Two-asset case
The point the workbook makes in miniature: equal dollars is not equal risk. Adjust the two volatilities and the correlation, then watch how much of the portfolio's risk the more volatile asset carries.
| Sizing | Capital A | Capital B | Risk share A | Risk share B | Portfolio vol |
|---|---|---|---|---|---|
| Equal capital (50 / 50) | 50.00% | 50.00% | 10.00% | 90.00% | 9.49% |
| Inverse volatility | 75.00% | 25.00% | 50.00% | 50.00% | 6.36% |
| Equal risk contribution | 75.00% | 25.00% | 50.00% | 50.00% | 6.36% |
At a 50/50 split the more volatile asset carries 90.0% of the risk. Sizing for equal risk moves capital to 75.0% / 25.0% and lowers portfolio volatility from 9.49% to 6.36%.
Correlation sweep
The same two assets across every possible correlation, from perfectly hedging (−1) to perfectly aligned (+1). The diversification benefit is the gap between the lines — it disappears entirely on the right-hand edge.
The dashed vertical line marks the correlation selected above. Where the risk-share line sits above 50%, equal dollars is quietly handing the volatile asset the majority of the portfolio's risk — which is exactly what the risk engine corrects for on a real sleeve.