τ-value for risk capital allocation problems

Value at Risk trade-off and capital allocation with copulas

This paper uses copula functions in order to evaluate tail probabilities and market risk trade-offs at a given confidence level, dropping the joint normality assumption on returns. Copulas enable to represent distribution functions separating the marginal distributions from the association structure. We present an application to two stock market indices: for each market we recover the marginal ...

Risk Based Capital Allocation

Risk capital allocation for RORAC optimization

This paper considers the financial optimization problem of a firm with several sub-businesses striving for its optimal RORAC. An insightful example shows that the implementation of classical gradient capital allocation can be suboptimal if division managers are allowed to venture into all business whose marginal RORAC exceeds the firm’s RORAC. The marginal RORAC requirements are refined by addi...

Coherent allocation of risk capital∗

The allocation problem stems from the diversification effect observed in risk measurements of financial portfolios: the sum of the “risks” of many portfolios is larger than the “risk” of the sum of the portfolios. The allocation problem is to apportion this diversification advantage to the portfolios in a fair manner, yielding, for each portfolio, a risk appraisal that accounts for diversificat...

Risk Measures , Risk Aggregation and Capital Allocation

We consider risk measures, risk aggregation and capital allocation in these lecture notes and build on our earlier introduction to Value-at-Risk (VaR) and Expected Shortfall (ES). We will follow Chapter 8 of the 2 edition of Quantitative Risk Management by MFE quite closely. This chapter, however, contains considerably more material than we will cover and it should be consulted if further detai...