the lookback period. Understand how VaR calculation can help enhance your skills in financial risk management.

The idea is simple. We calculate the z-score of the returns of the strategy based on the confidence level we want and then multiply it with the standard deviation to get the VaR. To get the VaR in dollar terms, we can multiply it with the investment in the strategy.

For example, if we want the 95% confidence VaR, we are essentially finding the cut-off point for the worst 5% of the losses from the returns distribution. If we assume that the stock returns are normally distributed, then their z-scores will have a standard normal distribution. So, the cut-off point for the worst 5% returns is -1.64:

Thus the 1-year 95% VaR of a simple strategy of investing in the ITC stock is given by:

VaR = (−1.64) ∗ (s) ∗ investment

where, s is the annualized standard deviation of the ITC stocks.

Output:

z_score_cut_off
-1.6448536269514722
VaR = z_score_cut_off * annual_standard_deviation * initial_investment
VaR
-45045.34407051503

Thus, we can say that the maximum loss that can be realised in 1 year with 95% confidence is INR 45045. Of course, this was calculated under the assumption that ITC stock returns follow a normal distribution.

### Confidence intervals

Another common use case for standard deviation is in computing the confidence intervals. In general, when we work with data, we assume that the population from which the data has been generated follows a certain distribution and the population parameters for that distribution are not known. These population parameters have to be estimated using the sample.

For example, the mean daily return of the ITC stock is a population parameter, which we try to estimate using the sample mean. This gives us a point estimate. However, financial market forecasts are probabilistic, and hence, it would make more sense to work with an interval estimate rather than a point estimate.

A confidence interval gives a probable estimated range within which the value of the population parameter may lie. Assuming the data to be normally distributed, we can use the empirical rule to describe the percentage of data that falls within 1, 2, and 3 standard deviations from the mean.

1. About 68% of the values lie between -1 and +1 standard deviation from the mean.
2. About 95% of the values lie within two standard deviations from the mean.
3. About 99.7% of the values lie within three standard deviations from the mean.

Output:

The 95% confidence interval of the ITC stock daily returns is: [-0.03,0.03]

Thus, we can say with 95% confidence that the stock’s daily returns will lie in a range of  -3% and +3% (assuming the ITC stock returns are normally distributed).

Let us now discuss the real world case studies of standard deviation in the trading domain to make the concept clearer.

## Real-world Case Studies of standard deviation

Here are a couple of real-world case studies demonstrating the application of standard deviation in different markets and its impact on trading decisions:

### Case Study: Standard Deviation in Forex Trading

• Application: Forex traders often use standard deviation to measure the volatility of currency pairs and assess the risk associated with their trading positions. For example, consider a trader who is analysing the EUR/USD currency pair. By calculating the standard deviation of the pair's daily returns over a specific period, the trader can gauge the level of price volatility.
• Impact on Trading Decisions: If the standard deviation of EUR/USD's daily returns is relatively high, it indicates greater price volatility and potentially higher risk. In such cases, the trader may adjust their position size or set wider stop-loss orders to account for the increased volatility. Conversely, if the standard deviation is low, the trader may opt for tighter risk management measures.

### Case Study: Standard Deviation in Stock Market Trading

• Application: Stock market traders use standard deviation to assess the risk and volatility of individual stocks or entire portfolios. For instance, consider an investor analysing the standard deviation of Apple Inc. (AAPL) stock returns over the past year. By calculating the standard deviation, the investor can quantify the level of price variability in AAPL stock.
• Impact on Trading Decisions: If the standard deviation of AAPL's returns is high, it suggests that the stock experiences significant price fluctuations, indicating higher risk. In response, traders may adopt risk mitigation strategies such as diversification or hedging. Conversely, a low standard deviation implies lower volatility and may lead traders to adjust their trading strategies accordingly, potentially by pursuing more aggressive trading opportunities.

Now that you are familiar with most of the standard deviation related concepts, in the next section you will see how correlation of standard deviation with other indicators can help.

