# How to Calculate the Standard Deviation of a Portfolio

The standard deviation of a portfolio represents the variability of the returns of a portfolio. To calculate it, you need some information about your portfolio as a whole, and each security within it.

## Steps

1. 1
Calculate the standard deviation of each security in the portfolio. First we need to calculate the standard deviation of each security in the portfolio. You can use a calculator or the Excel function to calculate that.
• Let's say there are 2 securities in the portfolio whose standard deviations are 10% and 15%.
2. 2
Determine the weights of securities in the portfolio. We need to know the weights of each security in the portfolio.
• Let's say we've invested \$1000 in our portfolio of which \$750 is in security 1 and \$250 is in security 2.
• So the weight of security 1 in portfolio is 75% (750/1000) and the weight of security 2 in portfolio is 25% (250/1000).
3. 3
Find the correlation between two securities. Correlation can be defined as the statistical measure of how two securities move with respect to each other.
• Its value lies between -1 and 1.
• -1 implies that the two securities move exactly opposite to each other and 1 implies that they move in exactly the same way in same direction.
• 0 implies that there is no relation as of how the securities move with respect to each other.
• For our example, let's take correlation as 0.25 which means that if one security increases by \$1, the other increases by \$0.25.
4. 4
Calculate the variance. Variance is the square of standard deviation.
• For this example, variance would be calculated as (0.75^2)*(0.1^2) + (0.25^2)*(0.15^2) + 2*0.75*0.25*0.1*0.15*0.25 = 0.008438.
5. 5
Calculate standard deviation. Standard deviation would be square root of variance.
• So, it would be equal to 0.008438^0.5 = 0.09185 = 9.185%.
6. 6
Interpret the standard deviation. As we can see that standard deviation is equal to 9.185% which is less than the 10% and 15% of the securities, it is because of the correlation factor:
• If correlation equals 1, standard deviation would have been 11.25%.
• If correlation equals 0, standard deviation would have been 8.38%.
• If correlation equals 1, standard deviation would have been 3.75%.

## Article Info

Categories: Funding