Review of Capital Allocation by Percentile Layer

Transcription

1 Review of Capital Allocation by Percentile Layer A review of Neil Bodoff s paper from Variance (vol 3/issue 1) and comparison to other capital allocation methods Mario DiCaro, FCAS Ultimate Risk Solutions

2 Why are we allocating capital? Capital allocation is generally not an end in itself, but rather an intermediate step in a decision-making process. Venter Determine which business units are most profitable relative to the risk they bring to the enterprise Include a risk charge in pricing Compensation/performance management Regulatory/Rating compliance? ERM processes allocate capital to risk categories: cat risk, market risk, counterparty risk

3 Capital Allocation Method Families Incremental Change in capital is calculated for the last increment of expected loss for a business unit Marginal Allocation based on impact to overall capital requirement of adding a risk type, business unit Shapley method (game theory) Proportional Allocation based on standalone statistics of the business units Co-measures Allocation based on the risk type/unit s contribution to a set of scenarios Capital Allocation by Percentile Layer fits in this family

4 Co-measures approaches covar (called Alternative covar in paper) Allocate all capital to the scenario at the Xth percentile Alternative covar Allocate capital evenly to the scenarios that are >= Xth percentile cotvar Allocate capital to all scenarios >= Xth percentile proportional to scenario magnitude Any other arbitrary scenario weighting ie Custom (I ll show an example of what I mean) CAPL Capital Allocation by Percentile Layer Cut your capital into layers and split those layers among the scenarios that use them

5 Now let s look at Experiment #2 from Bodoff s paper The point is to discuss how capital is allocated to the loss scenarios according to the various comeasures methods

6 Bodoff s main problem with most comeasures approaches In Experiment s 1 and 2 no capital is allocated to the wind only event using covar and cotvar! The result is a low allocation of capital to the wind peril Using the covar and cotvar methods we are not allocating capital to the events that don t have capacity to completely use the total capital Why? Let s talk about the language around these capital requirements

7 Why hold capital? Why allocate capital? We hold capital because losses can exceed premiums Allocating capital helps us measure which business units are causing us to hold capital Let s discuss Bodoff s statements about what it means to hold capital at the 99 th percentile

8 Articulating the meaning of holding capital based upon Value at Risk (VaR) Some common formulations state that the firm holds sufficient capital for the 99th percentile loss, which can lead unwittingly to the incorrect interpretation that the firm holds capital only for the 99th percentile loss. Indeed, the allocation approaches described above, which allocate all capital costs based only upon contribution to the VaR percentile loss scenario, are totally congruous with this interpretation. Rather, a more precise articulation of the meaning of holding VaR capital is that the firm holds sufficient capital even for the 99th percentile loss,

9 Bodoff, p 21

10 Tying quantification to business Let s look at examples of capital allocation based on 20 loss scenarios Intuitively, volatile lines use capital, CAPL effectively allocates according to volatility and size Other subjects in Bodoff s paper: Allocating the tail in TVaR Incorporating premium and expenses How capital allocation affects pricing, ie a risk load

11 Salient features of CAPL Allocates capital to all losses, rather than just to extreme losses in the tail Does not allocate in proportion to the average, rather it allocates disproportionate capital to the severe losses It doesn t rely on esoteric parameters or elusive risk preferences

12 References Neil Bodoff Capital Allocation by Percentile Layer Variance: volume 3 issue 1 Gary Venter Survey of Capital Allocation Methods with Commentary