What is Portfolio Volatility?

Portfolio volatility is a measure of the overall risk of a portfolio, calculated as the standard deviation of the portfolio's returns over time. It reflects how the combined assets in the portfolio fluctuate in value together. Unlike individual asset volatility, portfolio volatility takes into account the correlation between assets, which can help reduce risk through diversification.

Portfolio Volatility Calculation: Portfolio volatility is calculated using the following formula:

Portfolio Volatility = √(Σ w_i² * σ_i² + Σ Σ w_i * w_j * Cov(i,j)) Where:
  • w_i and w_j are the weights of assets i and j in the portfolio
  • σ_i is the standard deviation of asset i
  • Cov(i,j) is the covariance between assets i and j
The formula accounts for both individual asset volatility and the correlation between assets, which influences the overall risk.

Understanding Portfolio Volatility

Portfolio volatility helps evaluate the risk level of an entire investment portfolio:
  • Correlation and Diversification: When assets in a portfolio are less correlated or negatively correlated, portfolio volatility is reduced through diversification, as losses in one asset may be offset by gains in another.
  • Impact of Asset Weighting: The weight of each asset in the portfolio plays a significant role in determining overall volatility. A portfolio heavily weighted toward more volatile assets will have higher overall volatility.

Example Calculation

Suppose you have a portfolio with two assets, where Asset A has a volatility of 5% and Asset B has a volatility of 3%. The weight of Asset A is 60%, and the weight of Asset B is 40%. If the covariance between the two assets is 0.002, the portfolio volatility is calculated as:

Portfolio Volatility = √(0.6² * 0.05² + 0.4² * 0.03² + 2 * 0.6 * 0.4 * 0.002) = 0.0394 or 3.94% This means the portfolio’s expected volatility is 3.94%, reflecting the combined risk of both assets.

Evaluation

Portfolio volatility is a critical metric for risk management. By considering correlations between assets, it helps investors create balanced portfolios that mitigate risk through diversification. However, portfolio volatility assumes that historical correlations and volatilities will continue, which may not always be the case. To manage risk more effectively, investors often use other risk measures, such as value at risk (VaR) and conditional value at risk (CVaR), in conjunction with portfolio volatility.