Risk Contribution Ratio
The ratio if iVaR to VaR. This ratio can be useful for portfolio optimization. The contribution ratio generally varies between −1 and +1.* If certain conditions hold, it should be optimal to add to positions with low contribution ratios and to trim positions with high contribution ratios.
If all of the positions in a portfolio had the same correlation to the overall portfolio, then we would expect positions that are riskier in isolation to contribute more risk to the overall portfolio and positions that are less risky in isolation to contribute less. In other words, we would expect the ratio of iVaR to VaR to be equal for all positions.
In a real portfolio, some positions will be more or less correlated with the overall portfolio. If two long positions have the same VaR and the same expected return, but one is less correlated with the overall portfolio, then the less correlated portfolio will have a lower iVaR and contribute less to the overall risk of the portfolio and we should prefer that security. All other things being equal, at the margin, it would be optimal to add to the position with a lower contribution ratio and to trim the position with the higher contribution ratio. For longs:
| iVaR | |||
|---|---|---|---|
| High | Low | ||
| VaR | High | Expected | Add |
| Low | Reduce | Expected | |
With shorts, we want positions that reduce risk as much as possible. If two positions have the same VaR in isolation, and one has a more negative iVaR, all other things being equal, it would be optimal to short more of the position with the more negative iVaR, the position with the lower (more negative) contribution ratio.
*For non-parametric methods, the ratio can be slightly outside this range. This would be true for methods based on historical or hybrid VaR.