Values at risk sensitivities (or incremental value at risk) are similar to the marginal risk attribution as described in Risk Budgets. While a marginal risk budget measures the change in total value at risk attributed to an increased exposure in a portfolio component, incremental value at risk measures the impact of a reallocation across all asset exposures.
In practice, a portfolio manager with a 60% allocation in equities and a 40% allocation in fixed income may wish to evaluate a scenario where 5% of equity funds are reallocated to fixed income. The manager may then review the resultant change in total value at risk as part of a risk sensitivity analysis process. A negative change indicates that the reallocation is risk-reducing relative to the current allocation. A positive change indicates that the reallocation increases risk relative to the current allocation.
For each asset’s increment iteration, we reevaluate the portfolio’s value at risk measure against the initial portfolio value at risk.