Equal capital weights are not equal risk contributions

Capital weights and covariance

Capital weight is simply position value divided by portfolio value. Volatility measures return variability over a specified sample and frequency. Portfolio volatility depends on both individual volatilities and correlation, a measure of how returns co-move. Adding the assets' separate volatility numbers is generally incorrect.

For two uncorrelated assets, each contribution to portfolio variance is its squared weight multiplied by its variance. In that special case, weights inversely proportional to volatility equalise those contributions. With several correlated assets, the full covariance relationships matter; a mechanical inverse-volatility rule need not produce equal risk contributions.

Worked example: 90% of variance

Assume two hypothetical assets have annualised volatilities of 10% and 30%, measured consistently, and correlation zero. With 50/50 capital weights, the variance terms are (0.5 × 0.10)² = 0.0025 and (0.5 × 0.30)² = 0.0225. The second asset contributes 90% of total variance. Portfolio volatility is approximately 15.81%.

At 75/25 capital weights, both weighted volatilities are 7.5%, so each variance contribution is 0.005625. Total portfolio volatility becomes approximately 10.61%. This is a calculation under stated assumptions, not evidence that 75/25 is an optimal investment or will earn a particular return.

Where volatility misses the risk

Historical volatility and correlation are estimates. They may change together in a crisis, precisely when diversification is needed most. Equal variance contribution also says little about liquidity, credit events, drawdown or the cost of leverage. A quiet price history does not guarantee a low probability of a severe loss.

Compare swings before estimating weights

Compare the size and timing of historical swings on available closed daily, weekly or monthly bars, using the same date range for both assets. Record any periods when the assets fell together. Student Wyckoff Pro supports that chart investigation; portfolio covariance estimation and allocation calculations require a separate, consistently prepared dataset.

Primary sources

Sources explain the mechanics and limitations; the editorial examples use invented numbers rather than market quotations.

• Portfolio Risk and Return: Part I

Sources checked: 2026-10-23