értekezés - Budapesti Corvinus Egyetem

[Figure 13]
Hence, the business unit (or project) X shall be punished with the expected size of
deadweight costs, DL X , attributable to this unit, where p i means the probability of the
group EBITDA to end up in the i th partition, x i is the X item’s percentage of responsibility
that group EBITDA ended up in the i th partition, and m i represents the deadweight cost
endured if group EBITDA ends up in the i th partition.
The distance of partitions can be chosen based on the variation of risk contribution of the
building blocks, the steepness of the cost function, and the number of iterations to be
ideally run. 191 Below, I show the formula with which to calculate the risk contributions of
the identified units from the output data of the Monte Carlo run. I also show that this
calculation can be transformed into the covariance-approach used for normally distributed
variables.
Figure [14] shows that the same logic can be used to account for the deadweight costs of
the interplay between investment decisions and the cost of external finance (the Froot-
Schaferstein-Stein model, 1993).
[Figure 14]
Calculating the risk contributions of identified business units or projects to the distribution
of modeled output variable in a Monte Carlo simulation framework
Portfolio p is the sum of M number of arbitrarily distributed building blocks (whether each
representing a single source of risk factor or a sub-portfolio of risk factors), where x k
represents the k th such building block. After having run N number of iterations within the
MC model, we get the aggregate distribution of portfolio p. We now look for the relative
size of X k ’s contribution – contr(k) – to a given partition S(l) of p’s distribution.
191 The smaller partition distances are selected, the more iterations are needed to have the same sample size
within each partition.
187