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Portfolio risk is the general term for riskiness or dispersion of returns on a portfolio of assets. There are several different ways risk can be measured, calculated and interpreted depending on whether the source data requires a holdings-based calculation or returns-based calculation.
A holdings-based the calculation requires a bottom-up calculation using individual positions and weights. This requires three inputs: the weight of each asset in the portfolio, the variance of each asset and the covariance between each asset. Covariances are typically calculated and stored in a stock-by-stock or factor-based covariance matrix. Below is the formula for a two-stock portfolio for portfolio variance. Portfolio standard deviation is found by taking the square root of portfolio variance.
The ABC Weight^2 above means the portfolio weight to ABC is squared.
The number of terms for a two-asset portfolio is four, which matches the number of cells of a 2-by-2 stock-by-stock covariance matrix. The number of terms for a three asset portfolio is nine, and so forth.
When calculating returns-based portfolio risk using a stream of values of a portfolio, like the NAV on a mutual fund, the variance and standard deviation are the result. The tracking error portfolio risk measure is for relative risk and is the standard deviation of active returns. In addition, some consider VAR, or Value at Risk, a useful measure of portfolio risk, particularly in banking contexts.
Synonym: portfolio variability
For context, portfolio risk can be evaluated using other measures not discussed here. It is the analyst's job to be careful to select the appropriate measure for the appropriate context when evaluating and reporting portfolio risk when compared to other portfolios, or benchmarks, so on a relative basis, or an absolute basis.
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Absolute. You don't need a comparision benchmark to compute portfolio standard deviation.
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