Calculate The Standard Deviations of The Following Portfolios

Standard deviation measures the dispersion of returns in a portfolio. Lower standard deviation indicates less risk. This calculator helps you quantify portfolio volatility using historical return data.

What is Standard Deviation?

Standard deviation (σ) is a statistical measure that quantifies the amount of variation or dispersion in a set of values. In finance, it's commonly used to measure the volatility of a portfolio's returns.

Formula: σ = √(Σ(xi - μ)² / N)

Where:

σ = standard deviation
xi = each individual return value
μ = mean of the returns
N = number of returns

Standard deviation is expressed in the same units as the original data (e.g., percentage points for returns). A higher standard deviation indicates greater volatility and risk.

How to Calculate Portfolio Standard Deviation

Collect historical return data for your portfolio
Calculate the mean (average) return
For each return, subtract the mean and square the result
Calculate the average of these squared differences
Take the square root of this average to get the standard deviation

Note: For multiple assets, you'll need to calculate the covariance matrix and use portfolio weights to determine the overall standard deviation.

Example Calculation

Consider a portfolio with monthly returns: 2%, 5%, 3%, 4%, 6%.

Mean return = (2 + 5 + 3 + 4 + 6) / 5 = 4%
Calculate squared differences:
- (2-4)² = 4
- (5-4)² = 1
- (3-4)² = 1
- (4-4)² = 0
- (6-4)² = 4
Average squared difference = (4 + 1 + 1 + 0 + 4) / 5 = 1.6
Standard deviation = √1.6 ≈ 1.26%

This indicates moderate volatility in the portfolio's returns.

Interpreting Results

The standard deviation provides several key insights:

Risk level: Higher standard deviation means greater potential for large swings in returns
Volatility: Measures how much returns fluctuate over time
Comparison: Allows comparison of risk between different portfolios

Standard Deviation Range	Risk Level
0-5%	Low risk, stable returns
5-10%	Moderate risk, moderate volatility
10%+	High risk, volatile returns

FAQ

What is the difference between standard deviation and variance?

Variance is the square of standard deviation. While both measure dispersion, standard deviation is in the original units while variance is in squared units.

How does standard deviation relate to portfolio diversification?

Diversification reduces portfolio standard deviation by spreading risk across uncorrelated assets. The more uncorrelated assets you add, the lower the overall standard deviation.

What's the difference between population and sample standard deviation?

Population standard deviation uses N in the denominator while sample standard deviation uses N-1 to account for estimation from a sample.