## Correlation of standard deviation with other indicators

The correlation of standard deviation with other indicators can provide valuable insights into market dynamics and help traders make informed decisions. Here are some common indicators with which standard deviation is often correlated:

• Mean (Average): The mean and standard deviation are closely related. A higher standard deviation indicates greater variability of data points around the mean, while a lower standard deviation suggests less variability.
• Variance: Variance is the square of the standard deviation. As such, they are directly related. Higher variance implies a higher dispersion of data points from the mean, leading to a higher standard deviation.
• Volatility Measures: Standard deviation is a key component of volatility measures such as historical volatility and implied volatility. These measures assess the magnitude of price fluctuations in financial instruments. High standard deviation values indicate high volatility, while low values suggest low volatility.
• Bollinger Bands: Bollinger Bands consist of a moving average line and upper and lower bands, which are typically set at a certain number of standard deviations above and below the moving average. Changes in standard deviation affect the width of the bands, with wider bands indicating higher volatility and narrower bands suggesting lower volatility.
• Sharpe Ratio: The Sharpe ratio measures the risk-adjusted return of an investment. It is calculated by dividing the excess return (return above risk-free rate) by the standard deviation of returns. A higher standard deviation leads to a lower Sharpe ratio, indicating a higher risk for a given level of return.
• Sortino Ratio: Similar to the Sharpe ratio, the Sortino ratio measures risk-adjusted return but focuses only on downside risk, considering only the standard deviation of negative returns. A higher standard deviation of negative returns leads to a lower Sortino ratio, indicating higher downside risk.

Let us now see some limitations of standard deviation in trading.

## Limitations of standard deviation in trading

While standard deviation is a widely used and valuable tool in trading, it does have several limitations that traders should be aware of:

• Assumption of Normal Distribution: Standard deviation assumes that the data follows a normal distribution. However, financial markets often exhibit non-normal distributions, such as fat tails or skewness. In such cases, the standard deviation may not accurately capture the true risk and volatility of the market.
• Sensitivity to Outliers: Standard deviation is highly sensitive to outliers, or extreme values, in the data. A single outlier can significantly affect the standard deviation, leading to potentially misleading results. Traders should be cautious when interpreting standard deviation in the presence of outliers.
• Equal Weighting of Data Points: Standard deviation treats all data points equally, regardless of their significance or relevance. In financial markets, recent data points may be more informative than older ones, especially in fast-moving markets. Standard deviation may not adequately reflect changes in market conditions or sentiment.
• Limited Interpretation of Volatility: Standard deviation measures total volatility, including both upside and downside movements. However, traders may be more interested in downside volatility, as it represents the risk of losses. Other measures such as the downside deviation or semi-deviation may provide more relevant insights into downside risk.
• Lack of Context: Standard deviation provides a numerical measure of volatility but does not provide any context or explanation for the observed variability. Traders should complement standard deviation with qualitative analysis and market knowledge to fully understand the drivers of volatility and risk.
• Inability to Capture Non-linear Relationships: Standard deviation assumes a linear relationship between data points, which may not always hold true in financial markets. Complex interactions and non-linear relationships between variables may not be fully captured by standard deviation alone.

Overall, while standard deviation is a useful tool for measuring volatility and risk in trading, traders should be mindful of its limitations and use it in conjunction with other tools and techniques for a comprehensive analysis of market conditions.

Let us now find out some common misconceptions about standard deviation in trading next.

