# 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
**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
**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
**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
**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
**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
**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