# LO 18.5: Evaluate the marginal contribution to portfolio unexpected loss.

LO 18.5: Evaluate the marginal contribution to portfolio unexpected loss.
>From a portfolio perspective, it is also important to measure how an individual exposure, or the addition of a new exposure, contributes to overall portfolio risk. One such measure is marginal VaR, which calculates the incremental portfolio risk from an individual exposure. The marginal contribution can be calculated as:
U LG
(9ULportf0lio
<9wj
w
This measure can be expressed under the Markowitz mean-variance framework as:
ULC- = 0-
i
r i,portfolio
. r
X W- X UL
i
. r 1- portfolio
where: U LC = marginal contribution of the ft loan portfolio unexpected loss Pi p0rtf0ij0 = default correlation between the f t loan and the overall portfolio w- = weight of the ft loan in the overall portfolio ULportfoiio = portfolio unexpected loss
A practical interpretation of marginal contribution comes from calculating betas. For example, the beta of the ft loan can be valued by rearranging the previous formula as follows:
U LQ / Wi ULportfoiio
We can interpret this measure as the marginal risk contribution from the ft loan relative to the average portfolio risk. A beta greater than one would imply that the marginal risk from the ft loan is greater than the average portfolio risk and would, therefore, increase portfolio concentration risk. A beta less than one would reduce portfolio risk and increase the effect from diversification. With this measure, loans can be quickly selected based on their betas in order to identify which loans would lead to portfolio concentration or diversification.
R i s k -A d j u s t e d P r i c i n g