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Standard Deviation- Meaning, Calculation and How to interpret?

standard deviation
standard deviation

What is the standard deviation?

Standard deviation is a statistical measure that quantifies the spread of the individual dataset from its mean. Here, the mean is the average of the dataset. If a dataset is further away from its mean, it means there are a higher deviation and vice versa. 

How to calculate the standard deviation?

 It is the square root of variance. 

  1. Calculate the mean by adding all the datapoints and dividing by number of datapoints
  2. Calculate the variance of each datapoint from the mean. Here, subtract each datapoint value with the mean
  3. Calculate the square root of all the variances and divide by (N-1). Here, N-1 is the number of datapoints minus 1
  4. Calculate the square root of the variance calculated above. This is the standard deviation

Formula:

Standard Deviation = [1/n *  (xi – x)2]1/2

where:

xi = each datapoint

x = mean

n = number of datapoints or time periods

How to interpret standard deviation w.r.t investments?

It is a useful measure in investing strategies and it helps measure the market volatility. Here, the mean would be the average annual return. We can consider it as the volatility of the past mutual fund returns.

In other words, a higher deviation reflects higher volatility. The fund’s performance have fluctuated high above the average return or its mean. It is a useful tool when analyzing the past performance of the fund in isolation. But if the portfolio comprises several funds, it cannot be used just by averaging the standard deviation of all the funds. 

In that case, each fund’s correlation, as well as standard deviation, must be analyzed. In a multi-asset portfolio,  volatility is a function of how each fund performs in relation to each other in the portfolio. 

A greater standard deviation indicates higher volatility, which means the mutual fund’s performance fluctuated high above the average but also significantly below it. Therefore many investors use the terms volatility and standard deviation interchangeably.

Why Standard deviation is a good measure of risk in terms of volatility?

It is seen as a factor that determines the volatility and therefore also measures risk up to a point. Now the definition of risk in this context is arrived at by looking at it as a variance or deviation from the mean or the average price. The more price fluctuates, the higher is the variance and greater is the volatility risk.

As the price moves up, the standard deviation is high and so is the risk or volatility. While the prices move down, the deviation is low and the investment is at low risk in terms of volatility. 

The drawback of this tool is that it can be impacted by a few outliers and extreme values. Further depicting a less reliable number. 

It is one of the indicators of risk and not the only decisive factor to determine whether an investment is risky, not risky, or too risky. 

Published on August 3, 2020