Measuring Portfolio Volatility from Total Returns and Covariance

Summary

The document raises a core portfolio risk question: whether historical portfolio volatility can be calculated directly from the portfolio return series or whether each asset’s volatility and the covariances among assets must be calculated separately. It presents the question but does not provide an answer or a worked method.

In principle, when portfolio weights and return observations are aligned, the volatility of the portfolio return series already reflects the assets’ individual variability and their co-movement. A covariance-based calculation expresses the same aggregation explicitly and can help explain how diversification affects risk. The document itself offers no evidence, formula, or discussion of changing weights, missing data, or estimation choices, so it serves as a prompt for clarification rather than a complete guide.

Key ideas

• Portfolio volatility can be estimated from a time series of portfolio returns.
• A covariance calculation makes the contribution of asset co-movement explicit.
• The document poses the calculation question but supplies no answer or empirical example.

Tags

# Shortcut for cutting portfolio volatility


# Shortcut for cutting portfolio volatility












When calculating the portfolio's historical volatility, do I need to factor the volatility of each asset individually and then do a covariance calculation or can I get away by measuring the volatility of the total portfolio return?

My gut feeling says no, but I cant work out why?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.