Several misconceptions about standard deviation exist in trading, which can lead to misinterpretation of market data and incorrect decision-making. Here are some common misconceptions:

• Standard Deviation Predicts Future Returns: One common misconception is that high standard deviation implies high returns and vice versa. While volatility can indicate potential opportunities for maximising returns, it does not guarantee future returns. High volatility can also lead to significant losses if not managed properly.
• Standard Deviation is the Only Measure of Risk: While standard deviation is widely used to measure volatility and risk, it is not the only measure of risk. Other factors such as correlation, liquidity, and fundamental analysis should also be considered when assessing risk in trading.
• Standard Deviation Reflects Market Direction: Some traders mistakenly believe that changes in standard deviation indicate the direction of the market. However, standard deviation measures volatility, not market direction. It is possible for standard deviation to increase or decrease even if the market remains relatively unchanged.
• Standard Deviation is Static: Another misconception is that standard deviation remains constant over time. In reality, volatility can change dynamically in response to various factors such as news events, market sentiment, and economic conditions. Traders should regularly monitor and adjust their risk management strategies accordingly.
• Standard Deviation Measures Risk in Isolation: While standard deviation quantifies the variability of returns, it does not account for other factors that may influence risk, such as leverage, position size, and trading frequency. Traders should consider these factors holistically when assessing risk in their portfolios.
• Standard Deviation Provides Complete Information: Traders may mistakenly believe that standard deviation provides a comprehensive understanding of market risk. While standard deviation is a useful tool, it has limitations and should be used in conjunction with other risk measures and analysis techniques for a more accurate assessment of market conditions.

Now let us discuss the risk management tips for using standard deviation next. These tips can help traders successfully use this helpful concept, which is, standard deviation.

## Risk management tips for using standard deviation

Using standard deviation as part of a risk management strategy can help traders better understand and mitigate risks in their trading activities.

Here are some tips for incorporating standard deviation into your risk management approach:

• Set Risk Tolerance Levels: Determine your risk tolerance level based on factors such as your investment objectives, time horizon, and personal risk preferences. Use standard deviation to quantify the potential volatility and downside risk of your trades and investments.
• Use Stop-loss Orders: Set stop-loss orders based on the standard deviation of asset prices or portfolio returns. Place stop-loss levels at a certain number of standard deviations away from the mean to limit losses and protect capital in case of adverse price movements.
• Position Sizing: Adjust position sizes based on the standard deviation of asset returns. Increase position sizes for assets with lower volatility and decrease position sizes for assets with higher volatility to maintain consistent risk exposure across your portfolio.
• Diversify Your Portfolio: Diversification can help reduce overall portfolio risk by spreading investments across different asset classes, sectors, and geographical regions. Use standard deviation to assess the correlation between assets and ensure that your portfolio is adequately diversified.
• Monitor and Rebalance Regularly: Monitor the standard deviation of asset prices and portfolio returns regularly to identify changes in market conditions and adjust your risk management strategy accordingly. Rebalance your portfolio periodically to maintain desired risk levels and adapt to evolving market trends.
• Consider Risk-adjusted Performance: Evaluate the risk-adjusted performance of your trades and investments using metrics such as the Sharpe ratio or Sortino ratio, which take into account both returns and volatility. Aim to achieve positive risk-adjusted returns by optimising your risk-return trade-off.
• Stay Informed and Adapt: Stay informed about market news, economic indicators, and geopolitical events that may impact asset prices and market volatility. Be prepared to adjust your risk management strategy in response to changing market conditions and unexpected developments.

By incorporating these risk management tips into your trading approach and leveraging standard deviation as a tool for measuring and managing risk, you can improve your chances of achieving long-term success and preserving capital in the financial markets.

### Conclusion

Standard deviation is pivotal for traders, offering insights into volatility, risk, and informed decision-making. It quantifies uncertainty and variability of returns, aiding in options pricing, portfolio management, and volatility analysis.

Despite its usefulness, traders must acknowledge its limitations and supplement it with qualitative judgement. By integrating standard deviation into risk management practices, traders can navigate market complexities more effectively, optimise risk-return profiles, and strive for success in financial markets.

If you wish to learn more about standard deviation, you can enrol into the course on Volatility Trading Strategies for Beginners. With this course, you will learn how volatility can be your friend if you have the right tools and knowledge. In this course, you will learn four different ways to measure volatility, namely ATR, standard deviation, VIX and Beta. Hence, you will learn how to set dynamic stop loss and take profit levels, hedge your portfolio using VIX and select stocks in your portfolio.