# What is Portfolio Standard Deviation?

Definition: The portfolio standard deviation is the financial measure of investment risk and consistency in investment earnings. In other words, it measures the income variations in investments and the consistency of their returns.

## What Does Portfolio Standard Deviation Mean?

It’s an indicator as to an investment’s risk because it shows how stable its earning are. A high standard deviation in a portfolio indicates high risk because it shows that the earnings are highly unstable and volatile.

Factors that can affect the portfolio risk can be a change in the interest rates, the inflation rate, the unemployment rate, and the exchange rates. A firm can’t control any of these factors, but they can assume control over factors such as the bargaining power of its suppliers, research and development, and competition.

In order to calculate the PSD and use it to interpret investment risk, we need to understand a few other calculations. Portfolio variance and the standard deviation, which is the square root of the portfolio variance, both express the volatility of stock returns. Knowing the standard deviation, we calculate the coefficient of variance (CV), which expresses the degree of variation of returns.

Let’s look at an example.

## Example

Andrew works as an investment analyst in a prominent advisors’ firm and he provides investment counseling to his clients. For a portfolio of two stocks, Andrew wants to calculate the portfolio variance and the standard deviation.

Knowing the returns of each stock Andrew calculates the average return for each stock as follows:

Stock A: ( 3.40% + 4.28% + 3.95% + 5.80% + 5.50% ) / 5 = 4.59%

Stock B: ( 8.60% + 9.20% + 7.85% + 7.00% + 6.58% ) / 5 = 7.85%

Then, Andrew calculates the variance for each stock as follows:

Stock A: ( 3.40% – 4.59% )² + ( 4.28% – 4.59% )² + ( 3.95% – 4.59% )² + ( 5.80% – 4.59% )² + ( 5.50% – 4.59% )² = 0.04

Stock B: ( 8.60% – 7.85% )² + ( 9.20% – 7.85% )² + ( 7.85% – 7.85% )² + ( 7.00% – 7.85% )² + ( 6.58% – 7.85% )² = 0.05

Therefore, the standard deviation for each stock is:

Stock A: Square root of 0.04 = 2.05%

Stock B: Square root of 0.05 = 2.17%

The coefficient of variance CV for the two stocks is 0.80 and the portfolio weights for each stock are 65% for stock A and 35% for stock B. Andrew can calculate the variance and standard deviation as follows:

Portfolio variance = (65%² x 2.05%²) + (35%² x 2.17%²) + (2 x 65% x 2.05 x 35% x 2.17% x 0.80) = 0.0004 = 0.04%

Therefore, portfolio standard deviation is the square root of 0.04% = 2.0%

Andrew can now compare this with other portfolios to see if it is performing as consistently and if he wants to continuing investing in this fund.