Portfolio Variance and VaR: Asset-Level Versus Portfolio Returns

Summary

The document asks how to calculate variance and value at risk for a portfolio containing several stocks. It compares two approaches: estimate each asset’s risk and combine the results using portfolio weights and a correlation matrix, or first construct the portfolio return series and calculate its variance and VaR directly. The questioner views the direct portfolio-return calculation as simpler but wonders whether it differs from the component-based method.

For variance, the approaches can agree when they use the same return observations, weights, and consistent covariance estimates: portfolio variance is the weighted combination of asset covariances. VaR is not generally combined in the same way, since it depends on the distribution and tail behavior of portfolio returns. The document contains no answers, worked example, or empirical comparison, and does not specify a VaR horizon, confidence level, or estimation method, so it leaves those practical choices unresolved.

Key ideas

• Portfolio variance can be calculated from weighted asset covariances or from portfolio returns.
• The two variance approaches align when inputs, weights, and observations are consistent.
• VaR depends on portfolio return distribution and tail behavior, not only individual VaRs.
• The document poses the comparison but provides no answer or empirical evidence.
• A VaR calculation requires choices such as horizon, confidence level, and estimation method.

Tags

# Variance/VaR calculation for a Portfolio


# Variance/VaR calculation for a Portfolio












I'm considering a portfolio of multiple stocks (>2), and calculating their Standard Deviation/Variance and VaR for the portfolio. My question is about the below two ways to calculating them

- Consider the stocks indivisually, calculate their variance and Var, and then calculate the combined portfolio variance using the correlation matrix.

- Consider the returns of the combined portfolio, and then calculate the variance and Var.

While #2 seems a simpler approach, I've not really seen that approach followed anywhere. I'm curious to think what the difference would look like between the two approaches (if any). From my understanding #1 is usual approach that is followed.

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