értekezés - Budapesti Corvinus Egyetem

12. függelék - A kockázati hozzájárulás számszerűsítése MC szimulációval
I propose a simple technique that can be used along the traditional way of capital allocation
and performance measurement processes, but which adds to it by taking into account a
project’s or business unit’s contribution to the total risk of the portfolio. This method
assumes that the building blocks are linearly additive with respect to the output variable
modeled, which is a realistic assumption as long as business units’ or projects’ cash-flows
or earnings contributions are concerned. But the building blocks do not need to be
unanimously normally distributed. Hence, the contribution of the parts to the various
segments of the total distribution can continuously vary. Figure [12] compares a portfolio
distribution with normally-distributed and one with heterogeneously distributed building
blocks.
[Figure 12]
As to be seen, if all building blocks are normally distributed in the portfolio, the risk
contribution of each part will stay constant in the entire range of the aggregate distribution.
The contribution factors will be the same as if we used the covariance matrix of the
building blocks and inferred the incremental VaR of each element. However, having
asymmetrically (e.g. lognormally) distributed parts in the portfolio results in a varying rate
of risk contribution of the parts (the lognormal parts adding to the output variable’s
volatility more intensively in the upside than in the downside region). Hence, we can track
the impact of skewedness on the risk contributions of the analyzed business units, projects,
and punish them for the costs of the downside (‘red-zone’) accordingly.
Figure 14 demonstrates a firm’s EBITDA distribution on a given time horizon (e.g. 12
months). Provided that this firm faces higher external funding costs (due to increased
asymmetric information, loss in reputation, waiver costs of breaching covenant, increased
probability of financial distress, etc.) if its Net Debt / EBITDA ratio exceeds a prespecified
level, then the firm would need to incorporate these deadweight costs in the
evaluation of projects or business units to punish their expected performance according to
their contribution to such deadweight costs. Since the EBITDA evolution can be
functioned into the Net Debt / EBITDA ratio, we can link the outcome of EBITDA to the
size of extra costs endured.
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