How to Calculate Standard Deviation of a Portfolio?

Standard deviation is one of the most important attributes of statistics as it allows you to calculate the range of variation in a data set. But if you look at it from the financial point of view then, standard deviation allows an investor to determine the number of risks in any kind of investment. Alongside that, it also helps to calculate the rate of return.

What’s Portfolio Standard Deviation? Why Do You Need to Know It?

When you calculate the standard deviation of a portfolio, it helps you measure the dispersion of that portfolio’s return. It basically enables you to understand the volatility of that portfolio. Volatility means the amount of risk that a security holds.
If a standard deviation of a portfolio is low that means the portfolio is less risky and the rate of return is not volatile. In simple words, it means the return rate of that portfolio is more stable. If the standard deviation is higher, that indicates the portfolio is risky and the return rate is quite unstable. You can simply compare the stability by looking at the standard deviation of a portfolio and decide which one deserves your investment.

How to Calculate Standard Deviation of a Portfolio?

Step 1: Find out the standard deviation of every security in a portfolio.

The very first step of calculating the standard deviation of a portfolio is to measure the standard deviation of each security. In order to do that, you can use different functions of Excel. If you want to calculate manually, you’ll need a good statistical calculator. The Strategy Watch reviewed and rated some of the best calculators for statistics. Apart from this, standard deviation (σ) is referred to as calculate the amount of dispersion or variation of a dataset of values and it is the square root of the variation of the dataset. So, you can use an online standard deviation calculator that helps you to find the step-wise standard deviation (σ) for both sample and population standard deviation. The online SD calculator easily determines the total count, sum, mean, variance, coefficient of variance, standard error of the mean, and the sum of squares of the given numbers. Also, this standard deviation calculator displays a frequency table for the given dataset and the variability of a given set of data.

• Let’s assume there are 2 securities in a portfolio and the standard deviation of each of them are respectively 10% and 20%.

Step 2: Calculate the weight of each security.

Once you know the standard deviation of each security, you need to find out the weight of them.
• Suppose, you’ve invested $600 in your portfolio. Security 1 has $240, security 2 has $360.
• Now if you calculate the weight of each security, the weight of security 1 will be 40% (240/600) and the weight of security 2 will be 60% (360/600).

Step 3: Measure the correlation among the securities.

Correlation means how two variables move in respect of one another. In this case, securities are the variables.
• The value of correlation should be between -1 and 1. -1 means the variables are moving in the opposite direction and 1 means they are moving in a similar direction.
• 0 means there isn’t any relationship between the securities.
• Let’s say, the correlation between the securities is .30 which will indicate that if there’s an increase in a security by $100, the other one will increase by $30.

Step 4: Find out the variance of securities.

In statistics, variance is the square of standard deviation.
• Suppose if we want to calculate the variance of the previous securities, it would look something like this – (0.40^2)*(0.1^2) + (0.60^2)*(0.20^2) + 2*0.40*0.60*0.1*0.20*0.30 = .01888.
Step 6: Evaluate the standard deviation from variance.
You can calculate the standard deviation from the square root of the variance.
• Here the standard deviation will be: .01888^.05 = .1371 = 13.71%

Step 7: Explain the standard deviation.

Here the standard deviation is 13.71% which is more than 10% and less than 20%. The reason behind this is the correlation factor which was .30.
• If the correlation was 1, then the standard deviation would have been 16%.
• If the correlation was 0, then the standard deviation would have been 12.64%.
• If the correlation was -1, then the standard deviation would have been 8%.

By seeing the standard deviations, you can decide whether you want to invest in it or not. Portfolio standard deviation allows you to measure the return rate of each investment so that you don’t have to stress about which one is best for you. If you take a close look at the portfolio return and the volatility of the assets, you will be able to detect the most stable investment available for you. If the standard deviation is relatively higher, that means the market is more volatile indicating that the investment will be risky for you.
You should also remember that standard deviation is calculated by analyzing the previous data and it can change in future. This is why make sure you measure all the aspects before making any kind of investment.