Skip to main content

Portfolio Volatility Metrics

Portfolio volatility metrics are statistical measures used to quantify the degree of risk or uncertainty associated with a portfolio's returns over time. These metrics help investors and analysts assess the potential for losses, gains, or variability in investment outcomes, thereby enabling informed decision-making about portfolio construction, management, and optimization.

Calculating Portfolio Volatility​

There are several common metrics used to calculate portfolio volatility, each offering unique insights into different aspects of a portfolio's behavior. These include:

1. Standard Deviation (σ)​

Standard deviation is perhaps the most widely recognized volatility metric, providing an average measure of historical returns variability around the mean return. A higher standard deviation indicates greater variability and thus higher risk.

Formula: σ = √[(∑(R_i - μ)^2) / (n-1)]

Where:
    R_i = individual return
    μ = mean return
    n = number of periods

2. Variance (σ^2)​

Variance measures the average squared difference between returns and the mean, directly related to standard deviation by squaring it.

Formula: σ^2 = (∑(R_i - μ)^2) / (n-1)

This metric is useful for comparing portfolio risks on the same scale as returns.

3. Beta (β)​

Beta measures a portfolio's systematic risk or sensitivity compared to the overall market, essentially quantifying how much the portfolio’s volatility can be attributed to general market movements rather than specific investment decisions.

Formula: β = Cov(R_p, R_m) / σ^2_m

Where:
    R_p = return on portfolio
    R_m = market return
    Cov = covariance between returns
    σ^2_m = variance of the market return

4. Value-at-Risk (VaR)​

Value-at-risk is a more comprehensive risk metric that calculates the potential loss in value over a specific time frame with a given confidence level, taking into account both systematic and idiosyncratic risks.

Formula: VaR = (return quantile - mean return) * σ

Where:
    Return quantile = value below which there is a specified percentage of returns
    Mean return = average of all historical returns
    σ = standard deviation of those returns