Risk budgets are individual value at risk assignments of assets in an investor’s portfolio measured in isolation from the remaining assets. The total portfolio value at risk is apportioned to its various constituents; this allows an investor to associate a loss measure or threshold with an asset or asset class.
For example, the portfolio manager of a pension fund may estimate risk allocations using this methodology to impose a loss threshold mandate on investment managers across each asset class in the fund. If an asset class manager breaches the threshold at the end of the horizon, the portfolio manager may choose to review the asset class exposure. These mandates may be viewed as a part of the fund’s risk control policies.
An intuitive response to the described concept may be to divide the portfolio’s total value at risk proportionally into its constituents. However, since value at risk is a function of standard deviation which is not additive, we cannot dis-aggregate value at risk as such. Instead, we isolate each portfolio component and measure its value at risk and associate it with its dollar value allocation. These risk budget assignments are displayed under the Asset column in the risk budgets screen.
The individual value at risk estimates the exposure to loss of the various portfolio components, but it does not necessarily provide insight to the sources of the total portfolio’s exposure to loss. To understand how a portfolio’s component contributes to its total risk, we measure the sensitivity of a portfolio’s value at risk to a small change in the portfolio’s exposure to each component. This methodology is also known as calculating the marginal value at risk among many texts (Jorion 2001).
Marginal value at risk is a function of a portfolio’s total risk and therefore accounts for portfolio diversification and correlation effects that individual risk budgets do not. Two portfolios may have the same individual value at risk for an identical asset class with similar dollar values assigned, but not necessarily the same marginal risk attribution in the context of their respective investment portfolios.
We calculate marginal value at risk using the partial derivative o the portfolio's total value at risk with respect to each component weight and display it under the % of Portfolio column in the WPA.